Quantum critical behavior of the superfluid-Mott glass transition

TL;DR

This study analyzes the quantum superfluid-Mott glass transition in a disordered 2D system, revealing universal power-law critical behavior with specific exponents, confirmed through Monte Carlo simulations and applicable to experimental contexts.

Contribution

The paper provides the first comprehensive Monte Carlo analysis of the superfluid-Mott glass transition in a disordered 2D quantum rotor model, establishing universal critical exponents and confirming theoretical predictions.

Findings

Critical exponents are universal and dilution-independent.

The transition exhibits conventional power-law critical behavior.

Results agree with and refine previous Monte Carlo studies.

Abstract

We investigate the zero-temperature superfluid to insulator transitions in a diluted two-dimensional quantum rotor model with particle-hole symmetry. We map the Hamiltonian onto a classical $(2+1)$-dimensional XY model with columnar disorder which we analyze by means of large-scale Monte Carlo simulations. For dilutions below the lattice percolation threshold, the system undergoes a generic superfluid-Mott glass transition. In contrast to other quantum phase transitions in disordered systems, its critical behavior is of conventional power-law type with universal (dilution-independent) critical exponents $z=1.52(3)$, $\nu=1.16(5)$, $\beta/\nu= 0.48(2)$, $\gamma/\nu=2.52(4)$, and $\eta=-0.52(4)$. These values agree with and improve upon earlier Monte-Carlo results [Phys. Rev. Lett. 92, 015703 (2004)] while (partially) excluding other findings in the literature. As a further test of universality, we also consider a soft-spin version of the classical Hamiltonian. In addition, we study the percolation quantum phase transition across the lattice percolation threshold; its critical behavior is governed by the lattice percolation exponents in agreement with recent theoretical predictions. We relate our results to a general classification of phase transitions in disordered systems, and we briefly discuss experiments.