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This study introduces a new framework to understand quantum phase transitions (QPTs) by incorporating dissipative effects. It reveals three critical modes and a temperature-dependent effective dimension, unifying quantum and classical dynamics.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Dynamics
  • Statistical Mechanics

Background:

  • Quantum phase transitions (QPTs) are dynamic phenomena.
  • The role of dissipation in critical dynamics near quantum critical points (QCPs) remains poorly understood.

Purpose of the Study:

  • To develop a general approach for including both adiabatic and dissipative processes in critical dynamics.
  • To reveal distinct critical modes and understand the quantum-to-classical crossover.

Main Methods:

  • Development of a general theoretical framework.
  • Analysis of critical dynamics incorporating dissipation.
  • Identification of critical modes and effective system dimensions.

Main Results:

  • Three distinct critical modes identified: adiabatic quantum mode (AQM), classical critical dynamics mode (CCDM), and dissipative quantum critical mode (DQCM).
  • System acquires an effective dimension d + zΛ(T), where Λ(T) is a temperature-dependent parameter controlling the quantum-to-classical crossover.
  • Λ(T) transitions from 1 at T=0 to 0 at T→∞, signifying a crossover from quantum to thermal fluctuation dominance.

Conclusions:

  • A unified picture of quantum critical phenomena is presented, encompassing both dissipative and dissipationless quantum dynamics.
  • The findings offer a quantitative description of the crossover from quantum to classical behavior near QCPs.
  • The developed approach provides a new perspective on the complex interplay of quantum effects and dissipation in critical systems.