Proof of the absence of nontrivial local conserved quantities in the spin-1 bilinear-biquadratic chain and its anisotropic extensions

• URL: http://arxiv.org/abs/2411.04945v3
• Date: Wed, 29 Oct 2025 07:02:18 GMT
• Title: Proof of the absence of nontrivial local conserved quantities in the spin-1 bilinear-biquadratic chain and its anisotropic extensions
• Authors: Akihiro Hokkyo, Mizuki Yamaguchi, Yuuya Chiba,
• Abstract summary: We provide a complete classification of the integrability and nonintegrability of the spin-1 bilinear-biquadratic model with a uniaxial anisotropic field.<n>It is rigorously shown that, within this class, the only integrable systems are those that have been solved by the Bethe ansatz method.<n>We extend the proof of nonintegrability to more general spin-1 models that encompass anisotropic extensions of the bilinear-biquadratic Hamiltonian.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We provide a complete classification of the integrability and nonintegrability of the spin-1 bilinear-biquadratic model with a uniaxial anisotropic field, which includes the Heisenberg model and the Affleck-Kennedy-Lieb-Tasaki model. It is rigorously shown that, within this class, the only integrable systems are those that have been solved by the Bethe ansatz method, and that all other systems are nonintegrable, in the sense that they do not have nontrivial local conserved quantities. Here, "nontrivial" excludes quantities like the Hamiltonian or the total magnetization, and "local" refers to sums of operators that act only on sites within a finite distance. This result establishes the nonintegrability of the Affleck-Kennedy-Lieb-Tasaki model and, consequently, demonstrates that the quantum many-body scars observed in this model emerge independently of any conservation laws of local quantities. Furthermore, we extend the proof of nonintegrability to more general spin-1 models that encompass anisotropic extensions of the bilinear-biquadratic Hamiltonian, and completely classify the integrability of generic Hamiltonians that possess translational symmetry, $U(1)$ symmetry, time-reversal symmetry, and spin-flip symmetry. Our result accomplishes a breakthrough in nonintegrability proofs by expanding their scope to spin-1 systems.

Related papers

• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• Rigorous Test for Quantum Integrability and Nonintegrability [0.0]
  We introduce rigorously provable tests for integrability and nonintegrability of quantum spin systems with finite-range interactions. Results significantly simplify existing proofs of nonintegrability. Results also yield the first proof of nonintegrability for models such as the $S=1/2$ Heisenberg chain with a non-uniform magnetic field.
  arXiv  Detail & Related papers  (2025-01-30T14:55:03Z)
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{PT}$ symmetry [49.1574468325115]
  We analyze models governed by the replicator equation of evolutionary game theory and related Lotka-Volterra systems of population dynamics. We study the emergence of exceptional points in two cases: (a) when the governing symmetry properties are tied to global properties of the models, and (b) when these symmetries emerge locally around stationary states.
  arXiv  Detail & Related papers  (2024-11-19T02:15:59Z)
• Asymmetry Amplification by a Nonadiabatic Passage through a Critical Point [0.0]
  We generalize the Hamiltonian dynamics of the Painleve'-2 equation to the case with many degrees of freedom.<n>The evolution eventually leads to a highly asymmetric state, no matter how weak the symmetry breaking parameter of the Hamiltonian is.<n>This suggests a potential mechanism for strong asymmetry in the production of quasi-particles with nearly identical characteristics.
  arXiv  Detail & Related papers  (2024-08-28T16:06:56Z)
• Robustness and eventual slow decay of bound states of interacting microwave photons in the Google Quantum AI experiment [0.0]
  A recent Google Quantum AI experiment demonstrated the persistence of such collective excitations even when the integrability is broken. We study the spectrum of the model realized in the experiment using exact diagonalization and physical arguments. We find that isolated bands corresponding to the descendants of the exact bound states of the integrable model are clearly observable in the spectrum for a large range of system sizes.
  arXiv  Detail & Related papers  (2023-07-20T18:00:30Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Universal features of entanglement entropy in the honeycomb Hubbard model [44.99833362998488]
  This paper introduces a new method to compute the R'enyi entanglement entropy in auxiliary-field quantum Monte Carlo simulations. We demonstrate the efficiency of this method by extracting, for the first time, universal subleading logarithmic terms in a two dimensional model of interacting fermions.
  arXiv  Detail & Related papers  (2022-11-08T15:52:16Z)
• Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals [64.76138964691705]
  We discuss a sufficient condition for gapless excitations in the Lindbladian master equation for collective spin-boson systems. We argue that gapless modes can lead to persistent dynamics in the spin observables with the possible formation of dissipative time-crystals.
  arXiv  Detail & Related papers  (2022-09-26T18:34:59Z)
• Hidden Bethe states in a partially integrable model [4.965221313169878]
  We find integrable excited eigenstates corresponding to the totally anti-symmetric irreducible representation of the permutation operator in the otherwise non-integrable subspaces. We identify the integrable eigenstates that survive in a deformation of the Hamiltonian away from its integrable point.
  arXiv  Detail & Related papers  (2022-05-06T18:00:09Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Simultaneous Transport Evolution for Minimax Equilibria on Measures [48.82838283786807]
  Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling. In this work we focus instead in finding mixed equilibria, and consider the associated lifted problem in the space of probability measures. By adding entropic regularization, our main result establishes global convergence towards the global equilibrium.
  arXiv  Detail & Related papers  (2022-02-14T02:23:16Z)
• Interacting 1D Chiral Fermions with Pairing: Transition from Integrable to Chaotic [0.0]
  We study a generic one-dimensonal quantum model of two flavors (pseudospins) chiral complex fermions by exact diagonalization. We show that the model undergoes a transition from a quantum integrable model to a fully quantum chaotic model.
  arXiv  Detail & Related papers  (2022-02-13T00:32:13Z)
• Entanglement dynamics of thermofield double states in integrable models [0.0]
  We study the entanglement dynamics of thermofield double (TFD) states in integrable spin chains and quantum field theories. We show that, for a natural choice of the Hamiltonian eigenbasis, the TFD evolution may be interpreted as a quantum quench from an initial state. We conjecture a formula for the entanglement dynamics, which is valid for both discrete and continuous integrable field theories.
  arXiv  Detail & Related papers  (2021-12-03T16:40:36Z)
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice [0.0]
  We consider a non-Hermitian Hamiltonian with pseudo-Hermiticity for a system of bosons in a honeycomb lattice. Such a system is capable of acting as a topological amplifier, under time-reversal symmetry. We construct a convenient analytical description for the edge modes of the Haldane model in semi-infinite planes.
  arXiv  Detail & Related papers  (2021-10-07T02:00:12Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Semiclassical simulations predict glassy dynamics for disordered Heisenberg models [0.0]
  We numerically study out-of-equilibrium dynamics in a family of Heisenberg models with $1/r6$ power-law interactions and positional disorder. We find that both quantities display robust glassy behavior for almost any value of the anisotropy parameter of the Heisenberg Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-28T12:26:57Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Long-range level correlations in quantum systems with finite Hilbert space dimension [0.0]
  We study the spectral statistics of quantum systems with finite Hilbert spaces. We derive a theorem showing that eigenlevels in such systems cannot be globally uncorrelated.
  arXiv  Detail & Related papers  (2020-10-13T15:49:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.