We demonstrate an alternative approach based on a 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 test bed, 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.

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• Quantum phase transitions
• Quasiparticles & collective excitations
• Van Hove singularity
• Lee-Yang & Fisher zeroes
• Luttinger liquid model
• XY model