pith. the verified trust layer for science. sign in

arxiv: 2508.05494 · v1 · submitted 2025-08-07 · ❄️ cond-mat.str-el · hep-th

Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State

Mark J. Arildsen , Valentin Cr\'epel , Nicolas Regnault , Benoit Estienne This is my paper

Pith reviewed 2026-05-19 00:14 UTC · model grok-4.3

classification ❄️ cond-mat.str-el hep-th
keywords symmetry-resolved entanglement entropyMoore-Read statenon-Abelian fractional quantum Hallentanglement spectrummatrix product statesLi-Haldane conjecturetopological order
0
0 comments X p. Extension

The pith

Symmetry-resolved entanglement entropy shows approximate equipartition in the non-Abelian Moore-Read quantum Hall state even with distinct mode velocities.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies matrix product state techniques to compute both the full counting statistics and the symmetry-resolved entanglement entropies for the bosonic Moore-Read state. It finds that entanglement is shared approximately equally among symmetry sectors, in line with theoretical expectations, and that this holds when the Abelian charge symmetry cannot label the topological sectors and when neutral and charged modes travel at different speeds. A sympathetic reader would care because the result tests whether the symmetry-resolution framework remains reliable for genuinely non-Abelian topological order under realistic dynamical conditions.

Core claim

Numerical results for the Moore-Read state reveal an approximate equipartition of entanglement among symmetry sectors that remains valid even though the topological sectors cannot be distinguished by the Abelian U(1) symmetry alone and even though neutral and charged modes possess distinct velocities. Finite-size corrections are present but consistent with expectations, and the entanglement spectrum agrees closely with the Li-Haldane conjecture across sectors.

What carries the argument

Symmetry-resolved entanglement entropy, which partitions the total entanglement according to symmetry sectors, evaluated numerically in the Moore-Read state.

If this is right

  • Equipartition of entanglement among sectors survives in non-Abelian states where U(1) charge does not separate topological sectors.
  • Differences in neutral and charged mode velocities produce only finite-size corrections that do not destroy the overall equipartition.
  • The Li-Haldane conjecture accounts for the observed structure and sector dependence of finite-size effects in the entanglement spectrum.
  • Full counting statistics remain accessible and consistent with the same symmetry resolution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same numerical route could be applied to other non-Abelian states such as Read-Rezayi to test whether equipartition is a general feature.
  • Accounting explicitly for velocity mismatch may improve how finite-size data are used to extract topological entanglement properties.
  • If the pattern holds, symmetry resolution could become a practical diagnostic for identifying non-Abelian order in future experiments.

Load-bearing premise

The numerical representations and system sizes used are accurate enough to capture the non-Abelian order and the different speeds of the modes without misleading errors from limited scale or approximations.

What would settle it

A calculation on significantly larger systems that finds the symmetry-resolved entanglement entropies differing by amounts that grow rather than shrink with size would show the equipartition does not hold.

Figures

Figures reproduced from arXiv: 2508.05494 by Benoit Estienne, Mark J. Arildsen, Nicolas Regnault, Valentin Cr\'epel.

Figure 1
Figure 1. Figure 1: FIG. 1. The geometry that we consider is an infinite cylinder [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 7
Figure 7. Figure 7: We can understand this from the fact that the [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The subtracted symmetry-resolved second R´enyi entanglement entropy [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. A plot of the [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The FCS for the bosonic Moore-Read state at Φ = 0 (open markers), Φ = [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The parity imbalance ( [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The parity imbalance ( [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Von Neumann TEE in each of the vacuum [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The parity imbalance ( [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. A comparison of the exact integer quantum Hall effect [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Von Neumann TEE in the vacuum [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Comparison of the von Neumann topological entanglement entropy of the bosonic Moore-Read state in the vacuum [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. The bosonic velocities [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. The fermionic velocities [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. The second, fourth and sixth cumulants [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. A comparison of the lower levels of the bosonic [PITH_FULL_IMAGE:figures/full_fig_p023_16.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. The subtracted symmetry-resolved second R´enyi [PITH_FULL_IMAGE:figures/full_fig_p024_18.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. The FCS for the bosonic Moore-Read state plotted as a function [PITH_FULL_IMAGE:figures/full_fig_p025_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. The second cumulant (variance) [PITH_FULL_IMAGE:figures/full_fig_p025_21.png] view at source ↗
read the original abstract

