Nonequilibrium properties of correlated quantum matter are being intensively investigated because of the rich interplay between external driving and the many-body correlations. Of particular interest is the nonequilibrium behavior near a quantum critical point (QCP), where the system is delicately balanced between different ground states. We present both an analytical calculation of the nonequilibrium steady-state current in a critical system and experimental results to which the theory is compared. The system is a quantum dot coupled to resistive leads: a spinless resonant level interacting with an ohmic dissipative environment. A two channel Kondo-like QCP occurs when the level is on resonance and symmetrically coupled to the leads, conditions achieved by fine-tuning using electrostatic gates. We calculate and measure the nonlinear current as a function of bias ($I$-$V$ curve) at the critical values of the gate voltages corresponding to the QCP. The quantitative agreement between the experimental data and the theory, with no fitting parameter, is excellent. As our system is fully accessible to both theory and experiment, it provides an ideal setting for addressing nonequilibrium phenomena in correlated quantum matter.
We develop a mapping of quantum steady-state nonequilibrium to an effective equilibrium and solve the problem using a quantum simulation technique. A systematic implementation of the nonequilibrium boundary condition in steady-state is made in the electronic transport on quantum dot structures. This formulation of quantum manybody problem in nonequilibrium enables the use of existing numerical quantum manybody techniques. The algorithm coherently demonstrates various transport behaviors from phonon-dephasing to I-V staircase and phonon-assisted tunneling.
Based on the recent paper (Phys. Rev. Lett. 102, 216803, (2009)), we study the nonequilibrium occupation number and charge susceptibility of a resonance level close to a dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a de-localized phase for weak dissipation and a localized phase for strong dissipation. The resonance level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic bosonic bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. Within the nonequ…
The carrier generation in insulators subjected to strong electric fields is characterized by the Landau-Zener formula for the tunneling probability with a nonperturbative exponent. Despite its long history with diverse applications and extensions, study of nonequilibrium steady states and associated current response in the presence of the generated carriers has been mainly limited to numerical simulations so far. Here, we develop a framework to calculate the nonequilibrium Green's function of generic insulating systems under a DC electric field, in the presence of a fermionic reservoir. Using …
We extend the imaginary-time formulation of the equilibrium quantum many-body theory to steady-state nonequilibrium with an application to strongly correlated transport. By introducing Matsubara voltage, we keep the finite chemical potential shifts in the Fermi-Dirac function, in agreement with the Keldysh formulation. The formulation is applied to strongly correlated transport in the Kondo regime using the quantum Monte Carlo method.
By mapping steady-state nonequilibrium to an effective equilibrium, we formulate nonequilibrium problems within an equilibrium picture where we can apply existing equilibrium many-body techniques to steady-state electron transport problems. We study the analytic properties of many-body scattering states, reduce the boundary condition operator in a simple form and prove that this mapping is equivalent to the correct linear-response theory. In an example of infinite-U Anderson impurity model, we approximately solve for the scattering state creation operators, based on which we derive the bias op…
We calculate the finite-frequency current noise of a nonequilibrium resonance-level quantum dot close to a dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a de-localized phase for weak dissipation and a localized phase for strong dissipation. The resonance-level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic boson bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. To compute the finite-frequency noise, we combine two recently developed Functiona…
Understanding strongly correlated systems driven out of equilibrium is a challenging task necessitating the simultaneous treatment of quantum mechanics,dynamical constraints and strong interactions. A Mott insulator subjected to a uniform and static electric field is prototypical, raising key questions such as the fate of Bloch oscillations with increasing correlation strength, the approach to a steady state DC transport regime and the role of dissipation in it, and electric field driven phase transitions. We develop here an effective large-N Keldysh field theory for studying nonequilibrium tr…
We develop an exact non-perturbative framework to compute steady-state properties of quantum-impurities subject to a finite bias. We show that the steady-state physics of these systems is captured by nonequilibrium scattering eigenstates which satisfy an appropriate Lippman-Schwinger equation. Introducing a generalization of the equilibrium Bethe-Ansatz - the Nonequilibrium Bethe-Ansatz (NEBA), we explicitly construct the scattering eigenstates for the Interacting Resonance Level model and derive exact, nonperturbative results for the steady-state properties of the system.
