Correlations at a quantum phase transition in interacting Bose systems

TL;DR

This study examines correlation functions at a quantum phase transition in interacting bosons, revealing complex behaviors with short-range, long-range, and power-law characteristics in different correlation types.

Contribution

It uncovers unexpected non-power-law spatial correlations and detailed temporal correlation behaviors at the superfluid-insulator transition in two-dimensional bosonic systems.

Findings

Spatial correlations show non-power-law behavior with short-range and long-range parts.

Temporal correlations exhibit power-law behavior.

Distinct correlation behaviors are linked to particle-hole excitations and single-particle condensation.

Abstract

We have investigated the correlation functions of interacting bosons at the generic superfluid-insulator transition, a prototypical quantum phase transition, in two dimensions in the spherical limit. Unexpectedly the spatial correlation functions show non-power-law behavior consisting of two parts: short-range correlation due to the particle-hole pair excitations and long-range off-diagonal order due to the single-particle condensation. The temporal correlation functions, on the other hand, show power-law behavior.