Quantum-to-classical crossover near quantum critical point.

M Vasin,V M Vinokur,V Ryzhov

doi:10.1038/srep18600

Abstract

A quantum phase transition (QPT) is an inherently dynamic phenomenon. However, while non-dissipative quantum dynamics is described in detail, the question, that is not thoroughly understood is how the omnipresent dissipative processes enter the critical dynamics near a quantum critical point (QCP). Here we report a general approach enabling inclusion of both adiabatic and dissipative processes into the critical dynamics on the same footing. We reveal three distinct critical modes, the adiabatic quantum mode (AQM), the dissipative classical mode [classical critical dynamics mode (CCDM)], and the dissipative quantum critical mode (DQCM). We find that as a result of the transition from the regime dominated by thermal fluctuations to that governed by the quantum ones, the system acquires effective dimension d + zΛ(T), where z is the dynamical exponent, and temperature-depending parameter Λ(T) ∈ [0, 1] decreases with the temperature such that Λ(T = 0) = 1 and Λ(T → ∞) = 0. Our findings lead to a unified picture of quantum critical phenomena including both dissipation- and dissipationless quantum dynamic effects and offer a quantitative description of the quantum-to-classical crossover.

Highlights

Let us consider for concreteness a Bose system described by the one-component order parameter scalar field φ and with the potential energy given by the functional U{φ}, e.g. U ∝ φ4
To describe quantum critical dynamics we employ the Keldysh technique, initially formulated for quantum systems, where the role of the partition function is played by the functional path integral which after the Wick rotation assumes the form[18]:
These expressions set the ground for quantitative description of critical dynamics in the vicinity of the critical point

Summary

Scaling area

In this case the effective dimensionality is equal to the upper critical dimensionality of the system, Deff = 4, and all the critical exponents reach their mean-field values. The functional technique of theoretical description of non-equilibrium dynamics allows us to describe the entire spectrum of critical modes in the vicinity of quantum phase transition within a single formalism It describes the crossover between CCDM and DQCM, and the unusual temperature dependence of the system critical exponents. The results of[26] favors the quantum concept of effective increasing space dimensionality at low temperatures that suppresses a fluctuation divergence at a second order phase transition, in[24] it is shown that the crossover from the classical to the quantum criticality takes place with the corresponding continuous change of the critical indexes, see. One of the main consequences of our work is that due to the presence of dissipation, the experimental values of the critical exponents of one- and two-dimensional systems close to QCP can differ from the values obtained

Critical exponent

Methods

Additional Information