Group word dynamics from local random matrix Hamiltonians and beyond

• URL: http://arxiv.org/abs/2510.23716v1
• Date: Mon, 27 Oct 2025 18:00:06 GMT
• Title: Group word dynamics from local random matrix Hamiltonians and beyond
• Authors: Klée Pollock, Jonathan D. Kroth, Jonathon Riddell, Thomas Iadecola,
• Abstract summary: We study one dimensional quantum spin chains whose nearest neighbor interactions are random matrices that square to one.<n>We establish a mapping from the many-body quantum dynamics of energy density in the original chain to a single-particle hopping dynamics when the local Hilbert space dimension is large.<n>Our results put into contact ideas in free probability theory, quantum mechanics of hyperbolic lattices, and the physics of both generic and integrable Hamiltonian dynamics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study one dimensional quantum spin chains whose nearest neighbor interactions are random matrices that square to one. By employing free probability theory, we establish a mapping from the many-body quantum dynamics of energy density in the original chain to a single-particle hopping dynamics when the local Hilbert space dimension is large. The hopping occurs on the Cayley graph of an infinite Coxeter reflection group. Adjacency matrices on large finite clusters of this Cayley graph can be constructed numerically by leveraging the automatic structure of the group. The density of states and two-point functions of the local energy density are approximately computed and consistent with the physics of a generic local Hamiltonian: Gaussian density of states and thermalization of energy density. We then ask what happens to the physics if we modify the group on which the hopping dynamics occurs, and conjecture that adding braid relations into the group leads to integrability. Our results put into contact ideas in free probability theory, quantum mechanics of hyperbolic lattices, and the physics of both generic and integrable Hamiltonian dynamics.

Related papers

• The Converse Madelung Question [0.0]
  We work with minimal, physically motivated axioms on density and phase.<n>Within the resulting class of first order local Hamiltonian field theories, these axioms single out the canonical Poisson bracket on density and phase.<n> quantum mechanics emerges as a reversible fixed point of Fisher regularised information hydrodynamics.
  arXiv  Detail & Related papers  (2025-11-05T15:33:46Z)
• Average-case quantum complexity from glassiness [45.57609001239456]
  Glassiness -- a phenomenon in physics characterized by a rough free-energy landscape -- implies hardness for stable classical algorithms.<n>We prove that the standard notion of quantum glassiness based on replica symmetry breaking obstructs stable quantum algorithms for Gibbs sampling.
  arXiv  Detail & Related papers  (2025-10-09T17:37:33Z)
• A Quantum Approach to the Continuum Heisenberg Spin-Chain Model: Position-Dependent Mass Formalism and Pre-canonical Quantization [0.0]
  We study the equivalence of the Hamiltonian density to the nonlinear sigma model.<n>The resulting Schr"odinger-like equation was found to take the form of a confluent Heun equation.<n>This analysis provides a comprehensive quantum description of the system.
  arXiv  Detail & Related papers  (2025-06-25T04:43:39Z)
• Weak coupling limit for quantum systems with unbounded weakly commuting system operators [50.24983453990065]
  This work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a reservoir formed by Fermi or Bose particles.<n>We derive in the weak coupling limit the reservoir statistics, which is determined by whose terms in the multi-point correlation functions of the reservoir are non-zero in the WCL.<n>We prove that the resulting reduced system dynamics converges to unitary dynamics with a modified Hamiltonian which can be interpreted as a Lamb shift to the original Hamiltonian.
  arXiv  Detail & Related papers  (2025-05-13T05:32:34Z)
• Energy dynamics in a class of local random matrix Hamiltonians [0.0]
  We study the transport of the energy in few-body and 1D chains of nearest-neighbor random matrix terms that square to one.<n>In the few-body but large local Hilbert space dimension case, we develop a mapping for the energy dynamics to a single-particle hopping picture.<n>In the 1D chain, we numerically study the energy transport for a small local Hilbert space dimension.
  arXiv  Detail & Related papers  (2025-02-07T16:09:40Z)
• Observation of string breaking on a (2 + 1)D Rydberg quantum simulator [59.63568901264298]
  We report the observation of string breaking in synthetic quantum matter using a programmable quantum simulator. Our work paves a way to explore phenomena in high-energy physics using programmable quantum simulators.
  arXiv  Detail & Related papers  (2024-10-21T22:33:16Z)
• A non-hermitean momentum operator for the particle in a box [49.1574468325115]
  We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example. The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
  arXiv  Detail & Related papers  (2024-03-20T12:51:58Z)
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension [44.41126861546141]
  We provide a classification of Lie algebras generated by translation-invariant 2-local spin chain Hamiltonians. We consider chains with open and periodic boundary conditions and find 17 unique dynamical Lie algebras. In addition to the closed and open spin chains, we consider systems with a fully connected topology, which may be relevant for quantum machine learning approaches.
  arXiv  Detail & Related papers  (2023-09-11T17:59:41Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Quasienergy operators and generalized squeezed states for systems of trapped ions [0.0]
  Quantum stability is characterized by a discrete quasienergy spectrum, while quasienergy states are symplectic coherent states. We introduce the generators of the Lie algebra of the symplectic group $cal SL(2, mathbb R)$, which we use to build the coherent states associated to the system under investigation.
  arXiv  Detail & Related papers  (2021-08-26T07:48:09Z)
• Random Matrix Theory of the Isospectral twirling [0.0]
  We compute the Isospectral twirling of several classes of important quantities in the analysis of quantum many-body systems. We show how these quantities clearly separate chaotic quantum dynamics from non chaotic ones.
  arXiv  Detail & Related papers  (2020-12-14T16:29:15Z)
• Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
  Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. Operators of the form $hatcal H=hatA+ihatB$ are described. Rigorous analytical analysis is performed for both wave and Green's functions.
  arXiv  Detail & Related papers  (2020-10-13T15:50:49Z)

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.