Using a combination of numerically exact and renormalization-group techniques we study the nonequilibrium transport of electrons in an one-dimensional interacting system subject to a quasiperiodic potential. For this purpose we calculate the growth of the mean-square displacement as well as the melting of domain walls. While the system is nonintegrable for all studied parameters, there is no finite region of parameters for which we observe diffusive transport. In particular, our model shows a rich dynamical behavior crossing over from superdiffusion to subdiffusion. We discuss the implications of our results for the general problem of many-body localization, with a particular emphasis on the rare region Griffiths picture of subdiffusion.Introduction. -The finite energy transport properties of quantum-mechanical systems generally fall into one of the three standard categories: ballistic, diffusive, and the complete absence of transport altogether. Ballistic transport is only possible in special, so-called integrable cases (such as free fermions) where an extensive set of local conserved quantities prevents currents from scattering. Interacting, clean systems are generically diffusive, while the cessation of transport is a hallmark of systems that completely fail to equilibrate, such as those that undergo Anderson localization [1]. The study of the transition between such regimes has been energized by the recent focus on systems that undergo many-body localization (MBL) [2][3][4]. In the standard quenched disordered variants of such systems, dynamical behavior is observed that exhibits a rich set of distinct transport behaviors [5][6][7][8][9]. Interacting quasiperiodic (QP) systems are also believed to exhibit similar behavior, and are the basis for several recent experimental studies on MBL [10,11]. Unfortunately, very little is known about transport in such systems. Here, we fill this vital gap via a finite-temperature version [12][13][14] of the time-dependent matrix renormalization group (tDMRG) [15,16] as well as the functional renormalization group (FRG) [17,18].Model. -We consider a one-dimensional model of spinless fermions, subject to a quasiperiodic potential (QP),

No abstract

We investigate the thermodynamics and transient dynamics of the (unbiased) Ohmic two-state system by exploiting the equivalence of this model to the interacting resonant level model. For the thermodynamics, we show, by using the numerical renormalization group (NRG) method, how the universal specific heat and susceptibility curves evolve with increasing dissipation strength, α, from those of an isolated two-level system at vanishingly small dissipation strength, with the characteristic activated-like behavior in this limit, to those of the isotropic Kondo model in the limit α → 1 − . At any finite α > 0, and for sufficiently low temperature, the behavior of the thermodynamics is that of a gapless renormalized Fermi liquid. Our results compare well with available Bethe ansatz calculations at rational values of α, but go beyond these, since our NRG calculations, via the interacting resonant level model, can be carried out efficiently and accurately for arbitrary dissipation strengths 0 ≤ α < 1 − . We verify the dramatic renormalization of the low-energy thermodynamic scale T0 with increasing α, finding excellent agreement between NRG and density matrix renormalization group (DMRG) approaches. For the zero-temperature transient dynamics of the two-level system, P (t) = σz(t) , with initial-state preparation P (t ≤ 0) = +1, we apply the time-dependent extension of the NRG (TDNRG) to the interacting resonant level model, and compare the results obtained with those from the noninteracting-blip approximation (NIBA), the functional renormalization group (FRG), and the time-dependent density matrix renormalization group (TD-DMRG). We demonstrate excellent agreement on short to intermediate time scales between TDNRG and TD-DMRG for 0 α 0.9 for P (t), and between TDNRG and FRG in the vicinity of α = 1/2. Furthermore, we quantify the error in the NIBA for a range of α, finding significant errors in the latter even for 0.1 ≤ α ≤ 0.4. We also briefly discuss why the long-time errors in the present formulation of the TDNRG prevent an investigation of the crossover between coherent and incoherent dynamics. Our results for P (t) at short to intermediate times could act as useful benchmarks for the development of new techniques to simulate the transient dynamics of spin-boson problems.

We introduce a method to evaluate the steady-state non-equilibrium Keldysh–Schwinger Green’s functions for infinite systems subject to both an electric field and a coupling to reservoirs. The method we present exploits a physical quasi-translation invariance, where a shift by one unit cell leaves the physics invariant if all electronic energies are simultaneously shifted by the magnitude of the electric field. Our framework is straightaway applicable to diagrammatic many-body methods. We discuss two flagship applications, mean-field theories as well as a sophisticated second-order functional renormalization group approach. The latter allows us to push the renormalization-group characterization of phase transitions for lattice fermions into the out-of-equilibrium realm. We exemplify this by studying a model of spinless fermions, which in equilibrium exhibits a Berezinskii–Kosterlitz–Thouless phase transition.

We show that the single-particle spectral properties of gapless one-dimensional Fermi systems in the Luttinger liquid state reached at intermediate times after an abrupt quench of the two-particle interaction are highly indicative of the unusual nonequilibrium nature of this state. The line shapes of the momentum integrated and resolved spectral functions strongly differ from their ground state as well as finite temperature equilibrium counterparts. Using an energy resolution improved version of radio-frequency spectroscopy of quasi one-dimensional cold Fermi gases it should be possible to experimentally identify this nonequilibrium state by its pronounced spectral signatures.PACS numbers: 71.10. Pm, 02.30.Ik, 03.75.Ss, 05.70.Ln Closed one-dimensional (1d) Fermi systems are promising candidates to realize unusual nonequilibrium steady states. In many 1d out of equilibrium systems integrals of motion beyond energy conservation hinder that observables and the reduced density matrix of subsystems relax to values expected for one of the canonical ensembles. Even for generic models, in which those are absent, the restricted phase space available for scattering at least delays thermalization. An intensively studied question is under which conditions 1d systems prepared in the ground state of an initial Hamiltonian H i and brought out of equilibrium by time-evolving them with H f of similar form but with changed parameters eventually thermalize [1][2][3][4][5][6][7][8][9][10][11][12]. Quench protocols of this type can experimentally be realized in cold atomic gases [13, 14]. Increasing theoretical evidence was gathered that in an extended time regime following the after-quench transient one a quasi stationary state exists which does show nonthermal behavior [4, 8, 10, 12,15]. Here we are interested in the properties of this intermediate time steady state regardless if it is the true steady state or if further relaxation sets in on a well separated larger time scale [10]. For nongeneric models which are mappable on free ones the system is stuck in this state for all further times; it can be described by a generalized Gibbs ensemble (GGE) [1,2, 5,[16][17][18][19][20][21]. If the same holds for more complex models which cannot directly be linked to noninteracting ones but are characterized by an infinite set of local conservation laws is heavily investigated [2,[22][23][24][25].Already in equilibrium 1d metals are peculiar. They fall into the Luttinger liquid (LL) universality class which is characterized by power-law decay of correlation functions with interaction dependent exponents [26,27]. The Tomonaga-Luttinger model (TLM), a field theoretical model for which the exact computation of correlation functions is straightforward using bosonization, constitutes the low-energy fixed point model under a renormalization group (RG) procedure of all microscopic models falling into the LL class [26,27]. The power-law decay of the TLM's ground state lesser Green function, with the field operator ψ in the Heisenberg picture, le...