pith. sign in

arxiv: 2604.18425 · v1 · submitted 2026-04-20 · ❄️ cond-mat.quant-gas · cond-mat.str-el

Quantum quenches in a spin-1 chain with tunable symmetry

Luis Eduardo Ramos-Sol\'is , Sayan Choudhury , Freddy Jackson Poveda-Cuevas , Eduardo Ibarra-Garc\'ia-Padilla This is my paper

Pith reviewed 2026-05-10 03:08 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.str-el
keywords quantum quenchesspin-1 Heisenberg chainSU(3) symmetryconserved quantitiesnon-equilibrium dynamicsintegrable modelstime-evolving block decimation
0
0 comments X

The pith

Tuning a spin-1 chain to SU(3) symmetry reveals a new conserved quantity that limits the states reachable after a quantum quench.

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

The authors simulate quantum quenches in an anisotropic spin-1 Heisenberg chain using time-evolving block decimation. By varying the quadrupolar interaction strength, they tune the system from the non-integrable SU(2) regime to the integrable SU(3) regime. At the SU(3) point they identify an additional conserved quantity that is absent in the generic case. This quantity restricts the number of accessible states after the quench, which accounts for the distinct evolution of magnetization, entanglement entropy, and spin correlations seen in the numerics. The results indicate a concrete way to produce controlled non-equilibrium dynamics in spin-1 lattice models that can be engineered in ultracold-atom platforms.

Core claim

In the SU(3)-symmetric limit of the spin-1 Heisenberg chain, an additional conserved quantity exists that is not present in the SU(2) case. Numerical simulations of quenches from various initial states show that the post-quench dynamics are governed by the restricted number of accessible states allowed by this conservation law, leading to characteristic patterns in magnetization, entanglement entropy, and spin correlations.

What carries the argument

The new conserved quantity at the SU(3) symmetric point, which partitions the Hilbert space into sectors whose size determines the reachable states after a quench.

Load-bearing premise

The TEBD simulations remain accurate for the system sizes, evolution times, and parameter ranges studied, with truncation errors not affecting the identification of the conserved quantity or the reported dynamical features.

What would settle it

An exact diagonalization study on small systems that finds the proposed quantity is not conserved, or a quench where the measured long-time observables exceed the number of states permitted by the conservation law.

Figures

Figures reproduced from arXiv: 2604.18425 by Eduardo Ibarra-Garc\'ia-Padilla, Freddy Jackson Poveda-Cuevas, Luis Eduardo Ramos-Sol\'is, Sayan Choudhury.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of the model presented in Eq. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Two-site spin alignments that minimize the energy of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Graphical representation of the z-magnetization ini [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Time evolution of the local magnetization and corre [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (Color online) The time-evolution of the local magnetization [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (Color online) Time evolution of the local magnetization [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (Color online) Time evolution of the out-of-plane spin correlation [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (Color online) Logarithm of the number of available [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (Color online) Relative frequency of local bond align [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. (Color online) Time evolution of observables for [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Time evolution of the out-of-plane spin projection [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Absolute value of the matrix elements of the Heisen [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Absolute difference of the initial energy by site [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Absolute difference in local magnetization [PITH_FULL_IMAGE:figures/full_fig_p019_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Absolute difference of the initial energy by site [PITH_FULL_IMAGE:figures/full_fig_p020_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Absolute difference in local magnetization [PITH_FULL_IMAGE:figures/full_fig_p020_17.png] view at source ↗
read the original abstract

In recent years, the dynamics of interacting quantum systems far from equilibrium have attracted significant research interest. Driven by rapid progress in quantum simulators, various non-equilibrium phenomena have now been realized experimentally. In this work, we use the time-evolving block decimation (TEBD) method to investigate the dynamics of an anisotropic spin-1 Heisenberg chain for a wide range of experimentally accessible initial states. By adjusting the parameter $J_q$ that controls the quadrupolar interaction strength, we can tune the system from a non-integrable SU(2) Heisenberg model to an integrable SU(3) Heisenberg model. We examine the local magnetization, entanglement entropy, and spin correlations, and characterize their dependence on $J_q$. We identify a new conserved quantity at the SU(3) symmetric point and provide a theoretical framework to explain our numerical observations in terms of the number of accessible states permitted by this conservation law. Our results provide a route to realize a rich array of non-equilibrium behavior in spin-1 lattice models, which can be engineered in several experimental platforms such as ultracold atoms in optical lattices.

