Signatures of quantum criticality in the complex inverse temperature plane

TL;DR

This paper explores the behavior of Fisher zeros in the complex inverse temperature plane to identify and analyze quantum criticality and phase transitions in the transverse field Ising model, revealing new insights into quantum phase behavior.

Contribution

It extends the concept of Fisher zeros to quantum phase transitions, providing exact identification and analysis of their behavior in the transverse field Ising model.

Findings

Fisher zeros form lines or closed curves linked to domain-wall excitations.

Crossover behavior of Fisher zeros indicates criticality near quantum phase transitions.

Tensor network calculations confirm the disruption of zero curves signals deconfined meson excitations.

Abstract

Concepts of the complex partition functions and the Fisher zeros provide intrinsic statistical mechanisms for finite temperature and real time dynamical phase transitions. We extend the utility of these complexifications to quantum phase transitions. We exactly identify different Fisher zeros on lines or closed curves and elucidate their correspondence with domain-wall excitations or confined mesons for the one-dimensional transverse field Ising model. The crossover behavior of the Fisher zeros provides a fascinating picture for criticality near the quantum phase transition, where the excitation energy scales are quantitatively determined. We further confirm our results by tensor network calculations and demonstrate a clear signal of deconfined meson excitations from the disruption of the closed zero curves. Our results unambiguously show significant features of Fisher zeros for a quantum phase transition and open up a new route to explore quantum criticality.