Abstract
We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. The technique is based on a direct thermodynamic study of lattice entanglement Hamiltonians—recently proposed in the paper [Dalmonte et al 2018 Nat. Phys. 14 827] via field theoretical insights—and can be performed by quantum Monte Carlo methods. We benchmark our technique on critical quantum spin chains, and apply it to several two-dimensional quantum magnets, where we are able to unambiguously determine the onset of area law in the entanglement entropy, the number of Goldstone bosons, and to check a recent conjecture on geometric entanglement contribution at critical points described by strongly coupled field theories. The protocol can also be adapted to measure entanglement in experiments via quantum quenches.
Highlights
Introduction. - Over the last twenty years, entanglement has emerged as a paramount tool to characterize quantum wave-functions [1,2,3,4]
We benchmark our technique on critical quantum spin chains, and apply it to several two-dimensional quantum magnets, where we are able to unambiguously determine the onset of area law in the entanglement entropy, the number of Goldstone bosons, and to check a recent conjecture on geometric entanglement contribution at critical points described by strongly coupled field theories
A striking example is ground states |Ψ of many-body systems where, given a spatial bipartition dividing the system into regions A and B, the entanglement between A and B is measured by the von Neumann entropy (VNE): SA = −TrAρA ln ρA, ρA = TrB|Ψ Ψ|
Summary
We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. Our method allows to perform accurate entanglement-based measurements of universal quantitites, such as the number of NambuGoldstone modes [10] and central charges [5, 6], at the percent level, even for modest system sizes Most remarkably, it allows the calculation of the entanglement of many-body systems in a scalable manner (and well beyond what can be done with alternative numerical methods), thanks to its thermodynamic analogy. From the point of view of classical computations, this can be achieved using any algorithm based on metadynamics We illustrate this by applying the quantum version of the Wang-Landau method performed in the stochastic series expansion (SSE) QMC framework [44, 45]. DEH can be conveniently measured following the procedures proposed
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