Title: Quantum Simulation and Spectroscopy of Entanglement 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.