Phonon-induced modification of quantum criticality

Abstract

We study the effect of acoustic phonons on the quantum phase transition in the O($N$) model. We develop a renormalization group analysis near (3+1) space-time dimensions and derive the RG equations using an $\epsilon$-expansion. Our results indicate that when the number of flavors of the underlying O($N$) model exceeds a critical number $N_c=4$, the quantum transition remains second-order of the Wilson-Fisher type while, for $N\le 4$, it is a weakly first-order transition. We characterize this weakly first-order transition by a length-scale ${\xi }^{\ast }$, below which the behavior appears to be critical. At finite temperatures for $N\le 4$, a tricritical point separates the weakly first-order and second-order transitions.

11 pages, 5 figures

References in corpus (8)

• Metastable ferroelectricity in optically strained $SrTi{O}_3$
• Supersolidity around a critical point in dipolar Bose Einstein condensates
• Emergent supersymmetry at the Ising-Berezinskii-Kosterlitz-Thouless multicritical point
• Different critical behaviors in cubic to trigonal and tetragonal perovskites
• Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson
• Quantum Annealed Criticality: A Scaling Description
• Topological Order in an Antiferomagnetic Tetratic
• The Cubic Fixed Point at Large $N$