Nonequilibrium Quantum Criticality in Open Electronic Systems

Abstract

A theory is presented of quantum criticality in open (coupled to reservoirs) itinerant electron magnets, with nonequilibrium drive provided by current flow across the system. Both departures from equilibrium at conventional (equilibrium) quantum critical points and the physics of phase transitions induced by the nonequilibrium drive are treated. Nonequilibrium-induced phase transitions are found to have the same leading critical behavior as conventional thermal phase transitions.PACS numbers: 73.23.-b,05.30.-d,71.10-w,71.38.-k A central issue in condensed matter physics is the behavior of systems as one tunes parameters (for example pressure, or magnetic field) so as to change the symmetries characterizing the ground state [1,2,3,4]. The parameter values at which the ground state symmetries change (for example, from ferromagnetic metal to paramagnetic metal) define a quantum phase transition point (quantum critical point). At quantum phase transitions, spatial and temporal fluctuations are coupled, so that continuous quantum phase transitions in equilibrium systems are typically described by critical theories involving an effective dimensionality d eff greater than the spatial dimensionality d.While equilibrium quantum phase transitions have been extensively studied, the generalization to nonequilibrium conditions raises a largely open class of questions.Nonlinear transport near a superconductorinsulator phase transition [5,6] and a ferromagnetic transition driven by current flow in a closed one-dimensional system [7] have been studied; however, a general systematic understanding is lacking.In this paper we formulate a theory of nonequilibrium quantum criticality in itinerant electron systems coupled to reservoirs (c.f. upper panel of Fig. 1) with which particles may be exchanged. Nonequilibrium is imposed by differences between reservoirs; our systems are therefore subject to a time-independent drive, and are not characterized by any conserved quantities. A generic phase diagram is shown in the lower panel of Fig 1: we take a system which at temperature T = 0 may be tuned through an equilibrium quantum critical point by varying a parameter δ through a critical value δ c and determine the changes induced by a nonequilibrium drive (generically denoted as V ). Of particular interest is the transition generated by V if the V = 0 system is ordered (vertical arrow in lower panel of Fig. 1).Analysis of nonequilibrium systems proceeds from the time dependent density matrixρ(t) defined in terms of a HamiltonianĤ and an initial conditionρ(t init ) viâ ρ(t) = e −iĤ(t−tinit)ρ (t init )e iĤ (t−tinit) . The open systems we consider possess a well defined long-time state defined Schematic phase diagram in a plane of equilibrium distance from criticality, δ, and departure from equilibrium V . The quantum critical point δc separates the long range ordered (δ < δc) and disordered (δ > δc) phases. The solid line denotes a nonequilibrium phase transition. The dashed curves indicate the crossover from low V essentially equilibr...

Approach to a stationary state in a driven Hubbard model coupled to a thermostat

“…The convergence to the same NSS is evident, validating the simplifying approximations discussed above. A better understanding of the effects introduced by the inclusion of a thermostat on the non-equilibrium dynamics is obtained by looking at the time-evolution of the effective temperature 12,27,28 . This is defined, at any time, as the temperature T eff associated to an equilibrium solution with the same energy Ω(t) = K + V of the non-equilibrium state and the same value of the interaction T eff : Ω(t) !…”

Coarsening of disordered quantum rotors under a bias voltage

“…Some works have focused on non-linear transport properties close to an (equilibrium) quantum phase transition [17,18,19]. Others have studied how the critical properties are affected by non-equilibrium drives [20,21,22]. However, a global understanding of phase transitions in the control parameter space T, V, Γ, with T the temperature, V the driving strength, and Γ the strength of quantum fluctuations, is still lacking.…”

“…1 of [20].) In the simplest setting [20] each rotor is coupled to independent reservoirs; more realistic couplings are discussed in [22]. Using the Schwinger-Keldysh formalism [25,26] we obtain the complete out of equilibrium dynamics of these models in the large M limit.…”

“…(For a two-dimensional model the current flows perpendicular to it, see the sketch in Fig. 1 of [20].) In the simplest setting [20] each rotor is coupled to independent reservoirs; more realistic couplings are discussed in [22].…”

Nonequilibrium quantum transport through a dissipative resonant level

“…Much of the effort has been focused on the breakdown of the Kondo effect in transport of a quantum dot due to its coupling to a dissipative environment. However, relatively less is known about the corresponding out-ofequilibrium properties [16][17][18][19][20][21][22][23][24][25] . A finite bias voltage applied across a nanosystem is expected to smear out the equilibrium transition, but the current-induced decoherence might act quite differently as compared to thermal decoherence at finite temperature T , resulting in exotic behavior near the transition.…”