Dynamical critical exponent of the Jaynes-Cummings-Hubbard model

TL;DR

This paper investigates the critical behavior of the Jaynes-Cummings-Hubbard model, revealing that its superfluid-insulator transition at the lobe tip belongs to the 3D XY universality class with a dynamical critical exponent z=1.

Contribution

The study provides large-scale quantum Monte Carlo evidence that the transition's critical properties match those of the Bose-Hubbard model, correcting previous mean-field predictions.

Findings

Critical exponent z=1 at the lobe tip

Transition belongs to the 3D XY universality class

Contradicts earlier mean-field results

Abstract

An array of high-Q electromagnetic resonators coupled to qubits gives rise to the Jaynes-Cummings-Hubbard model describing a superfluid to Mott insulator transition of lattice polaritons. From mean-field and strong coupling expansions, the critical properties of the model are expected to be identical to the scalar Bose-Hubbard model. A recent Monte Carlo study of the superfluid density on the square lattice suggested that this does not hold for the fixed-density transition through the Mott lobe tip. Instead, mean-field behavior with a dynamical critical exponent z=2 was found. We perform large-scale quantum Monte Carlo simulations to investigate the critical behavior of the superfluid density and the compressibility. We find z=1 at the tip of the insulating lobe. Hence the transition falls in the 3D XY universality class, analogous to the Bose-Hubbard model.