arXiv:1804.03163 · Physical Review Letters

Entanglement Hamiltonian of Interacting Fermionic Models

Francesco Parisen Toldin, Fakher F. Assaad

Published Nov 14, 2018• 68 citations

Abstract

Recent numerical advances in the field of strongly correlated electron systems allow the calculation of the entanglement spectrum and entropies for interacting fermionic systems. An explicit determination of the entanglement (modular) Hamiltonian has proven to be a considerably more difficult problem, and only a few results are available. We introduce a technique to directly determine the entanglement Hamiltonian of interacting fermionic models by means of auxiliary field quantum Monte Carlo simulations. We implement our method on the one-dimensional Hubbard chain partitioned into two segments and on the Hubbard two-leg ladder partitioned into two chains. In both cases, we study the evolution of the entanglement Hamiltonian as a function of the physical temperature.

DOI: 10.1103/physrevlett.121.200602

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arXiv:1804.03163 · Physical Review Letters

Entanglement Hamiltonian of Interacting Fermionic Models

Francesco Parisen Toldin, Fakher F. Assaad

Published Nov 14, 2018• 68 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.121.200602

Related papers

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The Monte Carlo calculation of R\'enyi entanglement entropies

{S}_{n}^{}

of interacting fermions suffers from a well-known signal-to-noise problem, even for a large number of situations in which the infamous sign problem is absent. A few methods have been proposed to overcome this issue, such as ensemble switching and the use of auxiliary partition-function ratios. Here, we present an approach that builds on the recently proposed free-fermion decomposition method; it incorporates entanglement in the probability measure in a natural way; it takes advantage of the hybrid Monte Carlo algorithm (an essential tool in lattice quantum chromodynamics and other gauge theories with dynamical fermions); and it does not suffer from noise problems. This method displays no sign problem for the same cases as other approaches and is therefore useful for a wide variety of systems. As a proof of principle, we calculate

{S}_{2}^{}

for the one-dimensional, half-filled Hubbard model and compare with results from exact diagonalization and the free-fermion decomposition method.

\sim βN^3

) is much higher than that of spin/boson (

\sim βN

). Here,

N

is the total number of sites and

β

is the inverse temperature or projection length. To tackle this problem, we propose a fermionic quantum Monte Carlo algorithm based on the incremental technique along physical parameters, which greatly improves the efficiency of extracting entanglement entropy. We benchmark the developed algorithm by calculating the scaling behavior of the entanglement entropy in a two-dimensional square lattice Hubbard model. The obtained phase diagram including Fermi surface and Goldstone modes validates the correctness of the algorithm. Remarkably, our method shows the high-efficiency with respect to the existing algorithms, while keeping the high computation precision. We proceed to apply this algorithm to explore the scaling behavior of the entanglement entropy and particularly its derivative at Gross-Neveu criticality. Our results elucidate that such critical behavior can be quantified by the correlation length exponent.