Entanglement Entropy from Nonequilibrium Work

AMER PHYSICAL SOC, 2020
Journal paper

Abstract

The Renyi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field lambda that controls the partition function topology, allowing us to define a notion of nonequilibrium work as lambda is varied smoothly. Nonequilibrium fluctuation theorems of the work provide us with statistically exact estimates of the Renyi entanglement entropy. This framework also naturally leads to the idea of using quench functions with spatially smooth profiles, providing us a way to average over lattice scale features of the entanglement entropy while preserving long distance universal information. We use these ideas to extract universal information from quantum Monte Carlo simulations of SU(N) spin models in one and two dimensions. The vast gain in efficiency of this method allows us to access unprecedented system sizes up to 192 x 96 spins for the square lattice Heisenberg antiferromagnet.

Official source

https://infoscience.epfl.ch/record/276631?ln=en

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts

Related publications

Using strong-disorder renormalization group, numerical exact diagonalization, and quantum Monte Carlo methods, we revisit the random antiferromagnetic XXZ spin-1/2 chain focusing on the long-length and ground-state behavior of the average time-independent spin-spin correlation function C(l)=upsilon l(-eta). In addition to the well-known universal (disorder-independent) power-law exponent eta=2, we find interesting universal features displayed by the prefactor upsilon=upsilon(o)/3, if l is odd, and upsilon=upsilon(e)/3, otherwise. Although upsilon(o) and upsilon(e) are nonuniversal (disorder dependent) and distinct in magnitude, the combination upsilon(o)+upsilon(e)=-1/4 is universal if C is computed along the symmetric (longitudinal) axis. The origin of the nonuniversalities of the prefactors is discussed in the renormalization-group framework where a solvable toy model is considered. Moreover, we relate the average correlation function with the average entanglement entropy, whose amplitude has been recently shown to be universal. The nonuniversalities of the prefactors are shown to contribute only to surface terms of the entropy. Finally, we discuss the experimental relevance of our results by computing the structure factor whose scaling properties, interestingly, depend on the correlation prefactors.

2007

Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung by the infamous "sign problem." Here we exploit the fact that the sign problem is basis-dependent. Recent studies have shown that passing to a dimer (two-site) basis eliminates the sign problem completely for a fully frustrated spin model on the two-leg ladder. We generalize this result to all partially frustrated two-leg spin-1/2 ladders, meaning those where the diagonal and leg couplings take any antiferromagnetic values. We find that, although the sign problem does reappear, it remains remarkably mild throughout the entire phase diagram. We explain this result and apply it to perform efficient quantum Monte Carlo simulations of frustrated ladders, obtaining accurate results for thermodynamic quantities such as the magnetic specific heat and susceptibility of ladders up to L=200 rungs (400 spins 1/2) and down to very low temperatures.

2017

We present a study of a simple model antiferromagnet consisting of a sum of nearest-neighbor SO(N) singlet projectors on the kagome lattice. Our model shares some features with the popular S = 1/2 kagome antiferromagnet but is specifically designed to be free of the sign problem of quantum Monte Carlo. In our numerical analysis, we find as a function of N a quadrupolar magnetic state and a wide range of a quantum spin liquid. A solvable large-N generalization suggests that the quantum spin liquid in our original model is a gapped Z(2) topological phase. Supporting this assertion, a numerical study of the entanglement entropy in the sign free model shows a quantized topological contribution.

AMER PHYSICAL SOC2020