Symmetry breaking and physical properties of the bosonic single-impurity Anderson model

TL;DR

This paper demonstrates how exact diagonalization of small clusters effectively solves the bosonic single-impurity Anderson model, revealing phase diagrams, symmetry breaking, and Bose-Einstein condensation with results comparable to more complex methods.

Contribution

It introduces a fast, reliable impurity solver using exact diagonalization for the bosonic Anderson model, applicable to large-scale disordered systems and BEC studies.

Findings

Exact diagonalization accurately detects BEC through symmetry breaking.

Symmetry breaking signals BEC even with limited states.

Results agree well with numerical renormalization group methods.

Abstract

We show how exact diagonalization of small clusters can be used as a fast and reliable impurity solver by determining the phase diagram and physical properties of the bosonic single-impurity Anderson model. This is specially important for applications which require the solution of a large number of different single-impurity problems, such as the bosonic dynamical mean field theory of disordered systems. In particular, we investigate the connection between spontaneous global gauge symmetry breaking and the occurrence of Bose-Einstein condensation (BEC). We show how BEC is accurately signaled by the appearance of broken symmetry, even when a fairly modest number of states is retained. The occurrence of symmetry breaking can be detected both by adding a small conjugate field or, as in generic quantum critical points, by the divergence of the associated phase susceptibility. Our results show excellent agreement with the considerably more demanding numerical renormalization group (NRG) method. We also investigate the mean impurity occupancy and its fluctuations, identifying an asymmetry in their critical behavior across the quantum phase transitions between BEC and `Mott' phases.