Nonequilibrium pseudogap Anderson impurity model: A master equation tensor network approach

Abstract

We study equilibrium and nonequilibrium properties of the single-impurity Anderson model with a power-law pseudogap in the density of states. In equilibrium, the model is known to display a quantum phase transition from a generalized Kondo to a local moment phase. In the present work, we focus on the extension of these phases beyond equilibrium, i.e. under the influence of a bias voltage. Within the auxiliary master equation approach combined with a scheme based on matrix product states (MPS) we are able to directly address the current-carrying steady state. Starting with the equilibrium situation, we first corroborate our results by comparing with a direct numerical evaluation of ground state spectral properties of the system by MPS. Here, a scheme to locate the phase boundary by extrapolating the power-law exponent of the self energy produces a very good agreement with previous results obtained by the numerical renormalization group. Our nonequilibrium study as a function of the applied bias voltage is then carried out for two points on either side of the phase boundary. In the Kondo regime the resonance in the spectral function is splitted as a function of the increasing bias voltage. The local moment regime, instead, displays a dip in the spectrum near the position of the chemical potentials. Similar features are observed in the corresponding self energies. The Kondo split peaks approximately obey a power-law behavior as a function of frequency, whose exponents depend only slightly on voltage. Finally, the differential conductance in the Kondo regime shows a peculiar maximum at finite voltages, whose height, however, is below the accuracy level.

Electron-light interaction in nonequilibrium: exact diagonalization for time-dependent Hubbard Hamiltonians

“…27is the discrete analog of Eq. (11). For small times t, it can be approximated with sufficient accuracy by a Magnus-expansion of order zero [27], which gives…”

“…The description of these states necessitates nonequilibrium approaches, which are particularly demanding in cases where light brings a strongly correlated electronic system out of equilibrium. The approximate theoretical approaches to correlated systems are being successfully adapted to treat systems out of equilibrium (e.g., nonequilibrium dynamical mean-field theory (DMFT) [9], dynamical cluster approximation [10], auxiliary master equation approach [11], GW [12]). The numerically exact approaches, exact diagonalization (ED) [13], or density-matrix renormalization group [5,14], where the error can be systematically controlled, are still limited to relatively small system sizes or short times [15].…”

Reduced Dynamics of Full Counting Statistics

“…Research on numerical techniques for simulating nonequilibrium dynamics in impurity models is a lively and active field [18]. A few examples of paradigms where significant recent advances have been made are matrix product state representations [19][20][21][22][23][24][25], hierarchical equation of motion techniques [26][27][28][29][30] and quantum Monte Carlo algorithms [31][32][33][34][35][36][37][38][39][40][41][42]. Nevertheless, in many of the most successful methods it remains computationally difficult to reliably perform propagation to long times.…”

Performance of Reservoir Discretizations in Quantum Transport Simulations

“…Modern methods can accurately describe the atomic and band structure of many materials, often using density functional theory [1][2][3]. Moreover, dedicated many-body techniques, such as quantum Monte Carlo or tensor networks, can include contributions from explicit correlations [4][5][6][7][8][9][10][11]. The computational cost of these tools is nonetheless appreciable for large systems or long simulation timescales.…”

“…The computational cost of these tools is nonetheless appreciable for large systems or long simulation timescales. These limitations are particularly onerous for tensor networks, where an explicit treatment of the reservoirs will introduce many degrees of freedom [7][8][9][10][11][12][13][14][15].…”