Geometry of quantum states and chaos-integrability transition

• URL: http://arxiv.org/abs/2507.13067v1
• Date: Thu, 17 Jul 2025 12:33:15 GMT
• Title: Geometry of quantum states and chaos-integrability transition
• Authors: Ankit Gill, Keun-Young Kim, Kunal Pal, Kuntal Pal,
• Abstract summary: We consider the geometry of quantum states associated with classes of random matrix Hamiltonians.<n>In particular, we consider ensembles that show integrability to chaotic transition in terms of the nearest neighbour energy level spacing distribution.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the geometry of quantum states associated with classes of random matrix Hamiltonians, in particular ensembles that show integrability to chaotic transition in terms of the nearest neighbour energy level spacing distribution. In the case that the total Hamiltonian contains a single parameter, the distance between two states is captured by the fidelity susceptibility, whereas, when the total Hamiltonian contains multiple parameters, this distance is given by the quantum metric tensor. Since the fieldity susceptibility is closely related to the two-point correlation function, we first calculate the relevant correlation functions of a random matrix belonging to the Gaussian unitary ensemble in terms of the spectral form factor of the total Hamiltonian, show how to obtain the fidelity susceptibility from this correlation function, and explain the role played by energy level correlation. Next, by performing suitable coordinate transformations, we solve the geodesic equations corresponding to the quantum metric tensor obtained from an integrability-breaking random matrix Hamiltonian and obtain the geodesic distance between two points on the parameter manifold to show that any point far away from the integrable phase can be reached by a finite value of this distance. Finally, we obtain and discuss different properties of the fidelity susceptibility associated with Hamiltonians belonging to another random matrix ensemble which shows integrability to chaos transition, namely the Gaussian $\beta$-ensembles with general values of the Dyson index $\beta$, and show that the fidelity susceptibility shares generic features with the first class of Hamiltonians.

Related papers

• 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)
• On the Bisognano-Wichmann entanglement Hamiltonian of nonrelativistic fermions [0.0]
  We study the ground-state entanglement Hamiltonian of free nonrelativistic fermions for semi-infinite domains in one dimension. We prove that the Bisognano-Wichmann form of the entanglement Hamiltonian becomes exact.
  arXiv  Detail & Related papers  (2024-10-21T18:55:23Z)
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos [44.99833362998488]
  We develop an analytical approach to the spectral form factor and out-of-time ordered correlators in zero-dimensional Brownian models of quantum chaos.
  arXiv  Detail & Related papers  (2024-10-21T10:56:49Z)
• Exploring entanglement in finite-size quantum systems with degenerate ground state [0.0]
  We develop an approach for characterizing non-local quantum correlations in spin systems with exactly or nearly degenerate ground states.<n> Estimating the von Neumann entropy of the random wave functions helps to reveal previously unknown features of the quantum correlations in the phases with degeneracy of the ground state.<n>Digital quantum simulations performed with quantum computers can provide accurate description of the entanglement of the degenerate systems even in the presence of noise.
  arXiv  Detail & Related papers  (2024-10-01T08:56:34Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Coherence generation with Hamiltonians [44.99833362998488]
  We explore methods to generate quantum coherence through unitary evolutions. This quantity is defined as the maximum derivative of coherence that can be achieved by a Hamiltonian. We identify the quantum states that lead to the largest coherence derivative induced by the Hamiltonian.
  arXiv  Detail & Related papers  (2024-02-27T15:06:40Z)
• Characterization of partially accessible anisotropic spin chains in the presence of anti-symmetric exchange [0.0]
  We address quantum characterization of anisotropic spin chains in the presence of antisymmetric exchange. We investigate whether the Hamiltonian parameters of the chain may be estimated with precision approaching the ultimate limit imposed by quantum mechanics.
  arXiv  Detail & Related papers  (2024-01-25T19:26:35Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Multiple ground-state instabilities in the anisotropic quantum Rabi model [0.0]
  We study the anisotropic variant of the quantum Rabi model with different coupling strengths of the rotating and counter-rotating wave terms. The anisotropy preserves the parity symmetry of the original model. We find analytically that the ground-state and the first excited state can cross several times.
  arXiv  Detail & Related papers  (2021-01-29T04:21:08Z)
• Isospectral twirling and quantum chaos [0.0]
  We show that the most important measures of quantum chaos like frame potentials, scrambling, Loschmidt echo, and out-of-time correlators (OTOCs) can be described by the unified framework of the isospectral twirling. We show that, by exploiting random matrix theory, these measures of quantum chaos clearly distinguish the finite time profiles of probes to quantum chaos.
  arXiv  Detail & Related papers  (2020-11-11T19:01:08Z)
• Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
  We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
  arXiv  Detail & Related papers  (2020-11-06T19:00:07Z)
• Variational-Correlations Approach to Quantum Many-body Problems [1.9336815376402714]
  We investigate an approach for studying the ground state of a quantum many-body Hamiltonian. The challenge set by the exponentially-large Hilbert space is circumvented by approximating the positivity of the density matrix. We demonstrate the ability of this approach to produce long-range correlations, and a ground-state energy that converges to the exact result.
  arXiv  Detail & Related papers  (2020-01-17T19:52:54Z)

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.