Simulating the out-of-equilibrium dynamics of local observables by trading entanglement for mixture

Abstract

The fact that the computational cost of simulating a many-body quantum system on a computer increases with the amount of entanglement has been considered as the major bottleneck for simulating its out-of-equilibrium dynamics. Some aspects of the dynamics are, nevertheless, robust under appropriately devised approximations. Here we present a possible algorithm that allows to systematically approximate the equilibration value of local operators after a quantum quench. At the core of our proposal there is the idea to transform entanglement between distant parts of the system into mixture, and at the same time preserving the local reduced density matrices of the system. We benchmark the resulting algorithm by studying quenches of quadratic Fermionic Hamiltonians.

Operator content of entanglement spectra in the transverse field Ising chain after global quenches

“…The numerical results are obtained by using the mapping of the TFIC to free fermions [68][69][70][71][72] (see also Ref. [53] and references therein). Similar studies have been recently performed in an infinite harmonic chain and an infinite chain of free fermions at half filling [73].…”

“…This entanglement barrier prevents one from extracting reliable predictions at long time even when our best classical-simulation techniques are employed [47][48][49][50] (see Refs. [51][52][53][54][55] for recent proposals to overcome this barrier). As a result, important questions about strongly correlated many-body quantum systems out of equilibrium are only partially understood and currently can only be settled experimentally.…”

Light cone tensor network and time evolution

“…This so-called entanglement barrier limits the applicability of the matrix product state (MPS) [7][8][9][10] description, and makes it difficult to predict the asymptotic long-time behavior, even when local observables in this limit are expected to be well-described by a thermodynamic ensemble, itself well approximated by a matrix product operator (MPO) [11][12][13][14][15][16]. A number of methods have been suggested to try to overcome this issue and extract information about the long-time behavior of local properties [17][18][19][20][21][22][23][24]. While there is no universal solution, understanding the entanglement structures in the evolution TN can be crucial to identify the most adequate one for practical computations.…”

Fermionic Gaussian states: an introduction to numerical approaches

“…We also review how to perform real-time evolution using the correlation matrices, something that we have used for example in [15,16].…”