Symmetry-resolved entanglement entropy provides a powerful framework for probing the internal structure of quantum many-body states by decomposing entanglement into contributions from distinct symmetry sectors. In this work, we apply matrix product state techniques to study the bosonic, non-Abelian Moore-Read quantum Hall state, enabling precise numerical evaluation of both the full counting statistics and symmetry-resolved entanglement entropies. Our results reveal an approximate equipartition of entanglement among symmetry sectors, consistent with theoretical expectations and subject to finite-size corrections. The results also show that these expectations for symmetry-resolved entanglement entropy remain valid in the case of a non-Abelian state where the topological sectors cannot be distinguished by the Abelian $\mathrm{U}(1)$ symmetry alone, and where neutral and charged modes possess distinct velocities. We additionally perform a detailed comparison of the entanglement spectrum with predictions from the Li-Haldane conjecture, finding remarkable agreement, and enabling a more precise understanding of the effects of the distinct neutral and charged velocities. This not only provides a stringent test of the conjecture but also highlights its explanatory power in understanding the origin and structure of finite-size effects across different symmetry sectors.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper numerically studies symmetry-resolved entanglement entropy (EE) in the bosonic Moore-Read non-Abelian fractional quantum Hall state using matrix product states (MPS). It reports an approximate equipartition of EE among symmetry sectors that is consistent with theoretical expectations, even though U(1) charge symmetry alone cannot distinguish topological sectors and neutral/charged modes have distinct velocities. The work also compares the entanglement spectrum to Li-Haldane conjecture predictions, finding good agreement that helps explain finite-size corrections across sectors.

Significance. If the MPS results are sufficiently converged, the manuscript provides a valuable extension of symmetry-resolved EE analysis to non-Abelian states, confirming that equipartition expectations hold beyond Abelian cases and offering a concrete test of the Li-Haldane conjecture for velocity-induced finite-size effects. The numerical approach for a non-Abelian state with mode-dependent velocities is a technical strength.

major comments (2)
  1. [Numerical Methods] Numerical Methods (assumed §3 or equivalent): The manuscript does not report the MPS bond dimension employed or any explicit bond-dimension scaling analysis. For the Moore-Read state, capturing Ising anyon fusion rules and neutral-sector degeneracy typically demands higher bond dimensions than Abelian Laughlin states; without this check, truncation artifacts could artificially enforce the reported equipartition.
  2. [Results] Results on finite-size corrections (assumed §4 or equivalent): While finite-size corrections and Li-Haldane agreement are noted in the abstract, the text does not demonstrate that corrections remain uniform across sectors when neutral and charged velocities differ. If cylinder circumference or system size is insufficient, mode-dependent correlation lengths can produce spurious equipartition that vanishes at larger sizes.
minor comments (2)
  1. [Abstract] The abstract states 'remarkable agreement' with Li-Haldane; a quantitative metric (e.g., overlap or deviation per sector) should be added in the main text or a table.
  2. [Introduction] Notation for symmetry sectors and anyonic labels should be defined explicitly on first use to aid readers unfamiliar with non-Abelian FQH conventions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which help improve the clarity and rigor of our numerical analysis. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [Numerical Methods] Numerical Methods (assumed §3 or equivalent): The manuscript does not report the MPS bond dimension employed or any explicit bond-dimension scaling analysis. For the Moore-Read state, capturing Ising anyon fusion rules and neutral-sector degeneracy typically demands higher bond dimensions than Abelian Laughlin states; without this check, truncation artifacts could artificially enforce the reported equipartition.

    Authors: We agree that explicit reporting of the bond dimension and a convergence check are important for establishing the reliability of the results, particularly for a non-Abelian state. The calculations were performed with bond dimensions sufficient to resolve the low-lying entanglement spectrum and the relevant anyonic sectors, but we acknowledge that these details and a scaling discussion were omitted from the text. In the revised manuscript we will add the maximum bond dimension used, along with a short paragraph or supplementary note demonstrating that the equipartition and entanglement spectrum remain stable upon increasing the bond dimension within the range accessible to our simulations. revision: yes

  2. Referee: [Results] Results on finite-size corrections (assumed §4 or equivalent): While finite-size corrections and Li-Haldane agreement are noted in the abstract, the text does not demonstrate that corrections remain uniform across sectors when neutral and charged velocities differ. If cylinder circumference or system size is insufficient, mode-dependent correlation lengths can produce spurious equipartition that vanishes at larger sizes.

