arXiv:2206.15142 · SciPost Physics

The Floquet Baxterisation

Yuan Miao, Vladimir Gritsev, Denis V. Kurlov

Published Mar 18, 2024• 19 citations

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.

DOI: 10.21468/scipostphys.16.3.078

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arXiv:2206.15142 · SciPost Physics

The Floquet Baxterisation

Yuan Miao, Vladimir Gritsev, Denis V. Kurlov

Published Mar 18, 2024• 19 citations

arXiv HTML PDF

Abstract

DOI: 10.21468/scipostphys.16.3.078

Related papers

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ρ

, and demonstrate that the minimum possible circuit depth is four. We show that when these

ρ

-inhomogeneities are placed at the endpoints and in their immediate neighborhood, the resulting boundary gates can be interpreted as single gates acting on multiple sites. Our construction is fully general and applies to regular

R

-matrices, both of difference and non-difference type, together with their associated boundary matrices. As an application, we consider two-qubit gates corresponding to 6- and 8-vertex

R

-matrices of non-difference form satisfying the Yang-Baxter equation, and we construct the associated reflection matrices that generate integrable quantum circuits.

Abstract We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine

{D}_2^2

D 2 2 Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic Potts model, this mapping allows us to study the latter model using tools from integrability. We show that there is a simple interpretation of one of the known K -matrices of the

{D}_2^2

D 2 2 model in terms of Temperley-Lieb algebra generators, and use this to present an integrable Hamiltonian that turns out to be in the same universality class as the antiferromagnetic Potts model with free boundary conditions. The intriguing degeneracies in the spectrum observed in related works ([12, 13]) are discussed.

This work concerns to the studies of boundary integrability of the vertex models from representations of the Temperley-Lieb algebra associated with the quantum group

{\cal U}_{q}[X_{n}]

for the affine Lie algebras

X_{n}

A_{1}^{(1)}

B_{n}^{(1)}

C_{n}^{(1)}

and

D_{n}^{(1)}

. A systematic computation method is used to constructed solutions of the boundary Yang-Baxter equations. We find a

2n^{2}+1

free parameter solution for $A_{1}^{(1)} $ spin-

(n-1/2)

and $ C_{n}^{(1)}$ vertex models. It turns that for $A_{1}^{(1)} $ spin-

n

, $ B_{n}^{(1)}$ and

D_{n}^{(1)}

vertex models, the solution has

2n^{2}+2n+1

free parameters.

We develop a Floquet protocol for long-range entanglement generation in the one-dimensional quantum Potts model, which generalizes the transverse-filed Ising model by allowing each spin to have

n>2

states. We focus on the case of

n=3

, so that the model describes a chain of qutrits. The suggested protocol creates qutrit Bell-like pairs with nonlocal long-range entanglement that spans over the entire chain. We then conjecture that the proposed Floquet protocol is integrable and explicitly construct a few first nontrivial conserved quantities that commute with the stroboscopic evolution operator. Our analysis of the Floquet integrability relies on the deep connection between the quantum Potts model and a much broader class of models described by the Temperley-Lieb algebra. We work at the purely algebraic level and our results on Floquet integrability are valid for any representation of the Temperley-Lieb algebra. We expect that our findings can be probed with present experimental facilities using Rydberg programmable quantum simulators and can find various applications in quantum technologies.