Imaginary-Temperature Zeros for Quantum Phase Transitions

TL;DR

This paper introduces imaginary-temperature zeros (ITZs) as a novel tool to analyze quantum phase transitions at zero temperature, revealing universal behaviors and offering experimental detection methods.

Contribution

It extends the concept of partition function zeros to zero temperature by defining and analyzing ITZs, providing new insights into quantum phase transitions.

Findings

ITZs distinguish different quantum phases.

Universal singular behaviors are observed in ITZ-related quantities.

ITZs correlate with spectral form factor zeros, enabling experimental detection.

Abstract

While the zeros of complex partition functions, such as Lee-Yang zeros and Fisher zeros, have been pivotal in characterizing temperature-driven phase transitions, extending this concept to zero temperature remains an open question. In this work, we propose a solution to this issue by calculating the imaginary-temperature zeros (ITZs), which are defined as the roots of the imaginary-temperature partition function. We illustrate the analytical properties of ITZs in the transverse-field Ising chain, showing that the ITZs' distribution can distinguish between various phases and signify the critical exponents. Universal singular behaviors manifest in such quantities as the edge density of ITZs and the magnetization, with the scaling exponents remarkably differing from those in Lee-Yang theory. We further illuminate the consistency between ITZs and the zeros of the spectral form factor, which offers a practical path for the experimental detection of ITZs.