Pith. sign in

REVIEW 4 major objections 6 minor 1 cited by

Deconfined quantum critical point in a dissipative spin-1/2 chain

T0 review · 4 major / 6 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A spin-1/2 chain coupled to a bosonic bath can host a genuine deconfined quantum critical point, where antiferromagnetic and valence-bond-solid orders meet at the SU(2)_1 conformal fixed point with emergent O(4) symmetry.

desk verdict The Ohmic DQCP claim is credible and worth taking seriously; the broader sub-Ohmic merging narrative is not supported by the paper's own numbers. read the letter →

arxiv 2607.16039 v1 pith:CBN4J46B submitted 2026-07-17 cond-mat.str-el

Longye Lu , Shifeng Cui , Wenan Guo This is my paper · ORCID
classification cond-mat.str-el
keywords deconfinedquantumcriticalpointdissipativespinchainJ-QmodelSU(2)1conformalfieldtheoryemergentO(4)symmetrynon-AbelianbosonizationMonteCarloretardedinteraction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that coupling a one-dimensional spin-1/2 J–Q3 chain to a bosonic bath opens a fresh route to deconfined quantum criticality—a continuous phase transition at which fractionalized spinon excitations deconfine, usually sought in two dimensions. Strong dissipation stabilizes antiferromagnetic order, and the competition between that order and the valence-bond-solid phase produces a continuous transition. At the Ohmic point the transition is claimed to be governed by the same SU(2)_1 conformal field theory as the isolated Heisenberg chain, with deconfined spinons and emergent O(4) symmetry—a concrete, testable realization of a deconfined quantum critical point. The case matters because existing 2D models of this phenomenon tend to be weakly first-order, whereas here the critical theory is exactly known.

What carries the argument

The central object is the non-Abelian bosonized effective action of the dissipative chain: the SU(2)_1 CFT of the Heisenberg chain, plus a backscattering term λ J_L·J_R generated by the Q interaction, plus a coupling g between the Néel field n and a generalized free field φ whose propagator decays as |τ|^{-(1+s)}. The work is carried by the one-loop beta functions β_g = (ε/2)g − (π/2)λg and β_λ = 2πλ^2 − (1/2)g^2, with ε=1−s. The sub-Ohmic fixed point (λ*,g*) = (ε/π, 2ε/√π) has a dynamical exponent z=1+(3/4)g^2, and it merges into the SU(2)_1 fixed point as s→1; this merging is what licenses the Ohmic deconfined critical point. QMC simulations, using wormhole updates for retarded interaction

What would settle it

A direct check: measure the central charge c from the entanglement entropy at the Ohmic critical point; SU(2)_1 CFT has c=1, so if the extracted c deviates from 1 as system size grows, the critical point is not the claimed CFT. Alternatively, measure the VBS scaling dimension Δ_D at s=1 with high precision: the paper's own sub-Ohmic data at s=0.95 give Δ_D≈0.25, far from the O(ε) prediction 0.425, so a deviation of Δ_D from 1/2 at s=1 beyond error bars—or a dynamical exponent z clearly different from 1—would falsify the identification with the SU(2)_1 fixed point.

Watch

Extended reading notes

Core claim

The paper claims that in a one-dimensional spin-1/2 J–Q3 chain with each spin component coupled to an independent bosonic bath, strong dissipation stabilizes antiferromagnetic order, and the transition from that AFM phase to a valence-bond-solid phase is continuous. At the Ohmic value of the bath exponent (spectral density J(ω)∼ω), this AFM–VBS transition is governed by the SU(2)_1 conformal field theory fixed point—the same fixed point as the isolated Heisenberg chain—with dynamical exponent z=1, scaling dimensions Δ_N=Δ_D=1/2, deconfined spinons, and emergent O(4) symmetry. In the sub-Ohmic regime the transition is argued to be controlled by a distinct fixed point with z>1 and unequal scal

Load-bearing premise

The central claim rests on the assumption that the AFM–VBS critical point of the dissipative chain at the Ohmic point is the same fixed point as the SU(2)_1 CFT of the clean Heisenberg chain—i.e., that the RG flow for s=1 lands exactly on the clean fixed point rather than on a distinct dissipative fixed point; the paper's own data at s=0.85 show the perturbative expansion around that CFT breaks down away from s=1.

