Dirty Bosons: Twenty Years Later

TL;DR

This paper reviews the complex phenomena of superfluidity and quantum criticality in disordered Bose systems, highlighting symmetries, phase transitions, and experimental insights over twenty years.

Contribution

It synthesizes theoretical, numerical, and experimental findings on the insulator-superfluid transition in Bose systems, emphasizing symmetry considerations and exact results for phase boundaries.

Findings

Exact results constrain numerical simulations.

Scaling arguments elucidate transition nature.

Experimental systems illustrate theoretical concepts.

Abstract

A concise, somewhat personal, review of the problem of superfluidity and quantum criticality in regular and disordered interacting Bose systems is given, concentrating on general features and important symmetries that are exhibited in different parts of the phase diagram, and that govern the different possible types of critical behavior. A number of exact results for various insulating phase boundaries, which may be used to constrain the results of numerical simulations, can be derived using large rare region type arguments. The nature of the insulator-superfluid transition is explored through general scaling arguments, exact model calculations in one dimension, numerical results in two dimensions, and approximate renormalization group results in higher dimensions. Experiments on He-4 adsorbed in porous Vycor glass, on thin film superconductors, and magnetically trapped atomic vapors in a periodic optical potential, are used to illustrate many of the concepts.