Dual unitary circuits in random geometries

TL;DR

This paper extends the concept of dual unitary circuits to random geometries, showing that exact solvability and chaotic behavior persist even without regular lattice structures, by analyzing correlations in mikado-like arrangements.

Contribution

It introduces a new class of dual unitary circuits on random geometries and analytically computes correlation variances, broadening understanding of solvable quantum chaotic systems.

Findings

Variance of correlation functions computed analytically

Exact solvability extends to random geometries

Average correlator vanishes due to Haar randomness

Abstract

Recently introduced dual unitary brickwork circuits have been recognised as paradigmatic exactly solvable quantum chaotic many-body systems with tunable degree of ergodicity and mixing. Here we show that regularity of the circuit lattice is not crucial for exact solvability. We consider a circuit where random 2-qubit dual unitary gates sit at intersections of random arrangements of straight lines in two dimensions (mikado) and analytically compute the variance of the spatio-temporal correlation function of local operators. Note that the average correlator vanishes due to local Haar randomness of the gates. The result can be physically motivated for two random mikado settings. The first corresponds to the thermal state of free particles carrying internal qubit degrees of freedom which experience interaction at kinematic crossings, while the second represents rotationally symmetric (random euclidean) space-time.