Quantum Simulation and Spectroscopy of Entanglement Hamiltonians

TL;DR

This paper demonstrates how to experimentally access the entanglement spectrum of many-body quantum systems by simulating the entanglement Hamiltonian using quantum systems like atoms in optical lattices and trapped ions, based on the Bisognano-Wichmann theorem.

Contribution

It introduces a scalable method to measure the entanglement spectrum via quantum simulation of the entanglement Hamiltonian, grounded in the Bisognano-Wichmann theorem.

Findings

Experimental protocol for entanglement spectrum measurement.

Validation on models with topological order and quantum criticality.

Connection between entanglement spectrum and physical Hamiltonians.

Abstract

Entanglement is central to our understanding of many-body quantum matter. In particular, the entanglement spectrum, as eigenvalues of the reduced density matrix of a subsystem, provides a unique footprint of properties of strongly correlated quantum matter from detection of topological order to characterisation of quantum critical systems. However, direct experimental measurement of the entanglement spectrum has so far remained elusive due to lack of direct experimental probes. Here we show that the entanglement spectrum of the ground state of a broad class of Hamiltonians becomes directly accessible as quantum simulation and spectroscopy of an entanglement Hamil- tonian, building on the Bisognano-Wichmann (BW) theorem of axiomatic quantum field theory. Remarkably, this theorem gives an explicit physical construction of the entanglement Hamiltonian, identified as Hamiltonian of the many-body system of interest with spatially varying couplings. Building on this, we propose an immediate, scalable recipe for implementation of the entanglement Hamiltonian, and measurement of the corresponding entanglement spectrum as spectroscopy of the Bisognano-Wichmann Hamiltonian with synthetic quantum systems, including atoms in optical lat- tices and trapped ions. We illustrate and benchmark this scenario on a variety of models, spanning phenomena as diverse as conformal field theories, topological order, and quantum phase transitions.