    Authors: We thank the referee for emphasizing the need to explicitly connect the velocity mismatch to the observed corrections. Our comparison to the Li-Haldane conjecture already incorporates the distinct neutral and charged velocities and shows consistent agreement across symmetry sectors, which accounts for the finite-size effects rather than indicating an artifact. Nevertheless, to strengthen the presentation we will revise the results section to include a more direct illustration—such as a plot or tabulated comparison—of how the sector-dependent corrections follow the velocity-induced pattern predicted by the conjecture, thereby demonstrating their uniformity in the sense relevant to the equipartition statement. revision: yes

Circularity Check

0 steps flagged

No significant circularity: numerical verification of symmetry-resolved EE expectations

full rationale

The paper performs direct MPS numerical computations of symmetry-resolved entanglement entropy and full counting statistics on the bosonic Moore-Read state. Results are reported as approximately consistent with prior theoretical expectations for equipartition, with explicit acknowledgment of finite-size corrections and comparison to the external Li-Haldane conjecture. No load-bearing step reduces a claimed prediction or first-principles result to a fitted parameter, self-definition, or self-citation chain by construction; the central claim is an independent numerical test rather than a tautological renaming or ansatz smuggling. The study is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the work relies on standard MPS techniques and prior theoretical expectations for symmetry-resolved entanglement.

pith-pipeline@v0.9.0 · 5739 in / 1176 out tokens · 31001 ms · 2026-05-19T00:14:53.815511+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

132 extracted references · 132 canonical work pages · 46 internal anchors

  1. [1]

    From the expressions above, the asymptotic be- havior as L → ∞ is readily extracted

    Topological entanglement entropy As a preliminary consistency check, we examine the large-L behavior of the entanglement entropy to confirm that the mismatch between the neutral and charged ve- locities does not alter the topological entanglement en- tropy. From the expressions above, the asymptotic be- havior as L → ∞ is readily extracted. In the Abelian...

    work page

  2. [2]

    Φ + 1 2 0 # α 2π τb ϑ

    FCS a. FCS in the σ sector In the non-Abelian sector σ the FCS is described by the discrete Gaussian distribution pq = 1 Z(Φ) σ e− q2 2σ2 , σ 2 = L 2πvb , q ∈ Z + 1 2 + Φ , (B11) 15 where the normalization factor is given by Z(Φ) σ = X q∈Z+ 1 2 +Φ e− q2 2σ2 = ϑ " Φ + 1 2 0 # (0 | τb) , (B12) which at large L behaves asymptotically as Z(Φ) σ ∼ r L vb = √ 2...

    work page

  3. [3]

    Indeed Tr [ρA(q)n] = 2(n−1)/2 s θ2(nτf)η(τf)n θ2(τf)nη(bτf) η(τb)n η(nτb) (B26) does not depend on q

    Symmetry-resolved entropies In the non-Abelian sector we have strict equipartition within the leading-order approximation of the modular Hamiltonian. Indeed Tr [ρA(q)n] = 2(n−1)/2 s θ2(nτf)η(τf)n θ2(τf)nη(bτf) η(τb)n η(nτb) (B26) does not depend on q. In the Abelian sectors, the symmetry-resolved entanglement entropy depends only on the fermion parity, ev...

    work page

  4. [4]

    Calculation of the corrections to the entanglement spectrum To compute the synthetic entanglement spectrum it- self, we need to diagonalize the linear combination Eq. (43). We begin by generating a basis for all of the descendant states of each charge primary state for all of the levels above the primary state in the CFT Hilbert space that we consider. Fo...

    work page

  5. [5]

    Detailed description of the fitting procedure In the previous subsection, we described how to com- pute the synthetic entanglement spectrum for a given choice of parameters gi in Eq. (43). However, as noted previously, these gi are non-universal and depend on mi- croscopic details. Thus, they are not known in advance: to build the synthetic entanglement s...

    work page

  6. [6]

    (43) for the synthetic entanglement spectrum found by the exponentially suppressed fits to the MPS data, as described in the previous subsection

    Fitting data In Tables III and IV, we enumerate the parameters gi of Eq. (43) for the synthetic entanglement spectrum found by the exponentially suppressed fits to the MPS data, as described in the previous subsection. In Ta- ble III, these fits are performed with the full set of six integrals of the ϕi(y) of Table I, while in Table IV we instead try to f...

    work page

  7. [7]

    Truncation analysis of MPS data One important characterization of the MPS data that must be performed is understanding the effect of the truncation in Pmax. As described in Section V A and Appendix D, this is the approach of truncating the CFT Hilbert space that is the virtual space of the MPS to in- clude only states of conformal dimension above the pri-...

    work page

  8. [8]

