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Complex zeros are the solutions to polynomial equations that include imaginary numbers, specifically, numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit defined by i2=-1. These zeros satisfy the equation P(x) = 0, where P(x) is a polynomial with real or complex coefficients. Since the complex number system includes all real numbers, it provides a complete framework for analyzing all possible roots of a polynomial.Every polynomial of degree n≥1 can be...
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Detecting Many-Body Scars from Fisher Zeros.

Yuchen Meng1, Songtai Lv1, Yang Liu1

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|September 10, 2025
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Researchers introduce a new method to detect quantum many-body scars (QMBS) using Fisher zeros in the complex temperature plane. This approach aids in understanding systems that defy thermalization and distinguishes QMBS from other ergodicity breaking phenomena.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • Understanding far-from-equilibrium dynamics in interacting quantum systems remains challenging.
  • Quantum many-body scars (QMBS) are special eigenstates that evade thermalization, exhibiting long-lived oscillations.
  • Existing methods for studying QMBS (symmetry, algebra, quasiparticles) have limitations in explaining their underlying mechanisms and distinguishing them from other ergodicity-breaking phenomena.

Purpose of the Study:

  • To introduce a novel method for detecting and diagnosing QMBS.
  • To provide a framework for understanding the mechanism of QMBS and differentiating them from other forms of ergodicity breaking.
  • To connect QMBS phenomena with the broader concepts of thermal and dynamical phase transitions.

Main Methods:

  • Introduced a new approach based on Fisher zeros, which are zeros of the analytically continued partition function in the complex inverse temperature (β) plane.
  • Interpreted the complex partition function as the return amplitude of the thermofield double state.
  • Validated the method by analyzing two models exhibiting QMBS: the P[over ¯]XP[over ¯] model and the Ising chain in external fields.

Main Results:

  • Demonstrated that systems with QMBS exhibit a continuous line of Fisher zeros off the imaginary β axis, separating regions with different thermalization behaviors.
  • Showcased the ability of this method to distinguish QMBS from strong ergodicity breaking by analyzing their distinct renormalization group flows on the complex β plane.
  • Confirmed that the Fisher zero approach can identify QMBS without needing to examine individual quantum states exhaustively.

Conclusions:

  • Fisher zeros provide an effective statistical mechanics approach to detect and diagnose QMBS.
  • This method unifies the study of QMBS with thermal and dynamical phase transitions.
  • The complex β plane analysis offers a powerful tool for understanding quantum dynamics and ergodicity breaking.