Solvable Quantum Circuits from Spacetime Lattices

TL;DR

This paper introduces a new class of exactly solvable quantum circuits called completely reducible circuits, which extend dual-unitary models to more general geometries and provide analytical insights into entanglement dynamics and information flow.

Contribution

The authors develop a framework for completely reducible circuits that generalize dual-unitarity, allowing analytical characterization of entanglement and information flow in more complex lattice geometries.

Findings

Analytical expression for entanglement line tension.

Connection between entanglement dynamics and knot invariants.

Extension of solvable models beyond dual-unitarity.

Abstract

In recent years dual-unitary circuits and their multi-unitary generalizations have emerged as exactly solvable yet chaotic models of quantum many-body dynamics. However, a systematic picture for the solvability of multi-unitary dynamics remains missing. We present a framework encompassing a large class of such non-integrable models with exactly solvable dynamics, which we term \emph{completely reducible} circuits. In these circuits, the entanglement membrane determining operator growth and entanglement dynamics can be characterized analytically. Completely reducible circuits extend the notion of space-time symmetry to more general lattice geometries, breaking dual-unitarity globally but not locally, and allow for a rich phenomenology going beyond dual-unitarity. As example, we introduce circuits that support four and five directions of information flow. We derive a general expression for the entanglement line tension in terms of the pattern of information flow in spacetime. The solvability is shown to be related to the absence of knots of this information flow, connecting entanglement dynamics to the Kauffman bracket as knot invariant. Building on these results, we propose that in general non-integrable dynamics the curvature of the entanglement line tension can be interpreted as a density of information transport. Our results provide a new and unified framework for exactly solvable models of many-body quantum chaos, encompassing and extending known constructions.