Exactly solvable many-body dynamics from space-time duality

TL;DR

This paper reviews dual-unitary circuits, a class of models that treat space and time symmetrically, enabling exact analytical results in quantum many-body dynamics, including chaos, thermalisation, and entanglement.

Contribution

It highlights dual-unitary circuits as a minimal, exactly solvable framework for studying complex quantum many-body phenomena through space-time duality.

Findings

Dual-unitary circuits allow exact quantification of quantum chaos.

They enable full characterization of thermalization, scrambling, and entanglement.

These models can be realized in current quantum simulators.

Abstract

Recent years have seen significant advances, both theoretical and experimental, in our understanding of quantum many-body dynamics. Given this problem's high complexity, it is surprising that a substantial amount of this progress can be ascribed to exact analytical results. Here we review dual-unitary circuits as a particular setting leading to exact results in quantum many-body dynamics. Dual-unitary circuits constitute minimal models in which space and time are treated on an equal footings, yielding exactly solvable yet possibly chaotic evolution. They were the first in which current notions of quantum chaos could be analytically quantified, allow for a full characterisation of the dynamics of thermalisation, scrambling, and entanglement (among others), and can be experimentally realised in current quantum simulators. Dual-unitarity is a specific fruitful implementation of the more general idea of space-time duality in which the roles of space and time are exchanged to access relevant dynamical properties of quantum many-body systems.