Critical Behavior and Collective Modes at the Superfluid Transition in Amorphous Systems

TL;DR

This study explores the critical behavior and dynamics of the Higgs mode near the superfluid-insulator transition in amorphous systems with topological disorder, revealing delocalization of the amplitude mode and critical behavior similar to ordered systems.

Contribution

It demonstrates that topological disorder does not localize the Higgs mode and that the critical behavior remains unchanged, challenging typical localization expectations in disordered systems.

Findings

Amplitude mode remains delocalized despite topological disorder

Critical behavior matches that of translationally invariant systems

Disorder does not induce localization of collective excitations

Abstract

We investigate the critical behavior and the dynamics of the amplitude (Higgs) mode close to the superfluid-insulator quantum phase transition in an amorphous system (i.e., a system subject to topological randomness). In particular, we map the two-dimensional Bose-Hubbard Hamiltonian defined on a random Voronoi-Delaunay lattice onto a (2+1)-dimensional layered classical XY model with correlated topological disorder. We study the resulting model by laying recourse to classical Monte Carlo simulations. We specifically focus on the scalar susceptibility of the order parameter to study the dynamics of the amplitude mode. To do so, we harness the maximum entropy method to perform the analytic continuation of the scalar susceptibility to real frequencies. Our analysis shows that the amplitude mode remains delocalized in the presence of such topological disorder, quite at odds with its behavior in generic disordered systems, where the randomness localizes the Higgs mode. Furthermore, we show that the critical behavior of the topologically disordered system is identical to that of its translationally invariant counterpart, consistent with a modified Harris criterion. This suggests that the localization of the collective excitations in the presence of disorder is tied to the critical behavior of the quantum phase transition rather than a simple Anderson-localization-type interference mechanism.