Emergent phase transition in Cluster Ising model with dissipation

TL;DR

This paper investigates a non-Hermitian cluster Ising model, revealing four emergent phases and multiple phase transitions, with potential experimental realization in ultra-cold atom systems.

Contribution

It provides an exact solution and detailed characterization of new phases and phase transitions induced by non-Hermiticity in the cluster Ising model.

Findings

Identification of four distinct phases: cluster, gapless, paramagnetic, and antiferromagnetic.

Discovery of three critical lines including KT-like and Ising phase transitions.

Characterization of phase transitions through string order parameter and spin correlation functions.

Abstract

We study a cluster Ising model with non-Hermitian external field which can be exactly solved in the language of free fermions. By investigating the second derivative of energy density and fidelity, the possible new critical points are tentatively located. String order parameter and staggered magnetization are then detected to reveal emergent phases of brand new characteristics. To categorize the exotic phases and phase transitions induced by non-Hermiticity, we calculate the variation mode of spin correlation function as well as string parameter, which characterize the emergent phases and critical points with different patterns of decay and critical exponents. With the help of string order parameter and staggered magnetization, we find that there are four phases after introducing the non-Hermiticity -- the cluster phase, the gapless phase, the paramagnetic (PM) phase and the antiferromagnetic (AF) phase. A phase diagram is then presented to graphically illustrate, based on two "KT-like" phase transitions and an Ising phase transition, respectively, the generation of three critical lines as non-Hermitian strength increases. Our theoretical work is expected to be realized in the experiment of ultra-cold atoms, pushing for progress in exploring novel phases and phase transitions.