Integrable Floquet systems related to logarithmic conformal field theory

TL;DR

This paper investigates an integrable Floquet quantum system connected to dense polymer universality class, revealing algebraic structures, phase transitions, and potential logarithmic conformal field theory descriptions in the scaling limit.

Contribution

It introduces a novel integrable Floquet system linked to non-unitary algebra representations and explores its algebraic structure, phase behavior, and conformal field theory connections.

Findings

Identifies a Lie algebra structure within the Temperley-Lieb algebra

Shows the Floquet Hamiltonian's phase transition between local and non-local phases

Provides evidence for a logarithmic conformal field theory description in the scaling limit

Abstract

We study an integrable Floquet quantum system related to lattice statistical systems in the universality class of dense polymers. These systems are described by a particular non-unitary representation of the Temperley-Lieb algebra. We find a simple Lie algebra structure for the elements of Temperley-Lieb algebra which are invariant under shift by two lattice sites, and show how the local Floquet conserved charges and the Floquet Hamiltonian are expressed in terms of this algebra. The system has a phase transition between local and non-local phases of the Floquet Hamiltonian. We provide a strong indication that in the scaling limit this non-equilibrium system is described by the logarithmic conformal field theory.