Kubo-Martin-Schwinger relation for an interacting mobile impurity

We develop a microscopic theory of a quantum impurity propagating in a one-dimensional Bose liquid. As a result of scattering off thermally excited quasiparticles, the impurity experiences the friction. We find that, at low temperatures, the resulting force scales either as the fourth or the eighth power of temperature, depending on the system parameters. For temperatures higher than the chemical potential of the Bose liquid, the friction force is a linear function of tempera...

We investigate the effects of localized integrability-breaking perturbations on the large times dynamics of thermodynamic quantum and classical systems. In particular, we suddenly activate an impurity which breaks the integrability of an otherwise homogeneous system. We focus on the large times dynamics and on the thermalization properties of the impurity, which is shown to have mere perturbative effects even at infinite times, thus preventing thermalization. This is in clear...

We study the dynamics of a non-magnetic impurity interacting with the surface states of a 3D and 2D topological insulator. Employing the linked cluster technique we develop a formalism for obtaining the Greens function of the mobile impurity interacting with the low-energy Dirac fermions. We show that for the non-recoil case in 2D, similar to the case involving the parabolic spectrum, the Greens function in the long-time limit has a power-law decay in time implying the breakd...

We compute the DC conductance with two different methods, which both exploit the integrability of the theories under consideration. On one hand we determine the conductance through a defect by means of the thermodynamic Bethe ansatz and standard relativistic potential scattering theory based on a Landauer transport theory picture. On the other hand, we propose a Kubo formula for a defect system and evaluate the current-current two-point correlation function it involves with t...

The mapping of steady-state nonequilibrium dynamical mean-field theory from the lattice to the impurity is described in detail. Our focus is on the case with current flow under a constant dc electric field of arbitrary magnitude. In addition to formulating the problem via path integrals and functional derivatives, we also describe the distribution function dependence of the retarded and advanced Green's functions. Our formal developments are exact for the Falicov-Kimball mode...

We generalize the recently developed inchworm quantum Monte Carlo method to the full Keldysh contour with forward, backward, and equilibrium branches to describe the dynamics of strongly correlated impurity problems with time dependent parameters. We introduce a method to compute Green's functions, spectral functions, and currents for inchworm Monte Carlo and show how systematic error assessments in real time can be obtained. We then illustrate the capabilities of the algorit...

A Luttinger Liquid coupled to a quantum impurity describes a large number of physical systems. The Hamiltonian consists of left- and right-moving fermions interacting among themselves via a density-density coupling and scattering off a localised transmitting and reflecting impurity. We solve exactly the Hamiltonian by means of an incoming-outgoing scattering Bethe basis which properly incorporates all scattering processes. A related model, the Weak-Tunnelling model, wherein t...

We use a mobile impurity or depleton model to study elementary excitations in one-dimensional integrable systems. For Lieb-Liniger and bosonic Yang-Gaudin models we express two phenomenological parameters characterising renormalised inter- actions of mobile impurities with superfluid background: the number of depleted particles, $N$ and the superfluid phase drop $\pi J$ in terms of the corresponding Bethe Ansatz solution and demonstrate, in the leading order, the absence of t...

We introduce an integrable model of spin-polarized interacting electrons subject to a spin-conserving spin-orbit interaction. Using Bethe Ansatz and conformal field theory we calculate the exact large-time single-electron and density correlations and find that while the spin-orbit interaction enhances the single-electron Green's function, the density correlations get suppressed. Adding a localized impurity and coupling it to the electrons so that integrability is preserved, t...

We present a novel technique for the calculation of dynamical correlation functions of quantum impurity systems in equilibrium with Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson chain. In contrast to all previous methods, it does not suffer from overcounting of excitation. By construction, it always fulfills sum rules for spectral functions. Furthermore, it accurately reproduces local thermodynamic expectation values,...