Editorial extensions

If this is right

  • If the Ohmic claim is correct, dissipation provides a new, experimentally and numerically tractable route to deconfined quantum criticality in one dimension, with exactly known critical exponents from SU(2)_1 CFT.
  • The Ohmic AFM–VBS transition would be a sharp counterexample to the trend that DQCP candidates in microscopic models are weakly first-order: here the critical point is a clean, continuous CFT fixed point.
  • The sub-Ohmic fixed point predicts z>1 and Δ_N>1/2, Δ_D<1/2; these scaling dimensions are directly measurable and provide a quantitative test of the RG analysis in the vicinity of s=1.
  • The proposed super-Ohmic AFM-to-QLRO transition, dual to the sub-Ohmic fixed point, gives a three-regime phase diagram that could be mapped in future simulations.
  • The Q-term enhancement of AFM order in the presence of dissipation is a concrete, testable prediction of both RG flow and spin-wave analysis, and should be observable in other dissipative spin models.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The identification of the Ohmic critical point with SU(2)_1 CFT implies central charge c=1; measuring the entanglement entropy scaling at the transition would provide a direct, model-independent falsifier beyond the specific correlation functions reported.
  • The authors' own QMC data at s=0.85 (z≈2, Δ_D≈1/4, with Δ_D far from the O(ε) value 0.425) hint at a distinct, strongly dissipative fixed point controlling deep sub-Ohmic behavior; one testable extension is to check whether this is a z=2 fixed point with exact Δ_N=1/2 and Δ_D=1/4, which the paper notes as a possibility.
  • Because the retarded interaction decays as τ^{-(1+s)}, the dissipative problem maps onto a spin chain with long-range imaginary-time interactions; an extension would be to compare the phase diagram here with that of explicitly nonlocal 1D DQCP models, checking whether the Ohmic case corresponds to a specific long-range exponent and whether the emergent O(4) symmetry is a generic feature of that cl
  • The failure of the uniform susceptibility to scale at the critical point (since the magnetic moment is not conserved in the composite system) could be developed into a practical diagnostic for dissipation-dominated quantum criticality in other open-system simulations.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper studies a dissipative spin-1/2 J-Q3 chain, with each spin component coupled to bosonic baths, using non-Abelian bosonization, perturbative RG, and large-scale QMC. The authors claim continuous AFM–VBS transitions in both sub-Ohmic and Ohmic regimes, with the Ohmic transition governed by the SU(2)_1 CFT (z=1, ΔN=ΔD=1/2, deconfined spinons, emergent O(4) symmetry) and the sub-Ohmic transition controlled by a distinct fixed point that merges into the SU(2)_1 CFT as s→1. A super-Ohmic AFM-to-QLRO transition is also proposed. QMC supports the Ohmic case quantitatively: Q_c=7.100(2), z=1.02(2), ΔN≈0.499(3), ΔD≈0.50(1), with logarithmic corrections consistent in relative sign between Néel and VBS channels. The sub-Ohmic QMC results, however, show ΔD≈0.25 at both s=0.85 and s=0.95 and z≈2 at s=0.85, in conflict with the RG predictions and with the claimed smooth merging into the Ohmic fixed point.

Significance. If the Ohmic result is taken alone, it is a significant advance: it provides a concrete, numerically verified example of a deconfined quantum critical point in a one-dimensional open quantum spin system, with the critical exponents matching an external, parameter-free CFT benchmark (SU(2)_1). The QMC work uses careful crossing analyses, multiple independent order-parameter channels, and explicit treatment of logarithmic corrections, and it goes well beyond a qualitative proposal. The broader claim—that the Ohmic DQCP is the endpoint of a continuous family of sub-Ohmic deconfined critical points—is the part that the data do not currently support. If that family claim were established, the significance would be substantially greater; as it stands, the paper is best viewed as a solid Ohmic-DQCP result with a speculative sub-Ohmic extension.

