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Classical periodic trajectories and quantum scars in many-spin systems.
Igor Ermakov1,2,3, Oleg Lychkovskiy1,2,3, Boris V Fine2,4
1Steklov Mathematical Institute, Department of Mathematical Methods for Quantum Technologies, of Russian Academy of Sciences, 8 Gubkina St., Moscow 119991, Russia.
Physical Review. E
|January 21, 2026
Summary
This study explores dynamic thermalization in chaotic spin systems, finding that specific classical trajectories connect to quantum many-body scars. These scars slow down thermalization and reveal quantum signatures of classical motion.
Area of Science:
- Statistical Mechanics
- Quantum Dynamics
- Condensed Matter Physics
Background:
- Investigating dynamic thermalization in many-body systems is crucial for understanding statistical mechanics.
- Exceptional quantum nonthermal eigenstates, known as quantum many-body scars, challenge conventional thermalization theories.
- Chaotic classical trajectories and their stability offer insights into quantum dynamics.
Purpose of the Study:
- To probe the limits of dynamic thermalization by studying classical periodic trajectories in chaotic spin systems.
- To explore the connection between these classical trajectories and quantum many-body scars.
- To understand the role of quantum many-body scars in the thermalization process.
Main Methods:
- Numerical investigation of the stability of exceptional periodic classical trajectories in chaotic many-spin systems.
- Analysis of Lyapunov exponents for classical trajectories.
- Numerical simulation of quantum state dynamics in spin chains.
- Identification of quantum many-body scars in spin chains of varying spin values.
Main Results:
- Classical periodic trajectories exhibit nontrivial dependencies of Lyapunov exponents on interaction constants and chain lengths.
- Lyapunov stability of periodic trajectories was found in long spin chains within chaotic energy shells.
- Quantum many-body scars were identified in spin chains with spin-3/2 and higher, but not in spin-1/2 chains.
- Thermalization dynamics dominated by quantum scars show a slowdown compared to generic thermalization.
Conclusions:
- Exceptional classical trajectories can be Lyapunov stable in chaotic systems, with stability linked to symmetry properties.
- Quantum many-body scars exist in specific spin systems and influence thermalization dynamics.
- The study reveals quantum signatures related to the proximity of classical periodic motion to a separatrix.
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