Imaginary-Temperature Zeros for Quantum Phase Transitions

While the zeros of complex partition functions, such as Lee-Yang zeros and Fisher zeros, have been instrumental in characterizing temperature-driven phase transitions, the extension of this concept to zero temperature remains an open and active topic. In this paper, we introduce the concept of Imaginary-Temperature Zeros (ITZs) by calculating the zeros of the imaginary-temperature partition function. We delve into the properties of ITZs for the transverse-field Ising chain, and find that the ITZs are distributed in sectorial structures, accompanied by universal singular behaviors for such quantities as the edge density of ITZs and the magnetization. These singularities remarkably differ from those in the Lee-Yang theory, and are demonstrated to be intimately related to quantum criticality and the Ising critical exponents. We further illuminate the correspondence between ITZs and the zeros of the spectrum form factor, which offers a practical way for detecting ITZs and zero-temperature phase transitions through quantum dynamics.