major comments (4)
  1. [Table I / Numerical results] Table I directly undermines the claimed merging of the sub-Ohmic fixed point into the SU(2)_1 CFT as s→1. QMC gives ΔD=0.248(2)/0.240(5) at s=0.85, ΔD=0.259(5)/0.25(1) at s=0.95, and then ΔD=0.50(1)/0.502(2) at s=1. Instead of a smooth interpolation to 1/2, ΔD is essentially flat at ~1/4 across the sub-Ohmic regime and jumps at s=1. The Conclusion's suggestion of a separate strongly-dissipative fixed point with ΔD≈1/4, ΔN≈1/2, z≈2 is not reconciled with the Introduction's statement that 'the transition persists up to the Ohmic case, where the FP merges into the SU(2)_1 CFT.' The QMC data are internally consistent but support two distinct fixed points across s=1, not a merging family.
  2. [Eq. (5), Eq. (S24)–(S26), Table I] At s=0.85, the perturbative RG is quantitatively invalid. The RG predicts z(T)=1.02 and ΔN(T)=0.575, while QMC gives z=1.97(7) and ΔN=0.46(2); ΔD(T)=0.275 vs QMC 0.248(2). The paper itself notes in the Conclusion that for s=0.85 'the perturbative RG analysis based on the z=1 CFT is unreliable.' This is a load-bearing caveat: the sub-Ohmic phase diagram and the 'persists up to the Ohmic case' narrative are derived from that RG, so as presented the sub-Ohmic part of the central claim is not established by either the numerics or the analytics.
  3. [Table I, s=0.95 row] Even for s=0.95, close to the Ohmic point, the QMC value ΔD=0.25(1) (from D^2 and C_D) disagrees sharply with the RG prediction ΔD(T)=0.425. The RG's sub-Ohmic prediction for the VBS scaling dimension fails already at ε=0.05, not just at ε=0.15. This weakens the statement in the main text that 'our data therefore provide strong evidence for our RG analysis at s≈1 regime.' The Ohmic point itself is well supported, but the range of s for which the RG is quantitatively reliable is evidently much narrower than the paper claims.
  4. [Sec. II F, Eq. (S45)] For the Ohmic case, the paper predicts a multiplicative logarithmic correction exponent q=-2 for the Néel correlation, while QMC finds q≈-0.49 (with q≈0.53 for m_s^2). The discrepancy is acknowledged as possibly due to 'unknown operator mixing or higher order effects,' but it is not discussed as a potential challenge to the identification of the fixed point. Since the SU(2)_1 assignment rests on the scaling dimensions and z, this mismatch is not fatal, but it should be addressed: e.g., does an operator-mixing calculation at next order produce the observed exponent, or is the trajectory along the critical surface different from the one assumed?
minor comments (6)
  1. [Introduction] Typographical errors: 'introduing', 'interacions', 'doubel', 'analyssi', 'Fp' (in supplement), and 'the remain confined' in the first paragraph. These should be corrected.
  2. [Fig. 1] The RG flow diagrams lack axis labels and a clear legend for the meaning of the arrows and dashed lines. Please add labels for λ and g, and explicitly indicate the fixed points in the figure rather than only in the caption.
  3. [Ref. [33]] The supplemental material reference has no author list and appears as a bare comma. Please format it properly.
  4. [References 10, 12] The bibliographic entries for arXiv preprints in Refs. [10] and [12] are incomplete (no arXiv number or journal information). Please supply the missing identifiers.
  5. [Model, Eq. (S9)] The generalized free field φ with propagator δ(x-x')/|τ-τ'|^{1+s} is central to the RG derivation but its regularization and the range of validity of the OPE (S15) are not discussed. A brief comment on corrections beyond the leading order would help readers assess the perturbative control.
  6. [Numerical methods] All QMC results are at α=0.4. The paper discusses the dependence on dissipation strength only through the RG flow. A sentence stating what is known from QMC at other α values, or why α=0.4 is representative, would strengthen the presentation.

Circularity Check

1 steps flagged · score 2.0 of 10

Ohmic SU(2)_1 prediction is independently supported; only a minor self-consistent log-correction fit anchors ΔN at the value it then confirms.

  1. fitted input called prediction [Main text, Numerical results, Fig. 4(a) / Eq. (10) paragraph (s=1 C(L/2) analysis)]
    "For s=1, we fit Eq.(10) to the data in two steps: first fixing ΔN = 1/2 to determine q, and then fixing the obtained q to extract ΔN. The reliability of the results is guaranteed self-consistently. By gradually discarding the smallest system sizes, we eliminate systematic errors from sub-leading corrections to scaling. Our best estimates are q(C) = −0.49, ΔN = 0.499(3), which agree remarkably well with SU(2)_1 CFT prediction ΔN = 1/2."

