Entanglement entropy from non-equilibrium Monte Carlo simulations

Abstract

We study the entanglement entropy in lattice field theory using a simulation algorithm based on Jarzynski’s theorem. We focus on the entropic c-function for the Ising model in two and in three dimensions: after validating our algorithm against known analytical results from conformal field theory in two dimensions, we present novel results for the three-dimensional case. We show that our algorithm, which is highly parallelized on graphics processing units, allows one to precisely determine the subleading corrections to the area law, which have been investigated in many recent works. Possible generalizations of this study to other strongly coupled theories are discussed.

Entanglement entropy from non-equilibrium lattice simulations

“…In this contribution, we discussed the algorithm to compute the entropic c-function by means of non-equilibrium Monte Carlo simulations that we proposed in ref. [13], and the results that we obtained for the Ising model. After a benchmark of our code in two dimensions, we studied the three-dimensional case, where we compared our simulation results close to the critical point with the predictions of models based on a generalization of the predictions that can be derived in two dimensions, on a model in the quantum Lifshitz universality class, and on holographic calculations, with the latter providing the best fit to our data.…”

“…In ref. [13], we proposed to use eq. ( 3) to compute the entropic Rényi c-function by means of non-equilibrium simulations of a system in which we directly implemented the replica geometry.…”

“…While the analytical computation of entropic c-functions can be carried out only for highly symmetric systems, also their numerical estimate is difficult, due to the non-local nature of the observable, to the high computational costs to sample the space of configurations, and to the limited scalability to systems defined in more than 1 + 1 dimensions [7][8][9][10][11][12]. In this contribution we present a new method to tackle these challenges and to evaluate the entropic c-function by means of nonequilibrium Monte Carlo simulations, that we recently applied to the Ising model in two and in three dimensions [13]. In the following, we use natural units, denoting the coupling between spins in units of the temperature as 𝛽 and the linear extent of the lattice in the spatial directions as 𝐿.…”

Sampling Nambu-Goto theory using Normalizing Flows

“…Stochastic Normalizing Flows (SNFs) [8,9] are a class of deep generative models that combines Normalizing Flows (NFs) with non-equilibrium lattice calculations based on the Jarzynski's equality [12][13][14][15][16][17]. Jarzynski's equality [12] is an identity in non-equilibrium statistical mechanics which states that ratios of partition functions between two equilibrium states 𝜂 𝑖𝑛 and 𝜂 𝑓 𝑖𝑛 can be computed as an average of out-of-equilibrium processes:…”

Out-of-equilibrium simulations to fight topological freezing

“…[21], and of the entanglement entropy of lattice field theories, see Ref. [22]. Moreover, it has also been combined with Normalizing Flows (see Ref.…”