Reconstructing Entanglement Hamiltonian via Entanglement Eigenstates

TL;DR

This paper introduces a numerical method to reconstruct the entanglement Hamiltonian from a single eigenstate of the reduced density matrix, providing insights into quantum entanglement in many-body systems.

Contribution

It presents a novel scheme for explicitly reconstructing the entanglement Hamiltonian using entangled eigenstates, validated on quantum spin models.

Findings

Reconstructed $H_E$ resembles a physical Hamiltonian with spatially varying couplings.

Quantitative agreement with perturbation theory and conformal field theory.

Benchmarking demonstrates the scheme's effectiveness on lattice models.

Abstract

The entanglement Hamiltonian $H_E$, defined through the reduced density matrix of a subsystem $\rho_A=\exp(-H_E)$, is an important concept in understanding the nature of quantum entanglement in many-body systems and quantum field theories. In this work, we explore a numerical scheme which explicitly reconstructs the entanglement Hamiltonian using one entangled mode (i.e., an eigenstate) of $\rho_A$. We demonstrate and benchmark this scheme on quantum spin lattice models. The resulting $H_E$ bears a form similar to a physical Hamiltonian with spatially varying couplings, which allows us to make quantitative comparison with perturbation theory and conformal field theory.