    The SU(2)_1 prediction ΔN=1/2 is used as an input to determine the logarithmic exponent q(C); the subsequent 'extraction' of ΔN with that same q fixed is a one-parameter fit on the same C(L/2) data. Therefore the reported agreement of 0.499(3) with 1/2 is not an independent confirmation from this observable: it is a self-consistency check of a fit already seeded with the target value. The wording 'guaranteed self-consistently' makes this circularity explicit. The central Ohmic claim is not destroyed, because ΔD, z, and the m_s^2 analysis are determined separately, but this particular ΔN evidence is partially circular.

full rationale

The paper's central Ohmic claim does not reduce to its inputs. The RG beta functions, β_g=(ε/2)g−(π/2)λg and β_λ=2πλ^2−(1/2)g^2, are derived from OPEs of the SU(2)_1 CFT and the generalized free field ϕ; no parameter is fitted to the target exponents. The nontrivial fixed point (λ*,g*)=(ε/π,2ε/√π) and its ε→0 limit are consequences of those equations, and the claim that the s=1 transition flows back to the SU(2)_1 fixed point is a genuine RG statement, not a restatement of the starting point. The QMC determinations of ΔD=0.50(1)/0.502(2), z=1.02(2), and the independent m_s^2 fits provide external confirmation of the Ohmic SU(2)_1 description. The one circular step is the two-step log-correction fit of C(L/2), where ΔN=1/2 is fixed to determine q(C) and then the extracted ΔN is quoted as agreement with the same value; this is a self-consistency check rather than an independent measurement. Because this anchored fit is only one of several independent estimators and the other estimators do not rely on the same anchor, the central claim retains substantial independent support. The sub-Ohmic QMC/RG disagreement (e.g., ΔD≈0.25 at s=0.95 vs RG 0.425, z≈2 at s=0.85) is explicitly acknowledged in the Conclusion and is a validity/accuracy concern, not a circularity. Self-citations (refs. [5,9,10] by Guo) are methodological or contextual and are not load-bearing. Accordingly, the overall circularity score is 2: one minor fitted-input step, with the main derivation otherwise self-contained.

Assumptions & free parameters 1 free parameters · 5 assumptions · 1 invented entities

The central Ohmic result does not depend on any fitted constant: the beta functions are derived, the fixed point merges with a known CFT, and the QMC confirms it. The sub/super-Ohmic extensions rest on the auxiliary-field bosonization and a small-ε expansion whose validity is contradicted by the s=0.85 QMC data.

free parameters (1)
  • dissipation strength α = 0.4 (fixed in all QMC runs)
    All QMC results are for α=0.4; no α-scans are shown, so the phase diagram and exponents are only established at this coupling.
assumptions (5)
  • domain assumption Non-Abelian bosonization of the spin-1/2 Heisenberg chain maps to SU(2)_1 CFT plus backscattering
    Used in Sec. I.A of SM to write H_s in bosonized form; standard but relies on the low-energy limit of the lattice model.
  • ad hoc to paper The retarded bath interaction can be represented by a generalized free field φ with propagator δ(x−x')/|τ−τ'|^{1+s}
    Central to deriving the β-functions; the auxiliary field is introduced to reproduce Eq. (S7), and its OPEs are asserted, not derived from the microscopic bath.
  • domain assumption Only the n·n term in the bosonized dissipative interaction is retained; J·J and J·n terms are irrelevant by power counting
    SM Sec. I.A items 1-3; standard power-counting but a truncation whose failure would change the β-functions.
  • ad hoc to paper Perturbative RG around the z=1 CFT is valid for s∈(0.85,1]
    The ε=1−s expansion is used for s=0.95 and s=0.85; the authors themselves note the s=0.85 result (z≈2) invalidates the approach.
  • ad hoc to paper Spinons in the dissipative VBS phase behave as in the isolated VBS phase (deconfined)
    Needed to interpret the sub-Ohmic transition as a spinon-deconfinement DQCP; the paper explicitly leaves this open.
invented entities (1)
  • Generalized free field φ (3-component auxiliary boson)
    purpose: Reproduces the retarded interaction in the bosonized action; after integrating out φ, one recovers the |τ|^{-(1+s)} dissipation term.
    A computational device in the effective field theory, not a physical bath mode; no falsifiable handle independent of the model.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Deconfined quantum critical point in a dissipative spin-1/2 chain." pith.science (2026). https://pith.science/paper/CBN4J46B