We examine the recently proposed imaginary-time formulation for strongly correlated steady-state nonequilibrium for its range of validity and discuss significant improvements in the analytic continuation of the Matsubara voltage as well as the fermionic Matsubara frequency. The discretization error in the conventional Hirsch-Fye algorithm has been compensated in the Fourier transformation with reliable small frequency behavior of self-energy. Here we give detailed discussions for generalized spectral representation ansatz by including high order vertex corrections and its numerical analytic co…
We find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single bar…
Nonperturbative dynamic theory has a particular advantage in studying the transport in a quantum impurity system in a steady state. Here, we develop a new approach for obtaining the retarded Green's function expressed in resolvent form. We use the Heisenberg picture to facilitate dynamic theory and propose a new systematic method of collecting the basis vectors spanning the Liouville space, which is the most crucial step in obtaining the resolvent Green's function. We obtain all the linearly independent basis vectors for studying the single-impurity Anderson models with one and two reservoirs.…
A deeper theoretical understanding of driven-dissipative interacting systems and their nonequilibrium phase transitions is essential both to advance our fundamental physics understanding and to harness technological opportunities arising from optically controlled quantum many-body states. This paper provides a numerical study of dynamical phases and the transitions between them in the nonequilibrium steady state of the prototypical two-dimensional Heisenberg antiferromagnet with drive and dissipation. We demonstrate a nonthermal transition that is characterized by a qualitative change in the m…
Floquet engineering of closed quantum systems can lead to the formation of long-lived prethermal states that, in general, eventually thermalize to infinite temperature. Coupling these driven systems to dissipative baths can stabilize such states, establishing a true nonequilibrium steady state. We demonstrate that in a certain strongly interacting lattice model coupled to a bath and driven by an electric field, such steady states can have the remarkable property that the cycle-averaged rate of energy transfer between the lattice and the baths vanishes. Despite this, we show that these states r…
The numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but faces limitations for steady-state nonequilibrium, arising, e.g., due to an applied bias voltage. We show that these limitations can be overcome by describing the thermal leads using a thermofield approach, integrating out high energy modes using NRG, and then treating the nonequilibrium dynamics at low energies using a quench protocol, implemented using the time-dependent density matrix renormalization group (tDMRG). This yields quantitatively reliable results for the current (wit…
The formalism for exactly calculating the retarded and advanced Green's functions of strongly correlated lattice models in a uniform electric field is derived within dynamical mean-field theory. To illustrate the method, we solve for the nonequilibrium density of states of the Hubbard model in both the metallic and Mott insulating phases at half-filling (with an arbitrary strength electric field) by employing the numerical renormalization group as the impurity solver. This general approach can be applied to any strongly correlated lattice model in the limit of large dimensions.
The existence of more than one steady-state in a many-body quantum system driven out-of-equilibrium has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. In this Letter, we combine a reduced density matrix formalism with the multilayer multiconfiguration time-dependent Hartree method to address this problem. This allows to obtain a converged numerical solution of the nonequilibrium dynamics. Considering a generic model for quantum transport through a quantum dot with electron-phonon interaction, we prove that a unique steady…
We present a framework to determine nonequilibrium steady states in strongly correlated electron systems in the presence of dissipation. This is demonstrated for a correlated electron (Falicov-Kimball) model attached to a heat bath and irradiated by an intense pump light, for which an exact solution is obtained with the Floquet method combined with the nonequilibrium dynamical mean-field theory. On top of a Drude-like peak indicative of photometallization as observed in recent pump-probe experiments, new nonequilibrium phenomena are predicted to emerge, where the optical conductivity exhibits …
The nonequilibrium dynamics of correlated charge transfer along a one-dimensional chain in presence of a phonon environment is investigated within a dissipative Hubbard model. For this generalization of the ubiquitous spin-boson model the crucial role of symmetries is analysed in detail and corresponding invariant subspaces are identified. It is shown that the time evolution typically occurs in each of the disjunct subspaces independently leading e.g. asymptotically to a non-Boltzmann equilibrium state. Based on these findings explicit results are obtained for two interacting electrons by mean…
We calculate a nonequilibrium steady state of a quantum XX chain in the presence of dephasing and driving due to baths at chain ends. The obtained state is exact in the limit of weak driving while the expressions for one- and two-point correlations are exact for an arbitrary driving strength. In the steady state the magnetization profile and the spin current display diffusive behavior. Spin-spin correlation function on the other hand has long-range correlations which though decay to zero in either the thermodynamical limit or for equilibrium driving. At zero dephasing a nonequilibrium phase tr…
The mapping of steady-state nonequilibrium dynamical mean-field theory from the lattice to the impurity is described in detail. Our focus is on the case with current flow under a constant dc electric field of arbitrary magnitude. In addition to formulating the problem via path integrals and functional derivatives, we also describe the distribution function dependence of the retarded and advanced Green's functions. Our formal developments are exact for the Falicov-Kimball model. We also show how these formal developments are modified for more complicated models (like the Hubbard model).
We discuss current carrying non-equilibrium steady state of an open fermionic Hubbard chain that is strongly driven by markovian incoherent processes localized at the chain ends. An explicit form of exact many-body density operator for any value of the coupling parameter is presented. The structure of a matrix product form of the solution is encoded in terms of a novel diagrammatic technique which should allow for generalization to other integrable non-equillibrium models.
We describe a large family of nonequilibrium steady states (NESS) corresponding to forced flows over obstacles. The spatial structure at large distances from the obstacle is shown to be universal, and can be quantitatively characterised in terms of certain collective modes of the strongly coupled many body system, which we define in this work. In holography, these modes are spatial analogues of quasinormal modes, which are known to be responsible for universal aspects of relaxation of time dependent systems. These modes can be both hydrodynamical or non-hydrodynamical in origin. The decay leng…
Explicit matrix product ansatz is presented, in first two orders in the (weak) coupling parameter, for the non-equilibrium steady state of the homogeneous, nearest neighbor Heisenberg XXZ spin-1/2 chain driven by Lindblad operators which act only at the edges of the chain. The first order of the density operator becomes in thermodynamic limit an exact pseudo-local conservation law and yields -- via Mazur inequality -- a rigorous lower bound on the high temperature spin Drude weight. Such Mazur bound is a non-vanishing fractal function of the anisotropy parameter Delta for |Delta|<1.
We present a new variational method, based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate representation of the system evolution until the stationary state is attained, the algorithm directly targets the final state, thus allowing for a faster convergence when the steady state is a MPO with small bond dimension. Our numerical simulations for several dissipative spin models over a wide range of parameters illustrate the performance of the method and show t…