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

1 major / 2 minor

Summary. The manuscript uses TEBD simulations to study quantum quench dynamics in an anisotropic spin-1 Heisenberg chain, tuning the quadrupolar interaction J_q to interpolate between the non-integrable SU(2) and integrable SU(3) points. It reports the time evolution of local magnetization, entanglement entropy, and spin correlations across a range of initial states, identifies a new conserved quantity at the SU(3) symmetric point, and introduces a theoretical framework that attributes the observed dynamical features to the reduced number of accessible states enforced by this conservation law.

Significance. If the new conserved quantity is exactly conserved, the work would usefully illustrate how an additional integral of motion at the SU(3) point restricts the reachable Hilbert space and thereby shapes quench dynamics in a tunable spin-1 model. The numerical exploration over experimentally relevant initial states and the explicit link to ultracold-atom platforms are strengths. However, the central framework rests on an unverified numerical observation rather than an analytical demonstration, which limits the immediate impact until the conservation is placed on firmer ground.

major comments (1)
  1. [Section identifying the new conserved quantity at the SU(3) point] The section identifying the new conserved quantity at the SU(3) point: the claim that a specific operator is exactly conserved is supported only by the numerical observation that its expectation value remains time-independent in TEBD runs. No analytical verification that this operator commutes with the SU(3)-symmetric Hamiltonian (i.e., explicit computation of [H, Q] = 0 on the local interaction terms) is provided. Because the subsequent counting argument for accessible states depends on exact conservation, this numerical evidence alone is insufficient to establish the central claim.
minor comments (2)
  1. [Methods] The methods description provides insufficient detail on the TEBD bond dimensions employed, truncation thresholds, system sizes, and any convergence or error-bar analysis. These checks are needed to confirm that the reported constancy of the candidate conserved quantity is not influenced by numerical truncation.
  2. Figure captions and axis labels should explicitly indicate the values of J_q and the specific initial states corresponding to each curve to improve readability when comparing dynamics across the SU(2)–SU(3) crossover.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying the need for stronger analytical support of the conserved quantity. We address this point directly below and will incorporate the requested verification in the revised version.

read point-by-point responses

  1. Referee: [Section identifying the new conserved quantity at the SU(3) point] The section identifying the new conserved quantity at the SU(3) point: the claim that a specific operator is exactly conserved is supported only by the numerical observation that its expectation value remains time-independent in TEBD runs. No analytical verification that this operator commutes with the SU(3)-symmetric Hamiltonian (i.e., explicit computation of [H, Q] = 0 on the local interaction terms) is provided. Because the subsequent counting argument for accessible states depends on exact conservation, this numerical evidence alone is insufficient to establish the central claim.

    Authors: We agree that an explicit analytical demonstration is required to place the conservation law on firm ground. While the TEBD data show that the expectation value of the identified operator remains constant to machine precision across all simulated times and system sizes, this alone does not constitute a proof. We have now computed the commutator [H_SU(3), Q] directly on the local two-site interaction terms of the SU(3)-symmetric Hamiltonian and verified that it vanishes identically. The explicit form of Q and the step-by-step commutator evaluation will be added to the revised manuscript (new subsection in Sec. III). This analytical result confirms exact conservation, thereby justifying the Hilbert-space counting argument and the explanation of the observed dynamical restrictions. revision: yes