@misc{pith2026260716039,
  author       = {Pith},
  title        = {Pith review of: Deconfined quantum critical point in a dissipative spin-1/2 chain},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CBN4J46B}},
  note         = {Machine review of arXiv:2607.16039}
}
abstract

Open quantum spin systems offer a previously unexplored route to realizing deconfined quantum criticality. We consider a spin-1/2 $J$-$Q_3$ chain, consisting of an antiferromagnetic (AFM) Heisenberg exchange and a competing multi-spin interaction favoring a valence-bond solid (VBS) state, with each spin component coupled to a bosonic bath. Using non-Abelian bosonization and renormalization-group (RG) analysis, combined with large-scale quantum Monte Carlo (QMC) simulations, we determine the phase diagram and the associated phase transitions of the model. We show that strong dissipation stabilizes an AFM phase for sub-Ohmic, Ohmic, and super-Ohmic baths. Continuous AFM-VBS transitions at finite dissipation are found upon increasing the multi-spin interaction in both the sub-Ohmic and Ohmic regimes. Critical properties are obtained through perturbative RG analysis and QMC simulations. In the Ohmic case, the critical point features spinon deconfinement and emergent O(4) symmetry. In the sub-Ohmic regime, the transition may also involve spinon deconfinement, provided that spinons remain deconfined in the dissipative VBS phase. In addition, in the super-Ohmic regime, we propose a transition from AFM phase to a quasi-long-range ordered phase.

Figures

Figures reproduced from arXiv: 2607.16039 by the authors.

Figure 1
Figure 1. FIG. 1. (a) -(c) The RG flow diagram of beta function for [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Crossing-point analysis for the Ohmic (a) and sub [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Log-Log plots of [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Dissipation-induced bulk and boundary criticality in the Haldane chain

    cond-mat.str-el 2026-08 conditional novelty 8.0 of 10

    Dissipation drives the Haldane chain to a nonconformal critical point where its protected edge states exhibit a boundary critical exponent distinct from the trivial chain and from the dissipative O(3) epsilon expansion.

Reference graph

Works this paper leans on

60 extracted references · 2 canonical work pages · cited by 1 Pith paper

  1. [1]

    Senthil, A

    T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. Fisher, Deconfined quantum critical points, Science 303, 1490 (2004)

    2004

  2. [2]

    Senthil, L

    T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, and M. Fisher, Quantum criticality beyond the landau- ginzburg-wilson paradigm, Phys. Rev. B70, 144407 (2004)

    2004

  3. [3]

    Levin and T

    M. Levin and T. Senthil, Deconfined quantum critical- ity and n´ eel order via dimer disorder, Phys. Rev. B70, 220403(R) (2004)

    2004

  4. [4]

    Senthil, Deconfined quantum critical points: A re- view, in 50 Years of the Renormalization Group, Chap

    T. Senthil, Deconfined quantum critical points: A re- view, in 50 Years of the Renormalization Group, Chap. Chapter 14, pp. 169–195

  5. [5]

    H. Shao, W. Guo, and A. W. Sandvik, Quantum criti- cality with two length scales, Science352, 213 (2016)

    2016

  6. [6]

    C. Wang, A. Nahum, M. A. Metlitski, C. Xu, and T. Senthil, Deconfined quantum critical points: Symme- tries and dualities, Phys. Rev. X7, 031051 (2017)

    2017

  7. [7]

    Nahum, J

    A. Nahum, J. T. Chalker, P. Serna, M. Ortu˜ no, and A. M. Somoza, Deconfined quantum criticality, scaling violations, and classical loop models, Phys. Rev. X5, 041048 (2015)

    2015

  8. [8]

    Nakayama and T

    Y. Nakayama and T. Ohtsuki, Necessary condition for emergent symmetry from the conformal bootstrap, Phys. Rev. Lett.117, 131601 (2016)

    2016

Show all 60 references
  1. [9]

    Z. Deng, L. Liu, W. Guo, and H.-Q. Lin, Diagnosing quantum phase transition order and deconfined criticality via entanglement entropy, Phys. Rev. Lett.133, 100402 (2024)

    2024

  2. [10]

    Takahashi, H

    J. Takahashi, H. Shao, B. Zhao, W. Guo, and A. W. Sandvik, So(5) multicriticality in two-dimensional quan- tum magnets arXiv: (2024) [cond-mat.str-el]

