Critical behavior at superconductor-insulator phase transitions near one dimension

TL;DR

This paper analyzes the critical behavior of superconductor-insulator transitions near one dimension using a renormalization approach, providing exact and approximate critical exponents for various interactions.

Contribution

It introduces a renormalization framework near one dimension to study superfluid-insulator transitions, deriving critical exponents and stability conditions for the critical point.

Findings

Exact dynamical critical exponent z=d for short-range interactions.

Correlation length exponent =1/\u221a{3psilon} for short-range interactions.

Critical point stability in 1 to 2 range for both interaction types.

Abstract

I argue that the system of interacting bosons at zero temperature and in random external potential possesses a simple critical point which describes the proliferation of disorder-induced topological defects in the superfluid ground state, and which is located at weak disorder close to and above one dimension. This makes it possible to address the critical behavior at the superfluid-Bose glass transition in dirty boson systems by expanding around the lower critical dimension d=1. Within the formulated renormalization procedure near d=1 the dynamical critical exponent is obtained exactly and the correlation length exponent is calculated as a Laurent series in the parameter \sqrt{\epsilon}, with \epsilon=d-1: z=d, \nu=1/\sqrt{3\epsilon} for the short range, and z=1, \nu=\sqrt{2/3\epsilon}, for the long-range Coulomb interaction between bosons. The identified critical point should be stable against the residual perturbations in the effective action for the superfluid, at least in dimensions 1\leq d \leq 2, for both short-range and Coulomb interactions. For the superfluid-Mott insulator transition in the system in a periodic potential and at a commensurate density of bosons I find \nu=(1/2\sqrt{\epsilon})+ 1/4+O(\sqrt{\epsilon}), which yields a result reasonably close to the known XY critical exponent in d=2+1. The critical behavior of the superfluid density, phonon velocity and the compressibility in the system with the short-range interactions is discussed.