Out-of-equilibrium dynamics in a quantum impurity model: Numerics for particle transport and entanglement entropy

Abstract

We investigate the out-of-equilibrium properties of a simple quantum impurity model, the interacting resonant level model. We focus on the scaling regime, where the bandwidth of the fermions in the leads is larger than all the other energies, so that the lattice and the continuum versions of the model become equivalent. Using time-dependent density matrix renormalization group simulations initialized with states having different densities in the two leads we extend the results of Boulat, Saleur and Schmitteckert [Phys. Rev. Lett. 101, 140601 (2008)] concerning the current-voltage (I-V ) curves, for several values of the interaction strength U . We estimate numerically the Kondo scale TB and the exponent b(U ) associated to the tunneling of the fermions from the leads to the dot. Next we analyze the quantum entanglement properties of the steady states. We focus in particular on the entropy rate α, describing the linear growth with time of the bipartite entanglement in the system. We show that, as for the current, α/TB is described by some function of U and of the rescaled bias V /TB. Finally, the spatial structure of the entropy profiles is discussed. arXiv:1707.06111v2 [cond-mat.str-el] 5 Dec 2017 J. From now we take J = 1 = , thus defining the unit of time and energy. Left leadRight lead dot J J' J' J U

Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

“…When presenting our results in the next section, we compare them to the prior work in detail. We remark that inhomogeneous quenches in one-dimensional systems are being addressed in a wider context of interacting integrable models such as the XXZ chain [42,43] (the result of the latter reference for the Loschmidt echo is consistent with our result in the appropriate limit) and nonintegrable models such as the interacting resonant level model [44][45][46][47], nonintegrable Ising spin chain [48] and various models of the molecular and superconducting junctions [49][50][51][52].…”

“…They should be distinguished from transient oscillations observed e.g. in [46,70] which vanish at large times. The frequency of persistent oscillations of the current is determined by the energy of bound states and does not depend on the chemical potential (filling).…”

Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

“…[26]. Technically, we typically use systems of size L = 800 sites, Trotter time-step dt = 0.2 (matrix-product operator scheme W II [34] at order 4 [35]), a matrix-product state (MPS) truncation parameter equal to 10 −10 or 10 −11 and maximum bond dimension from 1000 to 2500. These state-of-the art simulations are pushed up to t = 300.…”

Quench dynamics of spin in quantum dots coupled to spin-polarized leads

“…However, an accurate description of dynamics in such systems poses a considerable challenge due to electronic correlations. Recently, there have been significant advances in this regard [25][26][27][28][29][30][31][32][33], especially by resorting to various renormalization group schemes [34][35][36][37][38][39][40][41][42][43][44].…”