Quantum criticality of bosonic systems with the Lifshitz dispersion

TL;DR

This paper investigates the quantum critical behavior of bosonic systems with Lifshitz dispersion, identifying fixed points, analyzing temperature and interaction effects, and providing testable predictions for spin-orbit coupled bosons.

Contribution

It offers a detailed analysis of quantum criticality in Lifshitz bosonic systems, including fixed points and scaling behaviors, extending understanding to systems with spin-orbit coupling.

Findings

Identification of Gaussian and non-Gaussian fixed points.

Different power-law behaviors of particle density at zero temperature.

Scaling laws in quantum critical and disordered regions.

Abstract

We study the quantum criticality of the Lifshitz $\varphi^4$-theory below the upper critical dimension. Two fixed points, one Gaussian and the other non-Gaussian, are identified with zero and finite interaction strengths, respectively. At zero temperature the particle density exhibits different power-law dependences on the chemical potential in the weak and strong interaction regions. At finite temperatures, critical behaviors in the quantum disordered region are mainly controlled by the chemical potential. In contrast, in the quantum critical region critical scalings are determined by temperature. The scaling ansatz remains valid in the strong interaction limit for the chemical potential, correlation length, and particle density, while it breaks down in the weak interaction one. As approaching the upper critical dimension, physical quantities develop logarithmic dependence on dimensionality in the strong interaction region. These results are applied to spin-orbit coupled bosonic systems, leading to predictions testable by future experiments.