Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality

TL;DR

This paper introduces a space-time duality approach to overcome the entanglement barrier in quantum many-body dynamics, enabling efficient simulation of local observables in both integrable and chaotic systems.

Contribution

It reveals the physical origin of the temporal entanglement barrier and proposes a new light-cone growth algorithm that avoids it, improving the efficiency of influence matrix methods.

Findings

The temporal entanglement barrier is ubiquitous in quantum dynamics.

A semiclassical quasiparticle picture explains the barrier in integrable systems.

An alternative algorithm avoids the barrier, enabling efficient thermodynamic-limit simulations.

Abstract

Describing non-equilibrium properties of quantum many-body systems is challenging due to high entanglement in the wavefunction. We describe evolution of local observables via the influence matrix (IM), which encodes the effects of a many-body system as an environment for local subsystems. Recent works found that in many dynamical regimes the IM of an infinite system has low temporal entanglement and can be efficiently represented as a matrix-product state (MPS). Yet, direct iterative constructions of the IM encounter highly entangled intermediate states - a temporal entanglement barrier (TEB). We argue that TEB is ubiquitous, and elucidate its physical origin via a semiclassical quasiparticle picture that exactly captures the behavior of integrable spin chains. Further, we show that a TEB also arises in chaotic spin chains, which lack well-defined quasiparticles. Based on these insights, we formulate an alternative light-cone growth algorithm, which provably avoids TEB, thus providing an efficient construction of the thermodynamic-limit IM as a MPS. This work uncovers the origin of the efficiency of the IM approach for thermalization and transport.