Circularity Check

0 steps flagged

No circularity: conservation law identified numerically then used to interpret independent dynamical features

full rationale

The manuscript reports TEBD simulations of quenches in the spin-1 chain, observes time-independent expectation values for a candidate operator at the SU(3) point, and labels this operator a new conserved quantity. It then invokes the resulting restriction on accessible states to account for the saturation behavior of entanglement entropy and correlation functions. This chain does not reduce any claimed prediction to a fitted parameter by construction, nor does it rely on self-citation for a uniqueness theorem or smuggle an ansatz; the numerical constancy and the subsequent counting argument remain logically distinct steps supported by the same simulation data but not tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard definition of the anisotropic spin-1 Heisenberg Hamiltonian with quadrupolar term, the validity of the TEBD truncation for the simulated dynamics, and the assumption that the identified conserved quantity is independent of the numerical method.

axioms (2)
  • domain assumption The Hamiltonian is the standard anisotropic spin-1 Heisenberg model plus quadrupolar interaction controlled by J_q
    Invoked to define the tunable symmetry between SU(2) and SU(3) points.
  • domain assumption TEBD accurately captures the unitary time evolution for the chosen initial states and evolution times
    Required for the numerical observations of magnetization, entanglement, and correlations to be reliable.

pith-pipeline@v0.9.0 · 5512 in / 1397 out tokens · 59833 ms · 2026-05-10T03:08:09.619933+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

97 extracted references · 97 canonical work pages

  1. [1]

    (1) in fixed magnetization sectors [73] and employ ED to simulate small chains up toL∼12 sites

    Exact diagonalization We block-diagonalize eq. (1) in fixed magnetization sectors [73] and employ ED to simulate small chains up toL∼12 sites. ED results were used to benchmark con- vergence of our TEBD simulations at short times and to diagnose finite-size effects (see Appendix C for a discus- sion)

    work page

  2. [2]

    boundary

    Time evolving block-decimation Tensor network algorithms exploit the entanglement area laws of quantum many-body systems, whose states access only a subspace of the exponentially growing Hilbert space. These algorithms include DMRG (Density Matrix Renormalization Group) [74, 75] and TEBD [76]. In this work, we implement the TEBD algorithm to compute the t...

    work page

  3. [3]

    Letℓ 1,ℓ −1 andℓ 0 be the number of sites withσ= 1,−1,0 respectively

    Number of accessible eigenstates Consider an initial state with a fixed magnetizationM and quadratic magnetizationM 2. Letℓ 1,ℓ −1 andℓ 0 be the number of sites withσ= 1,−1,0 respectively. Note thatℓ 1 +ℓ 0 +ℓ −1 =L, and thatℓ 1 −ℓ −1 =M. When Jq/J <1 only the total magnetization is conserved, and the number of available states can be obtained by sum- min...

    work page

  4. [4]

    First, we isolate the center bond, denoted as|σ 0, σ1⟩, and define a complementary chain of ˜L=L−2 sites

    Relative frequency of out-of-plane alignments A similar combinatorial argument explains the freez- ing of certain correlation functions in theJ q/J= 1 limit. First, we isolate the center bond, denoted as|σ 0, σ1⟩, and define a complementary chain of ˜L=L−2 sites. This re- duced chain has a fixed magnetization of ˜M=M−M bond and quadratic magnetization ˜M2...

    work page 2023

  5. [5]

    Sz j Sz j+1, X i Sz i # − = 0,(B3a)

    Net magnetization The magnetization operator, defined as M= X i Sz i ,(B1) commutes with the Hamiltonian, [H,P Sz i ] = 0, for every value of its parametersJ z, Jxy andJ q, and thus provides a conservation law valid for all of the systems considered in this work. To prove this, we first write the commutation relations ofS z i with spinS a i and quadrupola...

    work page

  6. [6]

    Sz i Sz i+1, X i λ8 i # − = 0,(B12a)

    Quadratic magnetization We show that the quadratic magnetization operator M2 = X i (Sz i )2 (B4) is a constant of motion whenJ q =J xy = 1 in equation (1). The proof is carried out using the Gell-Mann matri- ces, the usual representation of the SU(3) algebra. The SU(3) algebra is spanned by eight Hermitian and traceless matrices, given by: λ1 =   0 1 0 ...

    work page

  7. [7]

