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Detecting Many-Body Scars from Fisher Zeros.
Yuchen Meng1, Songtai Lv1, Yang Liu1
1East China Normal University, Key Laboratory of Polar Materials and Devices (MOE), School of Physics and Electronic Science, Shanghai 200241, China.
Physical Review Letters
|September 10, 2025
Summary
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.
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.
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