Quantum criticality of the imperfect Bose gas in d dimensions

TL;DR

This paper analyzes the quantum phase transition in the d-dimensional imperfect Bose gas, revealing a second-order transition to Bose-Einstein condensation and detailing the phase diagram and correlation length behavior across dimensions.

Contribution

It provides an exact analysis of the microscopic model, establishing the phase diagram and critical behavior of the imperfect Bose gas in various dimensions.

Findings

Existence of a second-order quantum phase transition to Bose-Einstein condensate.

Correlation length exhibits an essential singularity at d=2.

Results agree with renormalization-group analysis for d>2.

Abstract

We study the low-temperature limit of the d-dimensional imperfect Bose gas. Relying on an exact analysis of the microscopic model, we establish the existence of a second-order quantum phase transition to a phase involving the Bose-Einstein condensate. The transition is triggered by varying the chemical potential and persists at non-zero temperatures T for d>2. We extract the exact phase diagram and identify the scaling regimes in the vicinity of the quantum critical point focusing on the behavior of the correlation length \xi. The length \xi develops an essential singularity exclusively for d=2. We follow the evolution of the phase diagram varying d. For d>2 our results agree with renormalization-group based analysis of the effective bosonic order-parameter models with the dynamical exponent z=2.