    A general quantum state can be writ- ten as: |ψ⟩= X σ cσ |σ⟩(D1) whereσ= (σ 1,

    Matrix Product States Consider a chain ofLsites, each with a local Hilbert space dimensiond. A general quantum state can be writ- ten as: |ψ⟩= X σ cσ |σ⟩(D1) whereσ= (σ 1, . . . , σi, . . . , σL) denotes the basis con- figurations andc σ are the expansion coefficients⟨ψ|σ⟩. A full description of a general spin chain state requires dL coefficients to be ac...

    work page

  8. [8]

    Y nodd Ui,i+1(dt) #

    Suzuki-T rotter decomposition The time evolution of a quantum state|ψ(t)⟩is gov- erned by the unitary operatorU(dt) =e −iHdt, such that |ψ(t+dt)⟩=U(dt)|ψ(t)⟩. We consider the action of this operator on a quantum state in MPS form for an infinitesimal time stepdt. Spin chain Hamiltonians with nearest-neighbor inter- actions can be written asH=H even+Hodd, ...

    work page

  9. [9]

    The procedure depends on whether the op- erator associated with this observable acts on a single site or on two sites

    Calculation of observables and physical measures The evolution of relevant observables and physical measures can be computed using the updated MPS rep- resentation. The procedure depends on whether the op- erator associated with this observable acts on a single site or on two sites. Other measures rely on the inner product between two MPS (e.g., the fidel...

    work page

  10. [10]

    This error increases as the entropy approaches the numerical limit set byS max = log(χ)

    T runcation errors An approximation error in the TEBD algorithm occurs when the MPS matrices are truncated because their bond dimension exceeds the maximum bond allowedχ. This error increases as the entropy approaches the numerical limit set byS max = log(χ). Time evolution under a time-independent Hamiltonian should preserve the system’s initial energy. ...

    work page

  11. [11]

    Scaling asO(dt 2) [see Eq

    T rotter approximation errors In contrast to truncation errors, the Trotter error man- ifests during the short-time evolution. Scaling asO(dt 2) [see Eq. (D5)], this error implies a strict trade-off: while reducing the time stepdtenhances numerical precision, it significantly increases the computational cost. 20 FIG. 16. Absolute difference of the initial...

    work page

  12. [12]

    Nandkishore and D

    R. Nandkishore and D. A. Huse, Many-body localiza- tion and thermalization in quantum statistical mechan- ics, Annu. Rev. Condens. Matter Phys.6, 15 (2015)

    work page 2015

  13. [13]

    Altman, Many-body localization and quantum ther- malization, Nat

    E. Altman, Many-body localization and quantum ther- malization, Nat. Phys.14, 979 (2018)

    work page 2018

  14. [14]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Col- loquium: Many-body localization, thermalization, and entanglement, Rev. Mod. Phys.91, 021001 (2019)

    work page 2019

  15. [15]

    T. Mori, T. N. Ikeda, E. Kaminishi, and M. Ueda, Ther- malization and prethermalization in isolated quantum systems: a theoretical overview, J. Phys. B: At. Mol. Opt. Phys.51, 112001 (2018)

    work page 2018

  16. [16]

    Chandran, T

    A. Chandran, T. Iadecola, V. Khemani, and R. Moessner, Quantum many-body scars: A quasiparticle perspective, Annu. Rev. Conden. Ma. P.14, 443 (2023)

    work page 2023

  17. [17]

    Serbyn, D

    M. Serbyn, D. A. Abanin, and Z. Papi´ c, Quantum many- body scars and weak breaking of ergodicity, Nat. Phys. 17, 675 (2021)

    work page 2021

  18. [18]

    Moudgalya, B

    S. Moudgalya, B. A. Bernevig, and N. Regnault, Quan- tum many-body scars and Hilbert space fragmentation: a review of exact results, Rep. Prog. Phys.85, 086501 (2022)

    work page 2022

  19. [19]

    P. Sala, T. Rakovszky, R. Verresen, M. Knap, and F. Poll- mann, Ergodicity breaking arising from hilbert space fragmentation in dipole-conserving hamiltonians, Phys. Rev. X10, 011047 (2020)

    work page 2020

  20. [20]

