Abstract Quantum criticality has attracted considerable attention both theoretically and experimentally as a way to describe part of the phase diagram of strongly correlated systems. A scale‐invariant fluctuation spectrum at a quantum critical point (QCP) implies the absence of any intrinsic scale. Any experimental probe may therefore create an out‐of‐equilibrium setting; the system would be in a non‐linear response regime, which violates the fluctuation–dissipation theorem (FDT). Here, we study this violation and related out‐of equilibrium phenomena in a single‐electron transistor (SET) with ferromagnetic leads, which can be tuned through a quantum phase transition. We review the breakdown of the FDT and study the universal behavior of the fluctuation–dissipation relation of various correlators in the quantum critical regime. In particular, we explore the concept of effective temperature as a means to extend the FDT into the non‐linear regime.
Abstract Quantum criticality has attracted considerable attention both theoretically and experimentally as a way to describe part of the phase diagram of strongly correlated systems. A scale‐invariant fluctuation spectrum at a quantum critical point (QCP) implies the absence of any intrinsic scale. Any experimental probe may therefore create an out‐of‐equilibrium setting; the system would be in a non‐linear response regime, which violates the fluctuation–dissipation theorem (FDT). Here, we study this violation and related out‐of equilibrium phenomena in a single‐electron transistor (SET) with ferromagnetic leads, which can be tuned through a quantum phase transition. We review the breakdown of the FDT and study the universal behavior of the fluctuation–dissipation relation of various correlators in the quantum critical regime. In particular, we explore the concept of effective temperature as a means to extend the FDT into the non‐linear regime.
We study the out-of-equilibrium steady-state properties of the Bose-Fermi-Kondo model, describing a local magnetic moment coupled to two ferromagnetic leads that support bosonic (magnons) and fermionic (Stoner continuum electrons) low-energy excitations. This model describes the destruction of the Kondo effect as the coupling to the bosons is increased. Its phase diagram comprises three non-trivial fixed points. Using a dynamical large- N approach on the Keldysh contour, we study two different non-equilibrium setups: a) a finite bias voltage and b) a finite temperature gradient, imposed across the leads. The scaling behavior of the charge and energy currents is identified and characterized for all fixed points. We report the existence of a fixed-point–dependent effective temperature, defined though the fluctuation-dissipation relations of the local spin-susceptibility in the scaling regime, which permits to recover the equilibrium behavior of both dynamical and static spin-susceptibilities.
We study the out-of-equilibrium steady-state properties of the Bose-Fermi-Kondo model, describing a local magnetic moment coupled to two ferromagnetic leads that support bosonic (magnons) and fermionic (Stoner continuum electrons) low-energy excitations. This model describes the destruction of the Kondo effect as the coupling to the bosons is increased. Its phase diagram comprises three non-trivial fixed points. Using a dynamical large-N approach on the Keldysh contour, we study two different non-equilibrium setups: a) a finite bias voltage and b) a finite temperature gradient, imposed across the leads. The scaling behavior of the charge and energy currents is identified and characterized for all fixed points. We report the existence of a fixed-point-dependent effective temperature, defined though the fluctuation-dissipation relations of the local spin-susceptibility in the scaling regime, which permits to recover the equilibrium behavior of both dynamical and static spin-susceptibilities. Copyright (c) EPLA, 2013
We investigate bias-driven non-equilibrium quantum phase transitions in a paradigmatic quantum-transport setup: an interacting quantum dot coupled to non-interacting metallic leads. Using the Random Phase Approximation, which is exact in the limit of a large number of dot levels, we map out the zero-temperature non-equilibrium phase diagram as a function of interaction strength and applied bias. We focus our analysis on the behavior of the charge susceptibility and the current noise in the vicinity of the transition. Remarkably, despite the intrinsically non-equilibrium nature of the steady state, critical charge fluctuations admit an effective-temperature description, Teff(T,V), that collapses the steady-state behavior onto its equilibrium form. In sharp contrast, current fluctuations exhibit genuinely non-equilibrium features: the fluctuation-dissipation ratio becomes negative in the ordered phase, corresponding to a negative effective temperature for the current degrees of freedom. These results establish current noise as a sensitive probe of critical fluctuations at non-equilibrium quantum phase transitions and open new directions for exploring voltage-driven critical phenomena in quantum transport systems.
Quantum critical systems out of equilibrium are of extensive interest, but are difficult to study theoretically. We consider here the steady-state limit of a single-electron transistor with ferromagnetic leads. In equilibrium (i.e., bias voltage V = 0), this system features a continuous quantum phase transition with a critical destruction of the Kondo effect. We construct an exact quantum Boltzmann treatment in a dynamical large-N limit, and determine the universal scaling functions of both the nonlinear conductance and fluctuation-dissipation ratios. We also elucidate the decoherence properties as encoded in the local spin response.
We examine the Hall conductivity of a macroscopic two-dimensional quantum system and show that the observed quantities can sometimes violate the fluctuation dissipation theorem (FDT), even in the linear response (LR) regime infinitesimally close to equilibrium. At low temperature and in strong magnetic field, which are experimentally accessible, the violation can be by an order of magnitude larger than the Hall conductivity itself. We further generalize the results and obtain a necessary condition for such large-scale violation to happen. This violation is a genuine quantum phenomenon that appears on a macroscopic scale when the time-reversal symmetry is broken (by, e.g., a magnetic field). Our results are not only bound to the development of the fundamental issues of nonequilibrium physics, but the idea is also meaningful for practical applications, since the FDT is widely used for the estimation of noises from the LRs. We give an alternative formula evaluating precisely the fluctuations from the LRs even in the quantum systems with large FDT violation.
Quantum Phase Transitions Quantum phase transitions, in contrast to temperature-driven critical phenomena, occur due to a competition between different parameters describing the basic interactions of the system. Their specific feature is the quantum character of the critical fluctuations. This implies, through the uncertainty principle, that energy fluctuations and time are coupled. Then at zero temperature time plays a crucial and fundamental role, the static properties being entangled with the dynamics (Continentino, 1994a; Sondhi et al ., 1997; Sachdev, 1999). In this book we are mainly interested in quantum phase transitions that occur in electronic many-body systems and how scaling concepts can be useful to understand their properties close to these transitions (Continentino, 1994a). Even though a similar approach has been used in the case of interacting bosons (Fisher et al ., 1989) the fermionic problem has its own idiosyncrasies and difficulties. For example, there is no natural order parameter associated with the localisation transition in the electronic case, while bosons at zero temperature are either localised or superfluid so that the superfluid order parameter can be used to distinguish between both phases. If the results of the study of quantum phase transitions were restricted to zero temperature, this would be an interesting but purely academic area of research. What is really exciting about this subject is the effect of quantum critical points (QCP) in the finite temperature phase diagram of actual physical systems, even far away from the QCP (Freitas, 2015). As we will show, there is a special line in this phase diagram, the quantum critical trajectory , where the temperature dependence of the thermodynamic and transport properties is governed by the quantum critical exponents, i.e. those associated with the QCP. This and the observed crossover effects induced by temperature in the non-critical side of the phase diagram of a material with a QCP are sufficient to make the study of quantum phase transitions an inevitable subject. We start this chapter by introducing the scaling theory of quantum critical phenomena, since scaling concepts are used throughout this book.