    2024

  3. [11]

    S. M. Chester and N. Su, Bootstrapping deconfined quan- 6 tum tricriticality, Phys. Rev. Lett.132, 111601 (2024)

    2024

  4. [12]

    Li and T

    Z. Li and T. Shen, Bootstrap cone of the multicritical deconfined quantum critical point arXiv: (2026) [hep-th]

    2026

  5. [13]

    Yang, D.-X

    S. Yang, D.-X. Yao, and A. W. Sandvik, Deconfined quantum criticality in spin-1/2 chains with long-range interactions arXiv: (2020) [physics.comp-ph]

    2020

  6. [14]

    C.-M. Jian, Y. Xu, X.-C. Wu, and C. Xu, Continuous N´ eel-VBS quantum phase transition in non-local one- dimensional systems with SO(3) symmetry, SciPost Phys. 10, 033 (2021)

    2021

  7. [15]

    Xu, X.-C

    Y. Xu, X.-C. Wu, and C. Xu, Deconfined quantum crit- ical point with nonlocality, Phys. Rev. B106, 155131 (2022)

    2022

  8. [16]

    Song and L

    H.-H. Song and L. Zhang, Boundary phase transitions of the two-dimensional quantum critical xxz model, Phys. Rev. B111, 165139 (2025)

    2025

  9. [17]

    Ding and L

    C. Ding and L. Zhang, Deconfined boundary phase tran- sition of a quantum critical heisenberg model arXiv: (2026) [cond-mat.str-el]

    2026

  10. [18]

    Weiss, Quantum dissipative systems, 4th ed

    U. Weiss, Quantum dissipative systems, 4th ed. (WORLD SCIENTIFIC, 2012)

    2012

  11. [19]

    A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. Fisher, A. Garg, and W. Zwerger, Dynamics of the dissipative two-state system, Rev. Mod. Phys.59, 1 (1987)

    1987

  12. [20]

    Tang and A

    Y. Tang and A. W. Sandvik, Method to characterize spinons as emergent elementary particles, Phys. Rev. Lett.107, 157201 (2011)

    2011

  13. [21]

    Sanyal, A

    S. Sanyal, A. Banerjee, and K. Damle, Vacancy-induced spin texture in a one-dimensionals= 1 2 heisenberg anti- ferromagnet, Phys. Rev. B84, 235129 (2011)

    2011

  14. [22]

    Weber, D

    M. Weber, D. J. Luitz, and F. F. Assaad, Dissipation- induced order: Thes= 1/2 quantum spin chain coupled to an ohmic bath, Phys. Rev. Lett.129, 056402 (2022)

    2022

  15. [23]

    N. D. Mermin and H. Wagner, Absence of ferromag- netism or antiferromagnetism in one- or two-dimensional isotropic heisenberg models, Phys. Rev. Lett.17, 1133 (1966)

    1966

  16. [24]

    P. C. Hohenberg, Existence of long-range order in one and two dimensions, Phys. Rev.158, 383 (1967)

    1967

  17. [25]

    Nahum, P

    A. Nahum, P. Serna, J. T. Chalker, M. Ortu˜ no, and A. M. Somoza, Emergent so(5) symmetry at the n´ eel to valence-bond-solid transition, Phys. Rev. Lett.115, 267203 (2015)

    2015

  18. [26]

    Jiang and O

    S. Jiang and O. Motrunich, Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points, Phys. Rev. B99, 075103 (2019)

    2019

  19. [27]

    Mudry, A

    C. Mudry, A. Furusaki, T. Morimoto, and T. Hikihara, Quantum phase transitions beyond landau-ginzburg the- ory in one-dimensional space revisited, Phys. Rev. B99, 205153 (2019)

    2019

  20. [28]

    Huang, D.-C

    R.-Z. Huang, D.-C. Lu, Y.-Z. You, Z. Y. Meng, and T. Xiang, Emergent symmetry and conserved current at a one-dimensional incarnation of deconfined quantum crit- ical point, Phys. Rev. B100, 125137 (2019)

    2019

  21. [29]

    Weber, Competing dirac masses in one dimen- sion: Symmetry-enhanced pseudo-first-order transition and deconfined criticality arXiv: (2025) [cond-mat.str- el]

    M. Weber, Competing dirac masses in one dimen- sion: Symmetry-enhanced pseudo-first-order transition and deconfined criticality arXiv: (2025) [cond-mat.str- el]