    Khemani, M

    V. Khemani, M. Hermele, and R. Nandkishore, Local- ization from hilbert space shattering: From theory to physical realizations, Phys. Rev. B101, 174204 (2020)

    work page 2020

  21. [21]

    Moudgalya and O

    S. Moudgalya and O. I. Motrunich, Hilbert space frag- mentation and commutant algebras, Phys. Rev. X12, 011050 (2022)

    work page 2022

  22. [22]

    Heyl, Dynamical quantum phase transitions: a re- view, Rep

    M. Heyl, Dynamical quantum phase transitions: a re- view, Rep. Progr. Phys.81, 054001 (2018)

    work page 2018

  23. [23]

    D. V. Else, C. Monroe, C. Nayak, and N. Y. Yao, Discrete time crystals, Annu. Rev. Conden. Ma. P.11, 467 (2020)

    work page 2020

  24. [24]

    Sacha and J

    K. Sacha and J. Zakrzewski, Time crystals: a review, Rep. Progr. Phys.81, 016401 (2018)

    work page 2018

  25. [25]

    Sacha,Time crystals, Vol

    K. Sacha,Time crystals, Vol. 114 (Springer, 2020)

    work page 2020

  26. [26]

    Directed-graph epidemio- logical models of computer viruses,

    V. Khemani, R. Moessner, and S. Sondhi, A brief history of time crystals (2019), arXiv:1910.10745 [cond-mat.str- el]

    work page arXiv 2019

  27. [27]

    M. P. Zaletel, M. Lukin, C. Monroe, C. Nayak, F. Wilczek, and N. Y. Yao, Colloquium: Quantum and classical discrete time crystals, Rev. Mod. Phys.95, 031001 (2023)

    work page 2023

  28. [28]

    Borgonovi, F

    F. Borgonovi, F. M. Izrailev, L. F. Santos, and V. G. Zelevinsky, Quantum chaos and thermalization in iso- lated systems of interacting particles, Phys. Rep.626, 1 (2016)

    work page 2016

  29. [29]

    D’Alessio, Y

    L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65, 239 (2016)

    work page 2016

  30. [30]

    L. J. I. Moon, P. M. Schindler, R. J. Smith, E. Druga, Z.- R. Zhang, M. Bukov, and A. Ajoy, Sensing with discrete time crystals, Nat. Phys. , 1 (2026)

    work page 2026

  31. [31]

    Z. Li, S. Colombo, C. Shu, G. Velez, S. Pilatowsky- Cameo, R. Schmied, S. Choi, M. Lukin, E. Pedrozo- Pe˜ nafiel, and V. Vuleti´ c, Improving metrology with quan- tum scrambling, Science380, 1381 (2023)

    work page 2023

  32. [32]

    Oka and S

    T. Oka and S. Kitamura, Floquet engineering of quantum materials, Annu. Rev. Conden. Ma. P.10, 387 (2019)

    work page 2019

  33. [33]

    M. S. Rudner and N. H. Lindner, Band structure engi- neering and non-equilibrium dynamics in floquet topo- logical insulators, Nat. Rev. Phys.2, 229 (2020)

    work page 2020

  34. [34]

    Weitenberg and J

    C. Weitenberg and J. Simonet, Tailoring quantum gases by floquet engineering, Nat. Phys.17, 1342 (2021)

    work page 2021

  35. [35]

    Montenegro, C

    V. Montenegro, C. Mukhopadhyay, R. Yousefjani, S. Sarkar, U. Mishra, M. G. Paris, and A. Bayat, Quan- tum metrology and sensing with many-body systems, Phys. Rep.1134, 1 (2025)

    work page 2025

  36. [36]

    K. D. Agarwal, S. Mondal, A. Sahoo, D. Rakshit, A. Sen, and U. Sen, Quantum sensing with ultracold simulators in lattice and ensemble systems: A review, Int. J. Mod. Phys. C , 2543006 (2025)

    work page 2025

  37. [37]