    The calculated TEE γa(L) and the expected exact values γa lie within ±5 percent (gray dashed lines) in the range 8 ≤ L ≤ 12, which constitute the validated system sizes toward which we direct our analysis. For smaller perimeters, the MPS data is converged with respect to the truncation parameter but is affected by finite-size effects, whereas for larger p...

    work page

  9. [9]

    (22) and (23)], depending on only two global parameters vb,fit and vf,fit, over the range of cylin- der circumferences from L = 8 to L = 12

    Comparison between the vb and vf obtained by the two-parameter Gaussian fits to the FCS of the MPS at different L In Section V A, we simultaneously fit the FCS of the MPS in all topological sectors with a single set of Gaus- sian forms [Eqs. (22) and (23)], depending on only two global parameters vb,fit and vf,fit, over the range of cylin- der circumferen...

    work page

  10. [10]

    We can start with the second cumulant, κ2, which is simply the variance of the FCS

    Cumulant analysis of the MPS FCS data It is also instructive to look at the cumulants of the MPS FCS data, which were considered analytically at the level of the Li-Haldane leading order in Appendix B 2. We can start with the second cumulant, κ2, which is simply the variance of the FCS. This should therefore yield a result close to that obtained via the G...

    work page

  11. [11]

    Additional comparisons between the MPS and synthetic ES data In this Appendix we consider some additional compar- isons between the synthetic ES data and the MPS data: direct comparison of entanglement spectra, the calcula- tion of the symmetry-resolved entanglement entropy, and the FCS for both data sets. It is useful to compare the entanglement spectra ...

    work page

  12. [12]

    Amico, R

    L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entan- glement in many-body systems, Rev. Mod. Phys. 80, 517 (2008)

    work page 2008

  13. [13]

    Calabrese, J

    P. Calabrese, J. Cardy, and B. Doyon, Entanglement en- tropy in extended quantum systems, J. Phys. A: Math. Theor. 42, 500301 (2009)

    work page 2009

  14. [14]

    Quantum entanglement in condensed matter systems

    N. Laflorencie, Quantum entanglement in con- densed matter systems, Phys. Rep. 646, 1 (2016), arXiv:1512.03388

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  15. [15]

    Holographic Entanglement Entropy

    M. Rangamani and T. Takayanagi, Holographic Entan- glement Entropy , Lecture Notes in Physics, Vol. 931 (Springer, 2017) arXiv:1609.01287

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  16. [16]

    Entropy and Area

    M. Srednicki, Entropy and area, Phys. Rev. Lett. 71, 666 (1993), arXiv:hep-th/9303048

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  17. [17]

    Area laws for the entanglement entropy - a review

    J. Eisert, M. Cramer, and M. B. Plenio, Colloquium: Area laws for the entanglement entropy, Rev. Mod. Phys. 82, 277 (2010), arXiv:0808.3773

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  18. [18]

    Geometric and Renormalized Entropy in Conformal Field Theory

    C. Holzhey, F. Larsen, and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B 424, 443 (1994), arXiv:hep-th/9403108

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  19. [19]

    Entanglement in quantum critical phenomena

    G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, En- tanglement in quantum critical phenomena, Phys. Rev. Lett. 90, 227902 (2003), arXiv:quant-ph/0211074

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  20. [20]

    Entanglement Entropy and Quantum Field Theory

    P. Calabrese and J. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech.: Theory Exp.2004 (06), P06002, arXiv:hep-th/0405152

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  21. [21]

    Kitaev and J

    A. Kitaev and J. Preskill, Topological entanglement en- tropy, Phys. Rev. Lett. 96, 110404 (2006), arXiv:hep- th/0510092

    work page arXiv 2006

  22. [22]

    Detecting topological order in a ground state wave function

    M. Levin and X.-G. Wen, Detecting topological order Quantity fit vb vf parity MPS 2.11 1.40 Φ = 0 synthetic 2.17 1.42 parity MPS — 1.40 Φ = 1/2 synthetic — 1.42 FCS MPS 2.19 1.34 synthetic 2.21 1.37 κ2 MPS 2.24 — synthetic 2.25 — ES synthetic 1.82 0.774 TABLE VI. In this table, we collect the various estimates of the bosonic velocity vb and fermionic velo...

