The Floquet Baxterisation

Abstract

Quantum integrability has proven to be a useful tool to study quantum many-body systems out of equilibrium. In this paper we construct a generic framework for integrable quantum circuits through the procedure of Floquet Baxterisation. The integrability is guaranteed by establishing a connection between Floquet evolution operators and inhomogeneous transfer matrices obtained from the Yang-Baxter relations. This allows us to construct integrable Floquet evolution operators with arbitrary depths and various boundary conditions. Furthermore, we focus on the example related to the staggered 6-vertex model. In the scaling limit we establish a connection of this Floquet protocol with a non-rational conformal field theory. Employing the properties of the underlying affine Temperley--Lieb algebraic structure, we demonstrate the dynamical anti-unitary symmetry breaking in the easy-plane regime. We also give an overview of integrability-related quantum circuits, highlighting future research directions.

45 pages, 16 figures

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• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Integrability of open boundary driven quantum circuits
• Integrability is generic in homogeneous U(1)-invariant nearest-neighbor qubit circuits
• Inhomogeneous SU(2) symmetries in homogeneous integrable U(1) circuits and transport
• Generalized hydrodynamics of integrable quantum circuits
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Geometric representations of braid and Yang-Baxter gates
• Brick Wall Quantum Circuits with Global Fermionic Symmetry
• Integrable fishnet circuits and Brownian solitons