    S. Taie, R. Yamazaki, S. Sugawa, and Y. Takahashi, An su (6) mott insulator of an atomic fermi gas realized by large-spin pomeranchuk cooling, Nat. Phys.8, 825 (2012)

    work page 2012

  38. [38]

    Pagano, M

    G. Pagano, M. Mancini, G. Cappellini, P. Lombardi, F. Sch¨ afer, H. Hu, X.-J. Liu, J. Catani, C. Sias, M. In- guscio,et al., A one-dimensional liquid of fermions with tunable spin, Nat. Phys.10, 198 (2014)

    work page 2014

  39. [39]

    Zhang, M

    X. Zhang, M. Bishof, S. L. Bromley, C. V. Kraus, M. S. Safronova, P. Zoller, A. M. Rey, and J. Ye, Spectroscopic observation of su (n)-symmetric interactions in sr orbital magnetism, Science345, 1467 (2014)

    work page 2014

  40. [40]

    Hofrichter, L

    C. Hofrichter, L. Riegger, F. Scazza, M. H¨ ofer, D. R. Fernandes, I. Bloch, and S. F¨ olling, Direct probing of the mott crossover in the su (n) fermi-hubbard model, Phys. Rev. X6, 021030 (2016)

    work page 2016

  41. [41]

    Pasqualetti, O

    G. Pasqualetti, O. Bettermann, N. Darkwah Oppong, E. Ibarra-Garc´ ıa-Padilla, S. Dasgupta, R. T. Scalettar, K. R. Hazzard, I. Bloch, and S. F¨ olling, Equation of state and thermometry of the 2d su (n) fermi-hubbard model, Phys. Rev. Lett.132, 083401 (2024)

    work page 2024

  42. [42]

    M. A. Cazalilla and A. M. Rey, Ultracold fermi gases with emergent su (n) symmetry, Rep. Progr. Phys.77, 124401 (2014)

    work page 2014

  43. [43]

    Fallani, Multicomponent spin mixtures of two-electron fermions (2023), arXiv:2308.06591 [cond-mat.quant-gas]

    L. Fallani, Multicomponent spin mixtures of two-electron fermions (2023), arXiv:2308.06591 [cond-mat.quant-gas]

    work page arXiv 2023

  44. [44]

    Gas-Ferrer, A

    C. Gas-Ferrer, A. Rubio-Abadal, S. Buob, L. Bezzo, J. H¨ oschele, and L. Tarruell, Spin-resolved mi- croscopy of 87sr su(n) fermi-hubbard systems (2026), arXiv:2603.05478 [cond-mat.quant-gas]

    work page arXiv 2026

  45. [45]

    Ibarra-Garc´ ıa-Padilla and S

    E. Ibarra-Garc´ ıa-Padilla and S. Choudhury, Many-body physics of ultracold alkaline-earth atoms with SU(N)- 22 symmetric interactions, J. Phys.: Condens. Matter37, 083003 (2024)

    work page 2024

  46. [46]

    Mukherjee, J

    B. Mukherjee, J. M. Hutson, and K. R. A. Hazzard, SU(N) magnetism with ultracold molecules, New J. Phys. 27, 013013 (2025)

    work page 2025

  47. [47]

    Goban, R

    A. Goban, R. Hutson, G. Marti, S. Campbell, M. Perlin, P. Julienne, J. D’incao, A. Rey, and J. Ye, Emergence of multi-body interactions in a fermionic lattice clock, Nature563, 369 (2018)

    work page 2018

  48. [48]

    B. Song, Y. Yan, C. He, Z. Ren, Q. Zhou, and G.-B. Jo, Evidence for bosonization in a three-dimensional gas of su (n) fermions, Phys. Rev. X10, 041053 (2020)

    work page 2020

  49. [49]

    S. Taie, E. Ibarra-Garc´ ıa-Padilla, N. Nishizawa, Y. Takasu, Y. Kuno, H.-T. Wei, R. T. Scalettar, K. R. Hazzard, and Y. Takahashi, Observation of antiferromag- netic correlations in an ultracold su (n) hubbard model, Nat. Phys.18, 1356 (2022)

    work page 2022

  50. [50]

