Probing the anomalous dynamical phase in long-range quantum spin chains through Fisher-zero lines

TL;DR

This paper investigates the anomalous dynamical phase in long-range quantum spin chains by analyzing Fisher-zero lines, revealing qualitative differences from regular phases and enhancing understanding of non-equilibrium quantum dynamics.

Contribution

It introduces a detailed analysis of Fisher-zero lines in long-range transverse-field Ising chains, providing new insights into the anomalous dynamical phase beyond previous studies.

Findings

Fisher-zero lines show termination before crossing the imaginary axis in the anomalous phase.

Presence of smooth peaks in the return rate prior to cusps.

Methodology applicable to general quantum spin chains.

Abstract

Using the framework of infinite Matrix Product States, the existence of an \textit{anomalous} dynamical phase for the transverse-field Ising chain with sufficiently long-range interactions was first reported in [J.~C.~Halimeh and V.~Zauner-Stauber, arXiv:1610:02019], where it was shown that \textit{anomalous} cusps arise in the Loschmidt-echo return rate for sufficiently small quenches within the ferromagnetic phase. In this work we further probe the nature of the anomalous phase through calculating the corresponding Fisher-zero lines in the complex time plane. We find that these Fisher-zero lines exhibit a qualitative difference in their behavior, where, unlike in the case of the regular phase, some of them terminate before intersecting the imaginary axis, indicating the existence of smooth peaks in the return rate preceding the cusps. Additionally, we discuss in detail the infinite Matrix Product State time-evolution method used to calculate Fisher zeros and the Loschmidt-echo return rate using the Matrix Product State transfer matrix. Our work sheds further light on the nature of the anomalous phase in the long-range transverse-field Ising chain, while the numerical treatment presented can be applied to more general quantum spin chains.