Giant bubbles of Fisher zeros in the quantum XY chain

TL;DR

This paper introduces a novel method using complex inverse temperature and Fisher zeros to analyze quantum phases, revealing large-scale Fisher-zero bubbles in the quantum XY chain that challenge traditional low-energy theories.

Contribution

It presents an innovative approach connecting Fisher zeros with quantum dynamics, demonstrating giant bubbles of zeros in the XY chain and their relation to spectral weight transfer.

Findings

Giant Fisher-zero bubbles are identified near the XX limit.

Oscillations in the spectral form factor reflect gap behavior.

The energy scale of bubbles contradicts Luttinger liquid predictions.

Abstract

We demonstrate an alternative approach based on complex-valued inverse temperature and partition function to probe quantum phases of matter with nontrivial spectra and dynamics. It leverages thermofield dynamics (TFD) to quantitatively characterize quantum and thermal fluctuations, and exploit the correspondence between low-energy excitations and Fisher zeros. Using the quantum XY chain in an external field as a testbed, we show that the oscillatory gap behavior manifests as oscillations in the long-time dynamics of the TFD spectral form factor. We also identify giant bubbles, i.e. large-scale closed lines, of Fisher-zeros near the gapless XX limit. They provide a characteristic energy scale that seems to contradict the predictions of the low energy theory of a featureless Luttinger liquid. We identify this energy scale and relate the motion of these giant bubbles with varying external field to the transfer of spectral weight from high to low energies. The deep connection between Fisher zeros, dynamics, and excitations opens up promising avenues for understanding the unconventional gap behaviors in strongly correlated many-body systems.