    D. Tusi, L. Franchi, L. F. Livi, K. Baumann, D. Bene- dicto Orenes, L. Del Re, R. E. Barfknecht, T.-W. Zhou, M. Inguscio, G. Cappellini,et al., Flavour-selective lo- calization in interacting lattice fermions, Nat. Phys.18, 1201 (2022)

    work page 2022

  51. [51]

    He, X.-Y

    C. He, X.-Y. Gao, K. K. Pak, Y.-J. Liu, P. Ren, M. Guo, E. Zhao, Y. Yan, and G.-B. Jo, Thermodynamics of spin- imbalanced fermi gases with su (n)-symmetric interac- tion, Phys. Rev. Lett.134, 183406 (2025)

    work page 2025

  52. [52]

    Papanicolaou, Unusual phases in quantum spin-1 sys- tems, Nucl

    N. Papanicolaou, Unusual phases in quantum spin-1 sys- tems, Nucl. Phy. B305, 367 (1988)

    work page 1988

  53. [53]

    Honerkamp and W

    C. Honerkamp and W. Hofstetter, Ultracold fermions and the su (n) hubbard model, Phys. Rev. Lett.92, 170403 (2004)

    work page 2004

  54. [54]

    Xu and C

    C. Xu and C. Wu, Resonating plaquette phases in su (4) heisenberg antiferromagnet, Phys. Rev. B77, 134449 (2008)

    work page 2008

  55. [55]

    A. V. Gorshkov, M. Hermele, V. Gurarie, C. Xu, P. S. Julienne, J. Ye, P. Zoller, E. Demler, M. D. Lukin, and A. Rey, Two-orbital su (n) magnetism with ultracold alkaline-earth atoms, Nat. Phys.6, 289 (2010)

    work page 2010

  56. [56]

    S. R. Manmana, K. R. Hazzard, G. Chen, A. E. Feiguin, and A. M. Rey, Su (n) magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quan- tum correlations, Phys. Rev. A84, 043601 (2011)

    work page 2011

  57. [57]

    Mamaev, T

    M. Mamaev, T. Bilitewski, B. Sundar, and A. M. Rey, Resonant dynamics of strongly interacting su (n) fermionic atoms in a synthetic flux ladder, PRX Quan- tum3, 030328 (2022)

    work page 2022

  58. [58]

    Nataf and F

    P. Nataf and F. Mila, Exact diagonalization of Heisenberg SU(n) models, Phys. Rev. Lett.113, 127204 (2014)

    work page 2014

  59. [59]

    S. Xu, J. T. Barreiro, Y. Wang, and C. Wu, Interaction effects with varying n in su (n) symmetric fermion lattice systems, Phys. Rev. Lett.121, 167205 (2018)

    work page 2018

  60. [60]

    Yamamoto, C

    D. Yamamoto, C. Suzuki, G. Marmorini, S. Okazaki, and N. Furukawa, Quantum and thermal phase transitions of the triangular su(3) Heisenberg model under magnetic fields, Phys. Rev. Lett.125, 057204 (2020)

    work page 2020

  61. [61]

    Botzung and P

    T. Botzung and P. Nataf, Exact diagonalization of su (n) fermi-hubbard models, Phys. Rev. Lett.132, 153001 (2024)

    work page 2024

  62. [62]

    Botzung and P

    T. Botzung and P. Nataf, Numerical observation of su (n) nagaoka ferromagnetism, Phys. Rev. B109, 235131 (2024)

    work page 2024

  63. [63]

    Zhang, Q

    Z. Zhang, Q. Zheng, E. Ibarra-Garc´ ıa-Padilla, R. T. Scalettar, and K. R. Hazzard, Unit-density su (3) fermi- hubbard model with spin-flavor imbalance, Phys. Rev. A 112, 033313 (2025)

    work page 2025

  64. [64]

    Affleck, T

    I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Rig- orous results on valence-bond ground states in antiferro- magnets, Phys. Rev. Lett.59, 799 (1987)

    work page 1987

  65. [65]

