Dual unitary circuits in random geometries
- URL: http://arxiv.org/abs/2206.09665v1
- Date: Mon, 20 Jun 2022 09:11:43 GMT
- Title: Dual unitary circuits in random geometries
- Authors: Yusuf Kasim, Toma\v{z} Prosen
- Abstract summary: We show that regularity of the lattice circuit is not crucial for exact solvability.
We consider a circuit where random 2-qubit dual unitary gates sit at intersections of random arrangements straight lines in two dimensions.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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