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Summary

This study demonstrates the consistency between linear response theory and the Kibble-Zurek mechanism for describing quantum phase transitions. Linear response theory provides rigorous arguments for identifying the "gap" as a relaxation rate in these transitions.

Keywords:
Kibble–Zurek mechanismlinear response theoryquantum phase transition

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Area of Science:

  • Quantum physics
  • Condensed matter theory

Background:

  • Quantum phase transitions (QPTs) occur at zero temperature, differing from thermodynamic phase transitions.
  • The applicability of classical frameworks to QPTs requires careful examination.
  • The Kibble-Zurek mechanism and linear response theory are established tools for non-equilibrium dynamics.

Purpose of the Study:

  • To investigate the consistency of the Kibble-Zurek mechanism and linear response theory in describing QPTs.
  • To determine if linear response theory can enhance the understanding of the Kibble-Zurek mechanism.
  • To rigorously connect relaxation time in linear response theory to QPT dynamics.

Main Methods:

  • Comparative analysis of Kibble-Zurek mechanism and linear response theory predictions.
  • Derivation of relaxation time from linear response theory.
  • Verification of Kibble-Zurek scaling for excess work using linear response theory.

Main Results:

  • The Kibble-Zurek mechanism and linear response theory provide consistent descriptions of quantum phase transitions.
  • Linear response theory offers a rigorous basis for identifying the "gap" as a relaxation rate.
  • Excess work calculated via linear response theory exhibits Kibble-Zurek scaling.

Conclusions:

  • Linear response theory and the Kibble-Zurek mechanism are reconcilable frameworks for studying quantum phase transitions.
  • The findings provide deeper insights into the non-equilibrium dynamics of QPTs.
  • This work validates the use of linear response theory to inform Kibble-Zurek arguments.