We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the non-interacting case, due to Wannier-Stark localization, the single-particle wave functions are exponentially localized even though the model has no quenched disorder. We show that this system remains localized in the presence of interactions and exhibits physics analogous to models of conventional many-body localization (MBL). In particular, the entanglement entropy grows logarithmically with time after a quench, albeit with a slightly different functional form from the MBL case, and the level statistics of the many-body energy spectrum are Poissonian. We moreover predict that a quench experiment starting from a chargedensity wave state would show results similar to those of Schreiber et al. [Science 349, 842 (2015)]. arXiv:1808.01250v2 [cond-mat.dis-nn]

No abstract

We consider a single atom in an optical lattice, subject to a harmonic trapping potential. The problem is treated in the tight-binding approximation, with an extra parameter kappa denoting the strength of the harmonic trap. It is shown that the kappa-->0 limit of this problem is singular, in the sense that the density of states for a very shallow trap (kappa-->0) is qualitatively different from that of a translationally invariant lattice (kappa=0). The physics of this difference is discussed, and densities of states and wave functions are exhibited and explained.

This paper is concerned with the out-of-equilibrium two-lead Kondo model, considered as a model of a quantum dot in the Kondo regime. We revisit the perturbative expansion of the dot's magnetization, and conclude that, even at order 0 in the Kondo interactions, the magnetization is not given by the usual equilibrium result. We use the Schwinger-Keldysh method to derive a Dyson equation describing the steady state induced by the voltage between the two leads, and thus present the correct procedure for calculating perturbative expansions of steady-state properties of the system.where angle-brackets . . . denote an expectation value taken in the steady (i.e. long-time) state of the system. M Pauli is simply the Pauli paramagnetic contribution from the lead electrons which would be present even in the absence of the impurity, and which we therefore exclude from M tot . We consider the perturbative expansions of these steady state quantities; more precisely, we define:

Using the Majorana fermion representation of spin-1/2 local moments, we show how it is possible to directly read off the dynamic spin correlation and susceptibility from the one-particle propagator of the Majorana fermion. We illustrate our method by applying it to the spin dynamics of a nonequilibrium quantum dot, computing the voltage-dependent spin relaxation rate and showing that, at weak coupling, the fluctuation-dissipation relation for the spin of a quantum dot is voltagedependent. We confirm the voltage-dependent Curie susceptibility recently found by Parcollet and Hooley [Phys. Rev. B 66, 085315 (2002)].PACS numbers: 03.65. Ca, 72.15.Qm, 73.63.Kv, 76.20.+q The mathematical difficulties of representing spins in many body physics have long been recognized. The essence of the problem is that spin operators are nonabelian: they do not obey Wick's theorem and an expectation value of the product of many spin operators cannot be decomposed into products of two-operator expectation values, even within a free theory.A conventional response to this difficulty is to represent spins as bilinears of fermions [1] or as bosons [2]. One of the disadvantages of these approaches is that the Hilbert space of the fermions or bosons needs to be restricted by the application of constraints [3,4,5]. Another difficulty is the "vertex problem", which arises in the context of spin dynamics and spin relaxation. Once the spins are represented as bilinears, the spin-spin correlation functions are represented by two-particle Green's functions. The calculation of these quantities requires a knowledge of both the four-leg vertex and the single-particle Green's function. Typically, the vertex is simply neglected, or treated in a very approximate fashion.An alternative approach is to take advantage of the anticommuting properties of Pauli matrices, writing the spin operator in terms of Majorana fermions [6,7,8,9,10],where η = (η 1 , η 2 , η 3 ) is a triplet of Majorana fermions which satisfy {η a , η b } = δ ab . This representation does not require the imposition of a constraint: the fact that S 2 = 3/4 follows directly from the operator properties of the Majorana fermions. In this letter, we show how this representation also solves the vertex problem. To demonstrate this, we employ an alternative derivation [11] of the Majorana spin representation. Consider a spin-1/2 operator S with dynamics described by a Hamiltonian H. Let us now introduce a single Majorana fermion Φ which lives in a completely different Hilbert space, commuting with S and H. It follows that Φ is a fermionic constant of motion, dΦ/dt = −i[H, Φ] = 0: an object of fixed magnitude Φ 2 = 1/2 which anticommutes with all other fermion operators. We may now identify η in (1) with the operator identityWe may confirm that {η a , η b } = δ ab using the anticommuting algebra of spin-1/2 operators {S a , S b } = 1 2 δ ab . Furthermore, using the SU(2) algebra of spins, η × η = 2 S × S = 2i S, from which (1) follows immediately. As a last step in the derivation, we note tha...

We examine the two-lead Kondo model for a dc-biased quantum dot in the Coulomb blockade regime. From perturbative calculations of the magnetic susceptibility, we show that the problem retains its strong-coupling nature, even at bias voltages larger than the equilibrium Kondo temperature. We give a speculative discussion of the nature of the renormalization group flows and the strong-coupling state that emerges at large voltage bias.

No abstract

No abstract