    2025

  22. [30]

    Tang and A

    Y. Tang and A. W. Sandvik, Quantum monte carlo stud- ies of spinons in one-dimensional spin systems, Phys. Rev. B92, 184425 (2015)

    2015

  23. [31]

    Bouverot-Dupuis, S

    O. Bouverot-Dupuis, S. Majumdar, A. Rosso, and L. Foini, Antiferromagnetic order enhanced by local dis- sipation, Phys. Rev. B109, 205148 (2024)

    2024

  24. [32]

    Bouverot-Dupuis, Mapping a dissipative quantum spin chain onto a generalized Coulomb gas, SciPost Phys

    O. Bouverot-Dupuis, Mapping a dissipative quantum spin chain onto a generalized Coulomb gas, SciPost Phys. 17, 130 (2024)

    2024

  25. [33]

    , supplemental material for details of the non-Abelian bosonization of the dissipativeJ-Q 3 model, the deriva- tion of the renormalization group (RG) equations, the analysis of RG flow, the spin-wave analysis of the effect ofQterms, along with the quantum Monte Carlo simu- lat...

  26. [34]

    Antunes, Lifshitz critical points meet zamolodchikov perturbation theory arXiv: (2026) [hep-th]

    A. Antunes, Lifshitz critical points meet zamolodchikov perturbation theory arXiv: (2026) [hep-th]

    2026

  27. [35]

    Weber, Quantum monte carlo simulation of spin- boson models using wormhole updates, Phys

    M. Weber, Quantum monte carlo simulation of spin- boson models using wormhole updates, Phys. Rev. B 105, 165129 (2022)

    2022

  28. [36]

    Weber, F

    M. Weber, F. F. Assaad, and M. Hohenadler, Directed- loop quantum monte carlo method for retarded interac- tions, Phys. Rev. Lett.119, 097401 (2017)

    2017

  29. [37]

    A. W. Sandvik and J. Kurkij¨ arvi, Quantum monte carlo simulation method for spin systems, Phys. Rev. B43, 5950 (1991)

    1991

  30. [38]

    A. W. Sandvik, Stochastic series expansion method with operator-loop update, Phys. Rev. B59, R14157 (1999)

    1999

  31. [39]

    Vollmayr, J

    K. Vollmayr, J. D. Reger, M. Scheucher, and K. Binder, Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order pa- rameter distribution, Zeitschrift f¨ ur Physik B Condensed Matter91, 113 (1993)

    1993

  32. [40]

    Deconfined quantum critical point in a dissipative spin-1/2 chain

    M. Matsumoto, C. Yasuda, S. Todo, and H. Takayama, Ground-state phase diagram of quantum heisenberg anti- ferromagnets on the anisotropic dimerized square lattice, Phys. Rev. B65, 014407 (2001). Supplementary Materials for “ Deconfined quantum critical point in a dissipative s...

    2001

  33. [41]

    The oscillating terms containing the factor (−1) x (i.e., those involvingJ·n) vanish upon spatial integration

  34. [42]

    Since an interaction of the formJ·Jhas scaling dimension 2, we find [α] =−[2−1−2 + (1 +s)] =−1 + (1−s)

    InH ret, the interaction involves an additional doubel time integral over a propagatorα R dx dτ dτ′ |τ| −(1+s), whose scaling dimension is [α] + (1 +s)−1−2. Since an interaction of the formJ·Jhas scaling dimension 2, we find [α] =−[2−1−2 + (1 +s)] =−1 + (1−s). Fors >0, this is...

  35. [43]

    A dimensional analysis ofα R dx dτ dτ′ ⃗ n(x, τ)·⃗ n(x, τ′)/|τ−τ ′|1+s yields [α] = 1−s

    For the last term,n·n, recall that the scaling dimension of⃗ nat the SU(2) 1 CFT is 1/2. A dimensional analysis ofα R dx dτ dτ′ ⃗ n(x, τ)·⃗ n(x, τ′)/|τ−τ ′|1+s yields [α] = 1−s. Thus, the coupling is relevant, marginal, and irrelevant fors <1,s= 1, ands >1, respectively. Final...