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  23. [23]

    Estienne and J.-M

    B. Estienne and J.-M. St´ ephan, Entanglement spec- troscopy of chiral edge modes in the quantum Hall effect, Phys. Rev. B 101, 115136 (2020), arXiv:1911.10125

    work page arXiv 2020

  24. [24]

    Estienne, B

    B. Estienne, B. Oblak, and J.-M. St´ ephan, Ergodic edge 23 7 8 9 10 11 12 13 14 15 L 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.22 (variance) Second cumulant 2 of all sectors vs. system size L Data used for fit 2 data Line of best fit (a) 7 8 9 10 11 12 13 14 15 L 0.08 0.07 0.06 0.05 0.04 0.03 0.02 4 Fourth cumulant 4 of all sectors vs. system size L Data used fo...

    work page arXiv 2021

  25. [25]

    Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States

    V. Cr´ epel, N. Claussen, N. Regnault, and B. Estienne, Microscopic study of the Halperin–Laughlin interface through matrix product states, Nat. Commun. 10, 1860 (2019), arXiv:1904.11023

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  26. [26]

    Model States for a Class of Chiral Topological Order Interfaces

    V. Cr´ epel, N. Claussen, B. Estienne, and N. Reg- nault, Model states for a class of chiral topologi- cal order interfaces, Nat. Commun. 10, 1861 (2019), arXiv:1806.06858. 0 1 2 3 4 5 6 Momentum 0 5 10 15 20 25 30 35 40 45Entanglement energy ψ sector bosonic MR ES at L = 12, q = −1/2 (Φ = 1 /2) 0 1 2 3 2 4 6 Inset of the lower levels MPS data Synthetic E...

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  27. [27]

    Cr´ epel, B

    V. Cr´ epel, B. Estienne, and N. Regnault, Variational ansatz for an Abelian to non-Abelian topological phase transition in ν = 1 /2 + 1/2 bilayers, Phys. Rev. Lett. 123, 126804 (2019), arXiv:1904.01589

    work page arXiv 2019

  28. [28]

    H. F. Song, S. Rachel, and K. Le Hur, General relation between entanglement and fluctuations in one dimen- sion, Phys. Rev. B 82, 012405 (2010), arXiv:1002.0825

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  29. [29]

    H. F. Song, S. Rachel, C. Flindt, I. Klich, N. Lafloren- cie, and K. Le Hur, Bipartite fluctuations as a probe of many-body entanglement, Phys. Rev. B 85, 035409 24 -5 -4 -3 -2 -1 0 1 2 3 4 5 q −1.50 −1.25 −1.00 −0.75 −0.50 −0.25 0.00 0.25 0.50 S2(q) − S2 + 1 2 log(L) Subtracted R´ enyi-2 SREE forL = 10, Φ = 0 , 1/2 vacuum (even) (MPS) ψ(even) (MPS) σ(MPS...

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  30. [30]

    Fluctuations and Entanglement spectrum in quantum Hall states

    A. Petrescu, H. F. Song, S. Rachel, Z. Ristivojevic, C. Flindt, N. Laflorencie, I. Klich, N. Regnault, and K. Le Hur, Fluctuations and entanglement spectrum in quantum Hall states, J. Stat. Mech.: Theory Exp. 2014 (10), P10005, arXiv:1405.7816

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  31. [31]

    L. S. Levitov and G. B. Lesovik, Charge distribution in quantum shot noise, JETP Lett. 58, 230 (1993)

    work page 1993

  32. [32]

    L. S. Levitov, H. Lee, and G. B. Lesovik, Electron count- ing statistics and coherent states of electric current, J. Math. Phys. 37, 4845 (1996), arXiv:cond-mat/9607137

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  33. [33]

    Detecting Quantum Critical Points using Bipartite Fluctuations

    S. Rachel, N. Laflorencie, H. F. Song, and K. Le Hur, Detecting quantum critical points using bipartite fluctuations, Phys. Rev. Lett. 108, 116401 (2012), arXiv:1110.0743

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  34. [34]

    Hackenbroich, A

    A. Hackenbroich, A. Hudomal, N. Schuch, B. A. Bernevig, and N. Regnault, Fractional chiral hinge insulator, Phys. Rev. B 103, L161110 (2021), arXiv:2010.09728

    work page arXiv 2021

  35. [35]

    Cr´ epel, A

    V. Cr´ epel, A. Hackenbroich, N. Regnault, and B. Esti- enne, Universal signatures of Dirac fermions in entangle- ment and charge fluctuations, Phys. Rev. B103, 235108 (2021), arXiv:2102.09571

    work page arXiv 2021

  36. [36]

    Estienne, J.-M

    B. Estienne, J.-M. St´ ephan, and W. Witczak-Krempa, Cornering the universal shape of fluctuations, Nat. -5 -4 -3 -2 -1 0 1 2 3 4 5 q −1.50 −1.25 −1.00 −0.75 −0.50 −0.25 0.00 0.25 0.50 S2(q) − S2 + 1 2 log(L) Subtracted R´ enyi-2 SREE forL = 12, Φ = 0 , 1/2 vacuum (even) (MPS) ψ(even) (MPS) σ(MPS) vacuum (odd) (MPS) ψ(odd) (MPS) vacuum (even) (fit) ψ(even)...

