Aditi Mitra

Nonequilibrium quantum criticality in open electronic systems.

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.

Dissipative Floquet Topological Systems

Motivated by recent pump-probe spectroscopies, we study the effect of phonon dissipation and potential cooling on the nonequilibrium distribution function in a Floquet topological state. To this end, we apply a Floquet kinetic equation approach to study two dimensional Dirac fermions irradiated by a circularly polarized laser, a system which is predicted to be in a laser induced quantum Hall state. We find that the initial electron distribution shows an anisotropy with momentum dependent spin textures whose properties are controlled by the switching-on protocol of the laser. The phonons then smoothen this out leading to a non-trivial isotropic nonequilibrium distribution which has no memory of the initial state and initial switch-on protocol, and yet is distinct from a thermal state. An analytical expression for the distribution at the Dirac point is obtained that is relevant for observing quantized transport.

Mode-Coupling-Induced Dissipative and Thermal Effects at Long Times after a Quantum Quench

An interaction quench in a Luttinger liquid can drive it into an athermal steady state. We analyze the effects on such an out of equilibrium state of a mode coupling term due to a periodic potential. Employing a perturbative renormalization group approach we show that even when the periodic potential is an irrelevant perturbation in equilibrium, it has important consequences on the athermal steady state as it generates a temperature as well as a dissipation and hence a finite lifetime for the bosonic modes.

Out-of-equilibrium electrons and the Hall conductance of a Floquet topological insulator

Graphene irradiated by a circularly polarized laser has been predicted to be a Floquet topological insulator showing a laser-induced quantum Hall effect. A circularly polarized laser also drives the system out of equilibrium, resulting in nonthermal electron distribution functions that strongly affect transport properties. Results are presented for the Hall conductance for two different cases. One is for a closed system, such as a cold-atomic gas, where transverse drift due to nonzero Berry curvature can be measured in time-of-flight measurements. For this case the effect of a circularly polarized laser that has been suddenly switched on is studied. The second is for an open system coupled to an external reservoir of phonons. While for the former the Hall conductance is far from the quantized limit, for the latter, coupling to a sufficiently low temperature reservoir of phonons is found to produce effective cooling, and thus an approach to the quantum limit, provided the frequency of the laser is large as compared to the bandwidth. For laser frequencies comparable to the bandwidth, strong deviations from the quantum limit of conductance are found even for a very low temperature reservoir, with the precise value of the Hall conductance determined by a competition between reservoir-induced cooling and the excitation of photocarriers by the laser. For the closed system, the electron distribution function is determined by the overlap between the initial wave function and the Floquet states, which can result in a Hall conductance which is opposite in sign to that of the open system.

Quantum quenches in an XXZ spin chain from a spatially inhomogeneous initial state

Results are presented for the nonequilibrium dynamics of a quantum XXZ -spin chain whose spins are initially arranged in a domain wall profile via the application of a magnetic field in the z direction, which is spatially varying along the chain. The system is driven out of equilibrium in two ways: a). by rapidly turning off the magnetic field, b). by rapidly quenching the interactions at the same time as the magnetic field is turned off. The time evolution of the domain wall profile as well as various two-point spin correlation functions are studied by the exact solution of the fermionic problem for the XX chain and via a bosonization approach and a mean-field approach for the XXZ chain. At long times the magnetization is found to equilibrate (reach the ground state value), while the two-point correlation functions in general do not. In particular, for quenches within the gapless XX phase, the spin correlation function transverse to the z direction acquires a spatially inhomogeneous structure at long times whose details depend on the initial domain wall profile. The spatial inhomogeneity is also recovered for the case of classical spins initially arranged in a domain wall profile and shows that the inhomogeneities arise due to the dephasing of transverse spin components as the domain wall broadens. A generalized Gibbs ensemble approach is found to be inadequate in capturing this spatially inhomogeneous state.

Correlation functions in the prethermalized regime after a quantum quench of a spin chain

Results are presented for a two-point correlation function of a spin-chain after a quantum quench for an intermediate time regime where inelastic effects are weak. A Callan-Symanzik like equation for the correlation function is explicitly constructed which is used to show the appearance of three distinct scaling regimes. One is for spatial separations within a light-cone, the second is for spatial separations on the light-cone, and the third is for spatial separations outside the light-cone. In these three regimes, the correlation function is found to decay with power-laws with nonequilibrium exponents that differ from those in equilibrium, as well as from those obtained from quenches in a quadratic Luttinger liquid theory. A detailed discussion is presented on how the existence of scaling depends on the properties of the initial state before the quench.

Hydrodynamic long-time tails after a quantum quench

After a quantum quench, a sudden change of parameters, generic many particle quantum systems are expected to equilibrate. A few collisions of quasiparticles are usually sufficient to establish approximately local equilibrium. Reaching global equilibrium is, however, much more difficult as conserved quantities have to be transported for long distances to build up a pattern of fluctuations characteristic for equilibrium. Here we investigate the quantum quench of the one-dimensional bosonic Hubbard model from infinite to finite interaction strength U using semiclassical methods for weak, and exact diagonalization for strong quenches. Equilibrium is approached only slowly, as t^{-1/2} with subleading corrections proportional to t^{-3/4}, consistent with predictions from hydrodynamics. We show that these long-time tails determine the relaxation of a wide range of physical observables.

Aging and coarsening in isolated quantum systems after a quench: Exact results for the quantum O(N) model with N → ∞.

The nonequilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N, the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.

Optical Hall conductivity of a Floquet topological insulator

Results are presented for the optical Hall conductivity of a Floquet topological insulator (FTI) for an ideal closed quantum system, as well as an open system in a nonequilibrium steady-state with a reservoir. The steady-state, even for the open system, is strongly dependent on the topological phase of the FTI, with certain phases showing a remarkable near-cancellation from pockets of Berry-curvature of opposite signs, leading to a suppressed low-frequency Hall conductivity, that also shows an anomalous temperature dependence, by increasing as the temperature of the reservoir is increased. Such a behavior is in complete contrast to heating, and arises because of a strong modification of the effective system-reservoir coupling by the laser. The Berry curvature of the Floquet modes is time-dependent, and its frequency components are found to control the main features of the high-frequency Hall conductivity.

Current-driven quantum criticality in itinerant electron ferromagnets

We determine the effect of an in-plane current flow on the critical properties of a 2d itinerant electron system near a ferromagnetic-paramagnetic quantum critical point. We study a model in which a nonequilibrium steady state is established as a result of exchange of particles and energy with an underlying substrate. the current