Exploring Variational Entanglement Hamiltonians

TL;DR

This paper investigates the convergence and accuracy of variational methods for entanglement Hamiltonians in quantum systems, introducing improved algorithms and diagnostics for phase transitions and topological phases.

Contribution

It introduces a quadrature-based approach to reduce measurement costs and a modified ansatz to better capture deviations from theoretical models in lattice systems.

Findings

Quadrature schemes significantly reduce measurement requirements.

Modified ansatz improves convergence and detects phase transitions.

Low cost values reliably reproduce spectral features relevant to topological phases.

Abstract

Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally obtained solutions and compare them to numerically exact calculations in quantum critical systems. We demonstrate that interpreting the cost functional as an integral permits the deployment of iterative quadrature schemes, thereby reducing the required number of measurements by several orders of magnitude. We further show that a modified ansatz captures deviations from the Bisognano-Wichmann form in lattice models, improves convergence, and provides a cost-function-level diagnostic for quantum phase transitions. Finally, we establish that a low cost value does not by itself guarantee convergence in trace distance. Nevertheless, it faithfully reproduces degeneracies and spectral gaps, which are essential for applications to topological phases.