Quantum Monte Carlo Study Reconstructs Entanglement Hamiltonian on Lattices, Exploring Limits of the Bisognano-Wichmann Form

Entanglement, a fundamental property of quantum systems, profoundly influences the behaviour of many-body systems and remains a central focus of modern physics. Siyi Yang, Yi-Ming Ding, and Zheng Yan, from Fudan University and Westlake University, investigate the limits of a theoretical framework known as the Lattice-Bisognano-Wichmann form, which describes the entanglement Hamiltonian, a key construct for understanding entanglement. The team develops a novel computational approach, combining a theoretical scheme with advanced Monte Carlo methods, to numerically reconstruct this Hamiltonian in two dimensions and systematically assess its validity even when translational symmetry is absent. This work demonstrates the versatility of their method across diverse physical phases and establishes a general framework for exploring the analytical structure of entanglement in complex quantum systems, revealing that the Lattice-Bisognano-Wichmann form accurately approximates entanglement boundaries free from surface anomalies, extending its applicability beyond traditional, symmetrical scenarios.

Entanglement Entropy Reveals Quantum Phase Transitions

This research investigates entanglement entropy, a measure of quantum entanglement, and its application to understanding quantum phase transitions and critical phenomena in materials. Scientists explore how entanglement entropy can characterize different phases of matter and the points where these phases change, employing large-scale numerical simulations, including Monte Carlo and Density Matrix Renormalization Group methods. The study focuses on Rényi entropy, a versatile tool for both theoretical analysis and numerical calculations. A key challenge lies in accurately calculating entanglement entropy in complex materials, which this work addresses by refining existing computational methods.

Results demonstrate that entanglement entropy exhibits universal behavior near critical points, meaning systems with similar properties will display comparable scaling patterns, allowing scientists to extract accurate critical exponents from simulations. The study establishes connections between entanglement entropy and Conformal Field Theory, validating theoretical predictions. Researchers also explore how entanglement entropy can detect and characterize topological order, a unique form of quantum order. The accuracy of the Stochastic Variational Quantum Monte Carlo method is demonstrated in systems with strong interactions, applied to diverse model systems including the Quantum Ising Model, Heisenberg Model, Fermi-Hubbard Model, and exotic spin liquids. This work advances our understanding of quantum phase transitions and provides a powerful tool for characterizing materials.

Entanglement Hamiltonian Reconstruction via Multi-Replica Monte Carlo

Scientists have developed a new method for numerically reconstructing the entanglement Hamiltonian in two-dimensional systems, utilizing the lattice-Bisognano-Wichmann (LBW) ansatz combined with multi-replica quantum Monte Carlo methods. This innovative approach investigates systems lacking translational invariance, extending beyond traditional Bisognano-Wichmann theorems and allowing researchers to explore the analytical structure of entanglement in complex quantum materials without prior knowledge of the system’s specific form. The team employs the multi-replica trick, a computational technique that simulates an ensemble of entanglement Hamiltonians at various temperatures, circumventing the need to predefine the Hamiltonian’s structure. By simulating an ensemble of Hamiltonians, scientists probe the entanglement structure across a range of energy scales and accurately determine unknown parameters within the LBW ansatz, rigorously evaluating its accuracy even in systems lacking Lorentz invariance. This establishes a general framework for investigating entanglement in complex quantum systems, offering a powerful tool for characterizing quantum many-body phenomena.

Entanglement Hamiltonian Reconstruction Beyond Lorentz Invariance

This work establishes a general framework for reconstructing the entanglement Hamiltonian in two-dimensional systems, extending beyond the traditional scope of the Bisognano-Wichmann theorem. Researchers developed a numerical scheme, based on a lattice-Bisognano-Wichmann ansatz combined with Monte Carlo methods, to map the essential entanglement properties of complex systems, accurately reconstructing entanglement Hamiltonians even when translational invariance is absent. The team demonstrated that when the boundary between entangled regions is well-behaved, the lattice-Bisognano-Wichmann ansatz provides a reliable approximation, even in scenarios lacking Lorentz invariance, allowing for detailed investigation of the analytical structure of entanglement in complex systems. While the current study focuses on two-dimensional systems, the authors acknowledge that extending the method to higher dimensions presents a significant challenge for future research.