Scale invariance of the polaron energy at the Mott-superfluid critical point

TL;DR

This study shows that impurity energy measurements via quantum Monte Carlo reveal scale invariance at the Mott-superfluid critical point, offering a new probe for quantum phase transitions.

Contribution

It demonstrates that impurity energy exhibits scale invariance at the critical point, providing a novel method to study quantum criticality through impurity spectroscopy.

Findings

Impurity energy is scale invariant at the critical point.

Finite-size scaling reveals a new, unexplained critical exponent.

Density-density correlations flatten at the critical point, indicating diverging length scales.

Abstract

Continuous quantum phase transitions are characterized by an order parameter and correlation functions that are often challenging to access experimentally or in direct numerical simulations. The energy of an added impurity can on the other hand be probed by established polaron spectroscopy, or numerically with Monte Carlo methods. We provide evidence from ground-state quantum Monte Carlo calculations that the energy of a mobile impurity interacting weakly with a surrounding lattice Bose gas provides access to the critical behavior of the Mott insulator-superfluid phase transition. Finite-size scaling of the energy reveals that its value is scale invariant at the critical point of the quantum phase transition, and we extract a scaling exponent that is currently unexplained by theory. For a small lattice we further observe a flattening of the impurity-boson density-density correlations at the critical point, which hints at a divergence of a corresponding length scale in the thermodynamic limit. Our results suggest that impurity spectroscopy represents a useful way to probe the critical properties of quantum phase transitions in general.