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Characterization of Thermal Transport in One-dimensional Solid Materials
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Trade-off between diagonal and off-diagonal elements in the eigenstate thermalization hypothesis.

Zhiqiang Huang1

  • 1Chinese Academy of Sciences, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Wuhan 430071, China.

Physical Review. E
|August 19, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a new, observable-independent measure to verify the eigenstate thermalization hypothesis (ETH). It reveals a universal trade-off, showing how off-diagonal elements suppress diagonal deviations, crucial for understanding thermalization in quantum systems.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • The eigenstate thermalization hypothesis (ETH) describes thermalization in isolated quantum systems.
  • Verifying ETH typically relies on local observables, posing limitations.
  • A deeper understanding of thermalization mechanisms is needed.

Purpose of the Study:

  • To introduce an observable-independent measure for verifying ETH.
  • To establish a universal trade-off relation connecting diagonal and off-diagonal elements of this measure.
  • To provide new insights into thermalization dynamics in quantum systems.

Main Methods:

  • Developed an observable-independent measure of distinguishability using the variance of a rescaled local operator.
  • Established a universal trade-off relation between diagonal and off-diagonal elements of this measure.
  • Performed numerical simulations on a 1D Ising spin chain with tunable fields.

Main Results:

  • Demonstrated a universal trade-off where exponential growth of off-diagonal terms enforces their suppression.
  • Showcased stark contrasts between integrable and non-integrable regimes in numerical simulations.
  • Observed universal suppression of off-diagonal elements with system size, failing in integrable systems.

Conclusions:

  • The new measure rigorously connects eigenstate typicality and spatially averaged observables.
  • The findings unify subsystem ETH, weak ETH, and macroscopic observables under a single framework.
  • The study offers novel insights into the fundamental mechanisms of thermalization in quantum systems.