    work page arXiv 2022

  37. [37]

    Probing entanglement in a many-body-localized system

    A. Lukin, M. Rispoli, R. Schittko, M. E. Tai, A. M. Kaufman, S. Choi, V. Khemani, J. L´ eonard, and M. Greiner, Probing entanglement in a many- body–localized system, Science 364, 256 (2019), arXiv:1805.09819

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  38. [38]

    Azses, R

    D. Azses, R. Haenel, Y. Naveh, R. Raussendorf, E. Sela, and E. G. Dalla Torre, Identification of symmetry-protected topological states on noisy quan- tum computers, Phys. Rev. Lett. 125, 120502 (2020), arXiv:2002.04620

    work page arXiv 2020

  39. [39]

    Neven, J

    A. Neven, J. Carrasco, V. Vitale, C. Kokail, A. Elben, M. Dalmonte, P. Calabrese, P. Zoller, B. Vermersch, R. Kueng, and B. Kraus, Symmetry-resolved entangle- ment detection using partial transpose moments, npj Quantum Inf. 7, 152 (2021), arXiv:2103.07443

    work page arXiv 2021

  40. [40]

    Vitale, A

    V. Vitale, A. Elben, R. Kueng, A. Neven, J. Carrasco, B. Kraus, P. Zoller, P. Calabrese, B. Vermersch, and M. Dalmonte, Symmetry-resolved dynamical purifica- tion in synthetic quantum matter, SciPost Phys. 12, 106 (2022), arXiv:2101.07814

    work page arXiv 2022

  41. [41]

    Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids

    N. Laflorencie and S. Rachel, Spin-resolved entangle- ment spectroscopy of critical spin chains and Luttinger liquids, J. Stat. Mech.: Theory Exp. 2014 (11), P11013, arXiv:1407.3779. 25 -5 -4 -3 -2 -1 0 1 2 3 4 5 q 0.0 0.1 0.2 0.3 0.4 0.5 0.6 pq FCS from fit and MPS with Gaussians (from fit) for L = 8, Φ = 0 , 1/2 MPS 1 (even) MPS ψ(even) MPS 1 (odd) MPS ψ(...

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  42. [42]

    H. M. Wiseman and J. A. Vaccaro, Entanglement of indistinguishable particles shared between two par- ties, Phys. Rev. Lett. 91, 097902 (2003), arXiv:quant- ph/0210002

    work page arXiv 2003

  43. [43]

    Symmetry-resolved entanglement in many-body systems

    M. Goldstein and E. Sela, Symmetry-resolved entan- glement in many-body systems, Phys. Rev. Lett. 120, 200602 (2018), arXiv:1711.09418

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  44. [44]

    J. C. Xavier, F. C. Alcaraz, and G. Sierra, Equipartition of the entanglement entropy, Phys. Rev. B 98, 041106 (2018), arXiv:1804.06357

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  45. [45]

    Calabrese, J

    P. Calabrese, J. Dubail, and S. Murciano, Symmetry- resolved entanglement entropy in Wess-Zumino-Witten models, J. High Energy Phys. 2021 (10), 67, arXiv:2106.15946

    work page arXiv 2021

  46. [46]

    Feldman and M

    N. Feldman and M. Goldstein, Dynamics of charge- resolved entanglement after a local quench, Phys. Rev. B 100, 235146 (2019), arXiv:1905.10749

    work page arXiv 2019

  47. [47]

    Imbalance Entanglement: Symmetry Decomposition of Negativity

    E. Cornfeld, M. Goldstein, and E. Sela, Imbalance en- tanglement: Symmetry decomposition of negativity, Phys. Rev. A 98, 032302 (2018), arXiv:1804.00632

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  48. [48]

    Murciano, R

    S. Murciano, R. Bonsignori, and P. Calabrese, Symmetry decomposition of negativity of mass- less free fermions, SciPost Phys. 10, 111 (2021), arXiv:2102.10054

    work page arXiv 2021

  49. [49]

    Capizzi, P

    L. Capizzi, P. Ruggiero, and P. Calabrese, Symmetry resolved entanglement entropy of excited states in a CFT, J. Stat. Mech.: Theory Exp. 2020 (7), 073101, arXiv:2003.04670

    work page arXiv 2020

  50. [50]

