Mobile impurities in integrable models

In this work, analytical expressions for the Green function of a Luttinger liquid are derived with one and two mobile impurities (heavy particles) using a combination of bosonization and perturbative approaches. The calculations are done in the random phase approximation (RPA) limit using the powerful non-chiral bosonization technique (NCBT) which is nothing but the resummation of the most singular parts of the RPA terms of the Green function expanded out in powers of the for...

We show that thermalization and the breakdown of integrability in the one dimensional Lieb-Liniger model caused by local three-body elastic interactions is suppressed by pairwise quantum correlations when approaching the strongly correlated regime. If the relative momentum $k$ is small compared to the two-body coupling constant $c$ the three-particle scattering state is suppressed by a factor of $(k/c)^{12}$. This demonstrates that in one dimensional quantum systems it is not...

A t-J model for correlated electrons with impurities is proposed. The impurities are introduced in such a way that integrability of the model in one dimension is not violated. The algebraic Bethe ansatz solution of the model is also given and it is shown that the Bethe states are highest weight states with respect to the supersymmetry algebra gl(2/1)

Hydrodynamics is an efficient theory for describing the large-scale dynamics of many-body systems. The equations of hydrodynamics at the Euler scale are often obtained phenomenologically under the assumption of local entropy maximisation. With integrability, this has led to the theory of generalised hydrodynamics (GHD), based on local generalised Gibbs ensembles. But deriving such equations from the microscopic dynamics itself remains one of the most important challenges of m...

We consider one dimensional interacting quantum fluids, such as the Lieb Liniger gas. By computing the low temperature limit of its (generalised) hydrodynamics we show how in this limit the gas is well described by a conventional viscous (Navier Stokes) hydrodynamic for density, fluid velocity and the local temperature, and the other generalised temperatures in the case of integrable gases. The dynamic viscosity is proportional to temperature and can be expressed in a univers...

We study a single impurity driven by a constant force through a 1D Bose gas using a Lieb-Liniger based approach. Our calculaton is exact in the interaction amongst the particles in the Bose gas, and is perturbative in the interaction between the gas and the impurity. In contrast to previous studies of this problem, we are able to handle arbitrary interaction strength for the Bose gas. We find very good agreement with recent experiments [Phys. Rev. Lett. 103, 150601 (2009)].

We consider interacting one-dimensional, spinless Fermi gases, whose low-energy properties are described by Luttinger liquid theory. We perform a systematic, in-depth analysis of the relation between the macroscopic, phenomenological parameters of Luttinger liquid effective field theory, and the microscopic interactions of the Fermi gas. In particular, we begin by explaining how to model effective interactions in one dimension, which we then apply to the main forward scatteri...

We consider a linearly-dispersing quantum impurity interacting through a contact density-density term with a one-dimensional (1D) superfluid described by the Tomonaga-Luttinger liquid theory. Using a linked cluster expansion we characterize the impurity dynamics by calculating approximate expressions for the single-particle Green's function and for the time evolution of the density profile. We show the existence of two different dynamical regimes: (i) a $\textit{quasiparticle...

The nonlinear Luttinger liquid phenomenology of one-dimensional correlated Fermi systems is an attempt to describe the effect of the band curvature beyond the Tomonaga-Luttinger liquid paradigm. It relies on the observation that the dynamical structure factor of the interacting electron gas shows a logarithmic threshold singularity when evaluated to first order perturbation theory in the two-particle interaction. This term was interpreted as the linear one in an expansion whi...

In a recent paper, arxiv:1402.6362, Gamayun, Lychkovskiy, and Cheianov studied the dynamics of a mobile impurity embedded into a one-dimensional Tonks-Girardeau gas of strongly interacting bosons. Employing the Boltzmann equation approach, they arrived at the following main conclusions: (i) a light impurity, being accelerated by a constant force does not exhibit Bloch oscillations; (ii) a heavy impurity does undergo Bloch oscillations, accompanied by a drift with the velocity...