The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities

• URL: http://arxiv.org/abs/2412.18504v4
• Date: Sun, 09 Mar 2025 06:17:20 GMT
• Title: The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities
• Authors: Naoto Shiraishi, Hal Tasaki,
• Abstract summary: We prove that the model possesses no local conserved quantities except for the trivial ones, such as the Hamiltonian.<n>This result strongly suggests that the model is non-integrable.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the $S=\frac{1}{2}$ quantum spin system on the $d$-dimensional hypercubic lattice with $d\ge2$ with uniform nearest-neighbor interaction of the XY or XYZ type and arbitrary uniform magnetic field. By extending the method recently developed for quantum spin chains, we prove that the model possesses no local conserved quantities except for the trivial ones, such as the Hamiltonian. This result strongly suggests that the model is non-integrable. We note that our result applies to the XX model without a magnetic field, which is one of the easiest solvable models in one dimension.

Related papers

• Large N vector models in the Hamiltonian framework [0.0]
  We first present the method in the simpler setting of a quantum mechanical system with quartic interactions. We then apply these techniques to the $O(N)$ model in $2+1$ and $3+1$ dimensions. We recover various known results, such as the gap equation determining the ground state of the system.
  arXiv  Detail & Related papers  (2025-02-12T00:18:02Z)
• 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)
• Measurement-induced Lévy flights of quantum information [38.68022950138448]
  We explore a model of free fermions in one dimension subject to frustrated local measurements across adjacent sites. For maximal misalignment, superdiffusive behavior emerges from the vanishing of the measurement-induced quasiparticle decay rate. Our findings show how intricate fractal-scaling entanglement can be produced for local Hamiltonians.
  arXiv  Detail & Related papers  (2025-01-22T14:29:13Z)
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids [48.225436651971805]
  We employ the $mathrmSU(n)_k$ Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions.<n>The spins on all lattice sites are chosen to transform under the $mathrmSU(n)$ irreducible representation with a single row and $k$ boxes in the Young tableau.
  arXiv  Detail & Related papers  (2025-01-16T14:42:00Z)
• Gapped and gapless quantum spin liquids on the ruby lattice [0.0]
  We present a total of 50 U$bbZ(1) and 182 distinct states of ruby spin on mean-consistent structures. We also obtain a total of 64 anti-respecting space-group theories of spin on mean-consistent structures.
  arXiv  Detail & Related papers  (2024-09-24T18:00:00Z)
• Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
  We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions. We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
  arXiv  Detail & Related papers  (2024-07-09T14:04:11Z)
• Integrability and dark states of the XX spin-1 central spin model in a transverse field [44.99833362998488]
  The XX central spin model is integrable in the presence of a magnetic field oriented to the XY plane in which the coupling exists. In the spin-1/2 case, it was also shown, through an appropriate limit of the non-skew symmetric XXZ Richardson-Gaudin models, that it remained integrable even when the magnetic field is tilted to contain an in-plane component.
  arXiv  Detail & Related papers  (2024-07-03T11:47:22Z)
• 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)
• Dynamics of spin helices in the diluted one-dimensional $XX$ model [0.0]
  Motivated by discrepancies between recent cold atom experiments and the associated theory, we explore the effect of immobile holes on the quantum dynamics of $x$-$z$ spin helices. We calculate the exact spin dynamics by mapping onto a system of non-interacting fermions, averaging over the distribution of holes.
  arXiv  Detail & Related papers  (2024-04-26T17:36:27Z)
• On the Magnetization of the $120^\circ$ order of the Spin-1/2 Triangular Lattice Heisenberg Model: a DMRG revisit [0.552480439325792]
  We revisit the issue about the magnetization of the $120circ$ order in the spin-1/2 triangular lattice Heisenberg model (TLHM) with Density Matrix Renormalization Group (DMRG) The accurate determination of the magnetization of this model is challenging for numerical methods and its value exhibits substantial disparities across various methods.
  arXiv  Detail & Related papers  (2023-10-18T08:08:06Z)
• Cellular automata in $d$ dimensions and ground states of spin models in $(d+1)$ dimensions [0.0]
  We show how the trajectories of $d$-dimensional cellular automata (CA) can be used to determine the ground states of $(d+1)$-dimensional classical spin models.
  arXiv  Detail & Related papers  (2023-09-14T23:03:14Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions [0.0]
  An $n$-simplex represents the simplest possible polytope in $n$ dimensions. We show that $n$-simplex lattices can be constructed from the high-order field-moments space of quadratic bosonic systems.
  arXiv  Detail & Related papers  (2022-06-29T17:24:04Z)
• Mapping the charge-dyon system into the position-dependent effective mass background via Pauli equation [77.34726150561087]
  This work aims to reproduce a quantum system composed of a charged spin - $1/2$ fermion interacting with a dyon with an opposite electrical charge.
  arXiv  Detail & Related papers  (2020-11-01T14:38:34Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.