Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction

• URL: http://arxiv.org/abs/2501.15506v1
• Date: Sun, 26 Jan 2025 12:48:19 GMT
• Title: Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
• Authors: Naoto Shiraishi,
• Abstract summary: We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction. We classify the integrability and non-integrability of the above class of spin systems.
• Score: 0.0
• License:
• Abstract: We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction, also known as zigzag spin chains. We completely classify the integrability and non-integrability of the above class of spin systems. We prove that in this class there are only two integrable models, a classical model and a model solvable by the Bethe ansatz, and all the remaining systems are non-integrable. Our classification theorem confirms that within this class of spin chains, there is no missing integrable model. This theorem also implies the absence of intermediate models with a finite number of local conserved quantities.

Related papers

• Proof of the absence of local conserved quantities in the spin-1 bilinear-biquadratic chain and its anisotropic extensions [0.0]
  We provide a complete classification of the integrability and nonintegrability of the spin-1 bilinear-biquadratic model with a uniaxial anisotropic field. It is rigorously shown that all systems, except for the known integrable systems, are nonintegrable.
  arXiv  Detail & Related papers  (2024-11-07T18:22:58Z)
• Proof of the absence of local conserved quantities in general spin-1/2 chains with symmetric nearest-neighbor interaction [0.0]
  We provide a rigorous proof of the absence of nontrivial local conserved quantities in all spin-1/2 chains with symmetric nearest-neighbor interaction, except for known integrable systems. Our finding also implies that there is no intermediate systems with a finite number of nontrivial local conserved quantities.
  arXiv  Detail & Related papers  (2024-11-04T15:22:17Z)
• Complete Classification of Integrability and Non-integrability for Spin-1/2 Chain with Symmetric Nearest-Neighbor Interaction [0.0]
  General spin-1/2 chains with symmetric nearest-neighbor interaction are studied. We rigorously prove that all spin models in this class, except for known integrable systems, are non-integrable.
  arXiv  Detail & Related papers  (2024-11-04T15:22:14Z)
• Entanglement of Disjoint Intervals in Dual-Unitary Circuits: Exact Results [49.1574468325115]
  The growth of the entanglement between a disjoint subsystem and its complement after a quantum quench is regarded as a dynamical chaos indicator. We show that for almost all dual unitary circuits the entanglement dynamics agrees with what is expected for chaotic systems. Despite having many conserved charges, charge-conserving dual-unitary circuits are in general not Yang-Baxter integrable.
  arXiv  Detail & Related papers  (2024-08-29T17:45:27Z)
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
  We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
  arXiv  Detail & Related papers  (2024-05-27T16:11:39Z)
• Superdiffusion from nonabelian symmetries in nearly integrable systems [0.0]
  Heisenberg spin chain is a canonical integrable model. Spin transport is sub-ballistic at any nonzero temperature. Two-mode hydrodynamic description captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics.
  arXiv  Detail & Related papers  (2023-05-24T18:00:00Z)
• Slow relaxation of out-of-time-ordered correlators in interacting integrable and nonintegrable spin-1/2 XYZ chains [0.0]
  Out-of-time ordered correlators (OTOCs) help characterize the scrambling of quantum information. We compare the relaxation dynamics of OTOCs in interacting integrable and nonintegrable spin-1/2 XYZ chains in regimes without a classical counterpart. We show that the relaxation of the OTOCs is slow (fast) when there is (there is not) an overlap, independently of whether the chain is integrable or nonintegrable.
  arXiv  Detail & Related papers  (2022-11-14T02:41:08Z)
• Quantum Mechanics as a Theory of Incompatible Symmetries [77.34726150561087]
  We show how classical probability theory can be extended to include any system with incompatible variables. We show that any probabilistic system (classical or quantal) that possesses incompatible variables will show not only uncertainty, but also interference in its probability patterns.
  arXiv  Detail & Related papers  (2022-05-31T16:04:59Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Metrizing Weak Convergence with Maximum Mean Discrepancies [88.54422104669078]
  This paper characterizes the maximum mean discrepancies (MMD) that metrize the weak convergence of probability measures for a wide class of kernels. We prove that, on a locally compact, non-compact, Hausdorff space, the MMD of a bounded continuous Borel measurable kernel k, metrizes the weak convergence of probability measures if and only if k is continuous.
  arXiv  Detail & Related papers  (2020-06-16T15:49:33Z)

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.