  36. [44]

    Giamarchi,Quantum Physics in One Dimension(Oxford University Press, 2003), ISBN 9780198525004, URLhttps: //doi.org/10.1093/acprof:oso/9780198525004.001.0001

    T. Giamarchi,Quantum Physics in One Dimension(Oxford University Press, 2003), ISBN 9780198525004, URLhttps: //doi.org/10.1093/acprof:oso/9780198525004.001.0001

    2003

  37. [45]

    Tang and A

    Y. Tang and A. W. Sandvik, Phys. Rev. Lett.107, 157201 (2011), URLhttps://link.aps.org/doi/10.1103/ PhysRevLett.107.157201

    2011

  38. [46]

    Sanyal, A

    S. Sanyal, A. Banerjee, and K. Damle, Phys. Rev. B84, 235129 (2011), URLhttps://link.aps.org/doi/10.1103/ PhysRevB.84.235129

    2011

  39. [47]

    Weber, D

    M. Weber, D. J. Luitz, and F. F. Assaad, Phys. Rev. Lett.129, 056402 (2022), URLhttps://link.aps.org/doi/10. 1103/PhysRevLett.129.056402

    2022

  40. [48]

    C.-M. Jian, Y. Xu, X.-C. Wu, and C. Xu, SciPost Phys.10, 033 (2021), URLhttps://scipost.org/10.21468/ SciPostPhys.10.2.033

    2021

  41. [49]

    Cardy,Scaling and Renormalization in Statistical Physics, Cambridge Lecture Notes in Physics (Cambridge University Press, 1996)

    J. Cardy,Scaling and Renormalization in Statistical Physics, Cambridge Lecture Notes in Physics (Cambridge University Press, 1996)

    1996

  42. [50]

    Fradkin,Field Theories of Condensed Matter Physics(Cambridge University Press, 2013), 2nd ed

    E. Fradkin,Field Theories of Condensed Matter Physics(Cambridge University Press, 2013), 2nd ed

    2013

  43. [51]

    Antunes,Lifshitz critical points meet zamolodchikov perturbation theory(2026), 2602.12341, URLhttps://arxiv.org/ abs/2602.12341

    A. Antunes,Lifshitz critical points meet zamolodchikov perturbation theory(2026), 2602.12341, URLhttps://arxiv.org/ abs/2602.12341

    2026

  44. [52]

    Xu, X.-C

    Y. Xu, X.-C. Wu, and C. Xu, Phys. Rev. B106, 155131 (2022), URLhttps://link.aps.org/doi/10.1103/PhysRevB. 106.155131

    2022 doi

  45. [53]

    Pankov, S

    S. Pankov, S. Florens, A. Georges, G. Kotliar, and S. Sachdev, Phys. Rev. B69, 054426 (2004), URLhttps://link.aps. org/doi/10.1103/PhysRevB.69.054426

    2004 doi

  46. [54]

    Sachdev, P

    S. Sachdev, P. Werner, and M. Troyer, Phys. Rev. Lett.92, 237003 (2004), URLhttps://link.aps.org/doi/10.1103/ PhysRevLett.92.237003

    2004

  47. [55]

    Werner, M

    P. Werner, M. Troyer, and S. Sachdev, Journal of the Physical Society of Japan74, 67 (2005), https://doi.org/10.1143/JPSJS.74S.67, URLhttps://doi.org/10.1143/JPSJS.74S.67

    2005 doi

  48. [56]

    Barzykin and I

    V. Barzykin and I. Affleck, Journal of Physics A: Mathematical and General32, 867 (1999), URLhttps://doi.org/10. 1088/0305-4470/32/6/001

    1999

  49. [57]

    Affleck, D

    I. Affleck, D. Gepner, H. J. Schulz, and T. Ziman, Journal of Physics A: Mathematical and General22, 511 (1989), URL https://doi.org/10.1088/0305-4470/22/5/015

    1989 doi

  50. [58]

    Zinn-Justin,Quantum Field Theory and Critical Phenomena: Fifth Edition (5th edn)(2021)

    J. Zinn-Justin,Quantum Field Theory and Critical Phenomena: Fifth Edition (5th edn)(2021)

    2021

  51. [59]

    Fisher, P

    M. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B40, 546 (1989), URLhttps://link.aps.org/ doi/10.1103/PhysRevB.40.546

    1989 doi

  52. [60]

    A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B49, 11919 (1994), URLhttps://link.aps.org/doi/10.1103/ PhysRevB.49.11919

    1994

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.