Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study

• URL: http://arxiv.org/abs/2511.00950v2
• Date: Tue, 04 Nov 2025 08:27:20 GMT
• Title: Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study
• Authors: Siyi Yang, Yi-Ming Ding, Zheng Yan,
• Abstract summary: The entanglement Hamiltonian (EH) encapsulates the essential entanglement properties of a quantum many-body system.<n>While the Bisognano-Wichmann theorem gives an exact EH form for Lorentz-invariant field theories, its validity on lattice systems is limited.<n>We propose a general scheme based on the lattice-Bisognano-Wichmann (LBW) ansatz and multi-replica-trick quantum Monte Carlo methods.
• Score: 6.651114683578705
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The entanglement Hamiltonian (EH) encapsulates the essential entanglement properties of a quantum many-body system and serves as a powerful theoretical construct. From the EH, one can extract a variety of entanglement quantities, such as entanglement entropies, negativity, and the entanglement spectrum. However, its general analytical form remains largely unknown. While the Bisognano-Wichmann theorem gives an exact EH form for Lorentz-invariant field theories, its validity on lattice systems is limited, especially when Lorentz invariance is absent. In this work, we propose a general scheme based on the lattice-Bisognano-Wichmann (LBW) ansatz and multi-replica-trick quantum Monte Carlo methods to numerically reconstruct the entanglement Hamiltonian in two-dimensional systems and systematically explore its applicability to systems without translational invariance, going beyond the original scope of the primordial Bisognano-Wichmann theorem. Various quantum phases--including gapped and gapless phases, critical points, and phases with either discrete or continuous symmetry breaking--are investigated, demonstrating the versatility of our method in reconstructing entanglement Hamiltonians. Furthermore, we find that when the entanglement boundary of a system is ordinary (i.e., free from surface anomalies), the LBW ansatz provides an accurate approximation well beyond Lorentz-invariant cases. Our work thus establishes a general framework for investigating the analytical structure of entanglement in complex quantum many-body systems.

Related papers

• Path integral approach to quantum thermalization [39.25860941747971]
  We introduce a quasiclassical Green function approach describing the unitary yet irreversible dynamics of quantum systems.<n>We show that it is capable of describing a wide range of system classes and disorder models.<n>We present our formalism in a self-contained and pedagogical manner, aiming to provide a transferable toolbox for the first-principles description of many-body chaotic quantum systems.
  arXiv  Detail & Related papers  (2025-09-07T12:10:48Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders [0.0]
  We analytically investigate the entanglement Hamiltonian and entanglement energy spectrum of a non-Hermitian spin ladder. Our findings provide new insights into quantum entanglement in non-Hermitian systems.
  arXiv  Detail & Related papers  (2024-09-25T16:20:24Z)
• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders [9.617349193925188]
  Entanglement constitutes one of the key concepts in quantum mechanics and serves as an indispensable tool in the understanding of quantum many-body systems. We perform extensive numerical investigations of extensive entanglement properties of coupled quantum spin chains.
  arXiv  Detail & Related papers  (2023-11-03T04:06:20Z)
• Realizing the entanglement Hamiltonian of a topological quantum Hall system [10.092164351939825]
  Topological quantum many-body systems, such as Hall insulators, are characterized by a hidden order encoded in the entanglement between their constituents. Entanglement entropy, an experimentally accessible single number that globally quantifies entanglement, has been proposed as a first signature of topological order. We use a synthetic dimension, encoded in the electronic spin of dysprosium atoms, to implement spatially deformed Hall systems.
  arXiv  Detail & Related papers  (2023-07-12T15:40:06Z)
• Renormalized von Neumann entropy with application to entanglement in genuine infinite dimensional systems [0.0]
  Von Neumann quantum entropy is finite and continuous in general, infinite dimensional case. The renormalized quantum entropy is defined by the explicit use of the Fredholm determinants theory. Several features of majorization theory are preserved under then introduced renormalization as it is proved in this paper.
  arXiv  Detail & Related papers  (2022-11-10T12:56:07Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)

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.