Unbinding slave spins in the Anderson impurity model

We introduce and develop a slave-spin mean-field technique for describing a generic interacting two level systems under time-dependent drivings, where an auxiliary S = 1 spin is added to describe the localized character of the electrons. We show that the approach efficiently captures the main effects of the strong correlations as well as the dynamical nature of the driving, while remaining simple enough to allow for an analytical treatment. Our formalism provides a flexible solution method, which can be applied to different device configurations at an extremely small numerical cost. Furthermore, it leads to a very practical description of adiabatically driven systems in terms of frozen static solutions.

Section: Mean-field Dynamics: So Far We Have Just Introduced a New-lo...supporting

confidence: 56%

mentioning

confidence: 99%

Slave-spin-1 formulation: A simple approach to time-dependent transport through an interacting two-level system

Ludovico

Capone

2020

“…The proof of this equivalence follows the same steps of the equilibrium case, see Ref. 38 .However, we consider valuable to show, in the next section, the possibility to remove the constraint in the time-dependent average value of the charge current, defined in Eq. ( 9).…”

Section: The Modelmentioning

confidence: 81%

“…Indeed, as presented in section V C, the slave-spin mean-field evolution predicts, for large time, the existence of a steady-state due to the coupling of the dot with infinite contacts. Following the same reasoning of section III, the stationary mean-field approach consists in approximating 38 the ground-state wave function (23) with a factorized one:…”

Section: Mean-field For the Nonequilibrium Steady-statementioning

confidence: 99%

“…To the latter class of approaches belongs the nonequilibrium slave-spin technique for magnetic impurities we present in this paper. By means of a recently developed slave-spin technique 38 , we map without any constraint a single-orbital Anderson impurity model (AIM), characterized by a particle-hole symmetric hybridization with the contacts, onto a resonant level model coupled to a single quantum pseudospin. In this suitable representation, a simple self-consistent Hartree-Fock calculation is able to reproduce qualitatively the differential conductance of a single-orbital magnetic impurity both in the small and large bias regimes.…”

Section: Introductionmentioning

confidence: 99%

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Transport through a magnetic impurity: A slave-spin approach

Guerci

2019

Self Cite

We study transport across a magnetic impurity by means of a recently developed slave-spin technique that does not require any constraint. Within a conserving mean-field approximation we find a conductance that displays both the known zero-bias anomaly but also the expected peak at bias of order U . We extend the slave-spin mean-field approximation to study the out of equilibrium transient evolution of a quantum dot. We apply the method to investigate the time-evolution of a quantum dot induced by a time-dependent electrochemical potential applied to the contacts. Similarly to the time-dependent Gutzwiller approximation, the mean-field slave-spin dynamics is able to capture dissipation in the leads, so that a steady-state is reached after a characteristic relaxation time.arXiv:1901.03636v2 [cond-mat.mes-hall]

Exactly solvable Majorana-Anderson impurity models

Shankar¹,

Maciejko²

2019

Motivated by recent experimental progress in the realization of hybrid structures with a topologically superconducting nanowire coupled to a quantum dot, viewed through the lens of the emerging field of correlated Majorana fermions, we introduce a class of interacting Majorana-Anderson impurity models which admit an exact solution for a wide range of parameters, including on-site repulsive interactions of arbitrary strength. The model is solved by mapping it via the Z2 slave-spin method to a noninteracting resonant level model for auxiliary Majorana degrees of freedom. The resulting gauge constraint is eliminated by exploiting the transformation properties of the Hamiltonian under a special local particle-hole transformation. For a spin-polarized Kitaev chain coupled to a quantum dot, we obtain exact expressions for the dot spectral functions at both zero and finite temperature. We study how the interaction strength and localization length of the end Majorana zero mode affect physical properties of the dot, such as quasiparticle weight, double occupancy, and odd-frequency pairing correlations, as well as the local electronic density of states in the superconducting chain.Introduction.-The discovery of topological phases of quantum matter has led to a paradigm shift in condensed matter physics. The simplest such topological phase, the one-dimensional (1D) topological superconductor (SC) [1], hosts localized Majorana zero modes (MZMs) at its ends which can form a topological qubit immune to decoherence, with exciting prospects for quantum computation [2,3]. Strong evidence suggests MZMs have been observed in experiments on proximitized semiconductor nanowires [4] and ferromagnetic chains [5], following specific theoretical proposals [5][6][7].On the theoretical front, a new direction has emerged which explores the interplay of pure MZM physics, well understood from single-particle quantum mechanics, and electronic correlations [8]. Recently studied lattice models of interacting MZMs such as the Majorana-Hubbard [9][10][11][12][13][14] and 16] models may be relevant to describe Abrikosov vortex lattices in 2D topological SCs [17], where each vortex hosts an unpaired MZM [18,19]. Motivated by transport experiments on proximitized nanowires, another avenue of research has explored interacting Anderson-type quantum impurity models involving small numbers of MZMs coupled to dissipative baths, some of which are predicted to exhibit exotic Kondo effects [20][21][22]. A geometry of particular interest, that of an end MZM tunnelcoupled to a quantum dot (QD), is now experimentally accessible [23] and argued to directly probe the nonlocality of MZMs [24][25][26][27][28][29][30]. Existing theoretical studies of this problem have largely relied on mean-field approximations [27,28,30] or numerical methods [26,27] to treat correlation effects in the corresponding Anderson model [31]. Such studies also typically model the MZM as a unique on-site Majorana operator, whereas the MZM localization length is generically finite, as known...