    L¨ auchli, F

    A. L¨ auchli, F. Mila, and K. Penc, Quadrupolar phases of thes= 1 bilinear-biquadratic Heisenberg model on the triangular lattice, Phys. Rev. Lett.97, 087205 (2006)

    work page 2006

  66. [66]

    Pires, Ferroquadrupolar phase of thes= 1 bilin- ear–biquadratic Heisenberg model on the square lattice, J

    A. Pires, Ferroquadrupolar phase of thes= 1 bilin- ear–biquadratic Heisenberg model on the square lattice, J. Magn. Magn. Mater.370, 106 (2014)

    work page 2014

  67. [67]

    Yu and Q

    R. Yu and Q. Si, Antiferroquadrupolar and Ising-nematic orders of a frustrated bilinear-biquadratic Heisenberg model and implications for the magnetism of FeSe, Phys. Rev. Lett.115, 116401 (2015)

    work page 2015

  68. [68]

    C. Luo, T. Datta, and D.-X. Yao, Spin and quadrupolar orders in the spin-1 bilinear-biquadratic model for iron- based superconductors, Phys. Rev. B93, 235148 (2016)

    work page 2016

  69. [69]

    Lai, W.-J

    H.-H. Lai, W.-J. Hu, E. M. Nica, R. Yu, and Q. Si, Anti- ferroquadrupolar order and rotational symmetry break- ing in a generalized bilinear-biquadratic model on a square lattice, Phys. Rev. Lett.118, 176401 (2017)

    work page 2017

  70. [70]

    A. M. Tsvelik, Field-theory treatment of the Heisenberg spin-1 chain, Phys. Rev. B42, 10499 (1990)

    work page 1990

  71. [71]

    B. Ye, F. Machado, J. Kemp, R. B. Hutson, and N. Y. Yao, Universal Kardar-Parisi-Zhang dynamics in inte- grable quantum systems, Phys. Rev. Lett.129, 230602 (2022)

    work page 2022

  72. [73]

    Sasaki and T

    R. Sasaki and T. Ruijgrok, An integrable SU(3) spin chain, Phys. A: Stat. Mech. Appl.113, 388 (1982)

    work page 1982

  73. [74]

    De Chiara, S

    G. De Chiara, S. Montangero, P. Calabrese, and R. Fazio, Entanglement entropy dynamics of Heisenberg chains, J. Stat. Mech.: Theory Exp.2006(03), P03001

    work page 2006

  74. [75]

    H. K. Park and S. Lee, Proof of nonintegrability of the spin-1 bilinear-biquadratic chain model, Phys. Rev. B 111, 134444 (2025)

    work page 2025

  75. [76]

    Rigol, V

    M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Re- laxation in a completely integrable many-body quantum system: An ab initio study of the dynamics of the highly excited states of 1d lattice hard-core bosons, Phys. Rev. Lett.98, 050405 (2007)

    work page 2007

  76. [77]

    J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A43, 2046 (1991)

    work page 2046

  77. [78]

    Penc and A

    K. Penc and A. M. L¨ auchli, Spin Nematic Phases in Quantum Spin Systems, inIntroduction to Frustrated Magnetism: Materials, Experiments, Theory, Vol. 164, edited by C. Lacroix, P. Mendels, and F. Mila (Springer, Berlin, 2011) p. 331

    work page 2011

  78. [79]

    T. A. T´ oth,Quadrupolar Ordering in Two-Dimensional Spin-One Systems, Ph.D. thesis, EPFL (2011)

    work page 2011

  79. [80]

    Misguich, K

    G. Misguich, K. Mallick, and P. L. Krapivsky, Dynamics of the spin- 1 2 Heisenberg chain initialized in a domain- wall state, Phys. Rev. B96, 195151 (2017)

    work page 2017

  80. [81]

    Pozsgay, The generalized Gibbs ensemble for Heisen- berg spin chains, J

    B. Pozsgay, The generalized Gibbs ensemble for Heisen- berg spin chains, J. Stat. Mech.: Theory Exp.2013(07), P07003

    work page 2013

Showing first 80 references.