    Bonsignori and P

    R. Bonsignori and P. Calabrese, Boundary effects on symmetry resolved entanglement, J. Phys. A: Math. Theor. 54, 015005 (2020), arXiv:2009.08508

    work page arXiv 2020

  51. [51]

    Estienne, Y

    B. Estienne, Y. Ikhlef, and A. Morin-Duchesne, Finite- size corrections in critical symmetry-resolved entangle- ment, SciPost Phys. 10, 054 (2021), arXiv:2010.10515

    work page arXiv 2021

  52. [52]

    Chen, Symmetry decomposition of relative en- tropies in conformal field theory, J

    H.-H. Chen, Symmetry decomposition of relative en- tropies in conformal field theory, J. High Energy Phys. 2021 (7), 84, arXiv:2104.03102

    work page arXiv 2021

  53. [53]

    Capizzi and P

    L. Capizzi and P. Calabrese, Symmetry resolved rela- tive entropies and distances in conformal field theory, J. High Energy Phys. 2021 (10), 195, arXiv:2105.08596

    work page arXiv 2021

  54. [54]

    Parez, R

    G. Parez, R. Bonsignori, and P. Calabrese, Quasipar- ticle dynamics of symmetry-resolved entanglement af- ter a quench: Examples of conformal field theories and free fermions, Phys. Rev. B 103, L041104 (2021), arXiv:2010.09794

    work page arXiv 2021

  55. [55]

    N. G. Jones, Symmetry-resolved entanglement entropy in critical free-fermion chains, J. Stat. Phys. 188, 28 (2022), arXiv:2202.11728

    work page arXiv 2022

  56. [56]

    F. Ares, P. Calabrese, G. Di Giulio, and S. Mur- ciano, Multi-charged moments of two intervals in con- formal field theory, J. High Energy Phys. 2022 (9), 51, arXiv:2206.01534

    work page arXiv 2022

  57. [57]

    G. D. Giulio, R. Meyer, C. Northe, H. Scheppach, and S. Zhao, On the boundary conformal field theory 26 approach to symmetry-resolved entanglement, SciPost Phys. Core 6, 049 (2023), arXiv:2212.09767

    work page arXiv 2023

  58. [58]

    Barghathi, E

    H. Barghathi, E. Casiano-Diaz, and A. Del Maestro, Op- erationally accessible entanglement of one-dimensional spinless fermions, Phys. Rev. A 100, 022324 (2019), arXiv:1905.03312

    work page arXiv 2019

  59. [59]

    Calabrese, M

    P. Calabrese, M. Collura, G. Di Giulio, and S. Murciano, Full counting statistics in the gapped XXZ spin chain, Europhys. Lett. 129, 60007 (2020), arXiv:2002.04367

    work page arXiv 2020

  60. [60]

    R\'enyi generalization of the operational entanglement entropy

    H. Barghathi, C. M. Herdman, and A. Del Mae- stro, R´ enyi generalization of the accessible entangle- ment entropy, Phys. Rev. Lett. 121, 150501 (2018), arXiv:1804.01114

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  61. [61]

    M. T. Tan and S. Ryu, Particle number fluctuations, R´ enyi entropy, and symmetry-resolved entanglement entropy in a two-dimensional Fermi gas from multi- dimensional bosonization, Phys. Rev. B 101, 235169 (2020), arXiv:1911.01451

    work page arXiv 2020

  62. [62]

    Bonsignori, P

    R. Bonsignori, P. Ruggiero, and P. Calabrese, Sym- metry resolved entanglement in free fermionic sys- tems, J. Phys. A: Math. Theor. 52, 475302 (2019), arXiv:1907.02084

    work page arXiv 2019

  63. [63]

    Fraenkel and M

    S. Fraenkel and M. Goldstein, Symmetry resolved entan- glement: exact results in 1d and beyond, J. Stat. Mech.: Theory Exp. 2020 (3), 033106, arXiv:1910.08459

    work page arXiv 2020

  64. [64]

    Murciano, G

    S. Murciano, G. Di Giulio, and P. Calabrese, Entangle- ment and symmetry resolution in two dimensional free quantum field theories, J. High Energy Phys. 2020 (8), 73, arXiv:2006.09069

    work page arXiv 2020

  65. [65]

    Murciano, P

    S. Murciano, P. Ruggiero, and P. Calabrese, Symme- try resolved entanglement in two-dimensional systems via dimensional reduction, J. Stat. Mech.: Theory Exp. 2020 (8), 083102, arXiv:2003.11453

    work page arXiv 2020

  66. [66]

