Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

Abstract

Abstract. Abstract is missing.e investigate one-dimensional harmonically trapped twocomponent systems for repulsive interaction strengths ranging from the non-interacting to the strongly interacting regime for Fermi-Fermi mixtures. A new and powerful mapping between the interaction strength parameters from a continuous Hamiltonian and a discrete lattice Hamiltonian is derived. As an example, we show that this mapping does not depend neither on the state of the system nor on the number of particles. Energies, density profiles and correlation functions are obtained both numerically (DMRG and Exact diagonalization) and analytically. Since DMRG results do not converge as the interaction strength is increased, analytical solutions are used as a benchmark to identify the point where these calculations become unstable. We use the proposed mapping to set a quantitative limit on the interaction parameter of a discrete lattice Hamiltonian above which DMRG gives unrealistic results.

Analytical and numerical studies of Bose–Fermi mixtures in a one-dimensional harmonic trap

“…Analytically, new and different kinds of methods have been developed and are in use as well [73][74][75][76]. However, different kind of methods for all regimes have both advantages and disadvantages, and they must be used with care [77].…”

Ion-induced interactions in a Tomonaga-Luttinger liquid

“…When N A , N I ≪ N s and d ≪ R * (i.e. low filling factor), we can use DMRG on the discretised system to approximate the d → 0 continuum limit 77,78 . When we approach the thermodynamic limit numerically…”

Mobile spin impurity in an optical lattice

“…In appendix E we solve Hamiltonian (14) for the eigenstates and spectrum. Quoting the results of this derivation, the eigenstates are given by…”

“…Our studies, which go well beyond the single-band approximation, that is, the Hubbard model, pave the way for the realisation of interacting one-dimensional models of condensed matter physics.Recently, strongly-interacting trapped one-dimensional multicomponent systems, which suffer from huge ground state degeneracies, have been shown to be tractable by means of freezing the charge degrees of freedom and the reduction of the spin sector to an effective spin chain model [1][2][3]. With this development, there has been considerable theoretical work on strongly interacting one-dimensional systems in recent years [4][5][6][7][8][9][10][11][12][13][14][15][16], including for the case of a single spin impurity [17][18][19]. As a result in the last year, numerical methods have been developed to obtain the effective spin chain from an arbitrary confining potential [20,21].…”