Quantum-classical crossover close to quantum critical point

TL;DR

This paper investigates the quantum-classical crossover near a quantum critical point in a Boson system, revealing how critical exponents change dynamically as the system transitions between different fluctuation regimes.

Contribution

It introduces a Keldysh-based analysis of non-equilibrium quantum dynamics near QCP, identifying three regimes and explaining the change in critical exponents without altering universality class.

Findings

Critical behavior exhibits three regimes: AQM, CCDM, QCDM.

Crossover causes effective dimension to change from d to d+2.

Critical exponents vary dynamically during the crossover.

Abstract

We analyze the quantum-classical crossover in the vicinity of the continuous quantum critical point (QCP) of a Boson system. The analysis is based on the Keldysh approach for the description of of the non-equilibrium quantum dynamics. The critical behavior close to QCP has three different regimes (modes): adiabatic quantum mode (AQM), dissipative classical mode (classical critical dynamics mode (CCDM) and dissipative quantum critical mode (QCDM). Crossover among these regimes (modes) is possible: it is shown that the experimentally observed changing of the critical exponents close to QCP is the dynamical effect accompanying the crossover from CCDM where the thermal fluctuations dominate to QCDM where the quantum fluctuations determine the critical behavior. In this case the effective dimension of the $d$-dimensional system continuously changes from $D_{eff}=d$ to $D_{eff}=d+2$ while the universality class of the system does not change.