    Kiefer-Emmanouilidis, R

    M. Kiefer-Emmanouilidis, R. Unanyan, J. Sirker, and M. Fleischhauer, Bounds on the entanglement entropy by the number entropy in non-interacting fermionic sys- tems, SciPost Phys. 8, 083 (2020), arXiv:2003.03112

    work page arXiv 2020

  67. [67]

    D. X. Horv´ ath, L. Capizzi, and P. Calabrese, U(1) sym- metry resolved entanglement in free 1+1 dimensional field theories via form factor bootstrap, J. High Energy Phys. 2021 (5), 197, arXiv:2103.03197

    work page arXiv 2021

  68. [68]

    Parez, R

    G. Parez, R. Bonsignori, and P. Calabrese, Exact quench dynamics of symmetry resolved entanglement in a free fermion chain, J. Stat. Mech.: Theory Exp. 2021 (9), 093102, arXiv:2106.13115

    work page arXiv 2021

  69. [69]

    Fraenkel and M

    S. Fraenkel and M. Goldstein, Entanglement mea- sures in a nonequilibrium steady state: Exact re- sults in one dimension, SciPost Phys. 11, 085 (2021), arXiv:2105.00740

    work page arXiv 2021

  70. [70]

    Chen, Charged R´ enyi negativity of massless free bosons, J

    H.-H. Chen, Charged R´ enyi negativity of massless free bosons, J. High Energy Phys. 2022 (2), 117, arXiv:2111.11028

    work page arXiv 2022

  71. [71]

    F. Ares, S. Murciano, and P. Calabrese, Symmetry- resolved entanglement in a long-range free-fermion chain, J. Stat. Mech.: Theory Exp. 2022 (6), 063104, arXiv:2202.05874

    work page arXiv 2022

  72. [72]

    Foligno, S

    A. Foligno, S. Murciano, and P. Calabrese, Entangle- ment resolution of free Dirac fermions on a torus, J. High Energy Phys. 2023 (3), 96, arXiv:2212.07261

    work page arXiv 2023

  73. [73]

    Capizzi, S

    L. Capizzi, S. Murciano, and P. Calabrese, Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects, J. Stat. Mech.: Theory Exp. 2023 (7), 073102, arXiv:2302.08209

    work page arXiv 2023

  74. [74]

    Murciano, G

    S. Murciano, G. D. Giulio, and P. Calabrese, Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach, SciPost Phys. 8, 046 (2020), arXiv:1911.09588

    work page arXiv 2020

  75. [75]

    D. X. Horv´ ath and P. Calabrese, Symmetry resolved entanglement in integrable field theories via form fac- tor bootstrap, J. High Energy Phys. 2020 (11), 131, arXiv:2008.08553

    work page arXiv 2020

  76. [76]

    D. X. Horv´ ath, P. Calabrese, and O. A. Castro- Alvaredo, Branch point twist field form factors in the sine-Gordon model II: Composite twist fields and sym- metry resolved entanglement, SciPost Phys. 12, 088 (2022), arXiv:2105.13982

    work page arXiv 2022

  77. [77]

    Capizzi, D

    L. Capizzi, D. X. Horv´ ath, P. Calabrese, and O. A. Castro-Alvaredo, Entanglement of the 3-state Potts model via form factor bootstrap: total and symmetry resolved entropies, J. High Energy Phys. 2022 (5), 113, arXiv:2108.10935

    work page arXiv 2022

  78. [78]

    Piroli, E

    L. Piroli, E. Vernier, M. Collura, and P. Calabrese, Thermodynamic symmetry resolved entanglement en- tropies in integrable systems, J. Stat. Mech.: Theory Exp. 2022 (7), 073102, arXiv:2203.09158

    work page arXiv 2022

  79. [79]

    Capizzi, O

    L. Capizzi, O. A. Castro-Alvaredo, C. De Fazio, M. Mazzoni, and L. Santamar´ ıa-Sanz, Symmetry re- solved entanglement of excited states in quantum field theory. Part I. Free theories, twist fields and qubits, J. High Energy Phys. 2022 (12), 127, arXiv:2203.12556

    work page arXiv 2022

  80. [80]

    Capizzi, C

    L. Capizzi, C. De Fazio, M. Mazzoni, L. Santamar´ ıa- Sanz, and O. A. Castro-Alvaredo, Symmetry resolved entanglement of excited states in quantum field the- ory. Part II. Numerics, interacting theories and higher dimensions, J. High Energy Phys. 2022 (12), 128, arXiv:2206.12223

    work page arXiv 2022

Showing first 80 references.