Emergent Symmetry and Dimensional Reduction at a Quantum Critical Point

TL;DR

This paper demonstrates that in certain layered quantum systems with frustrating interactions, the effective dimensionality at the quantum critical point is reduced from three to two, due to emergent symmetry and validated by experiments.

Contribution

It introduces a mean field and renormalization group analysis showing dimensional reduction at quantum critical points with emergent symmetry in layered Bose systems.

Findings

Critical temperature matches experimental data in BaCuSi₂O₆.

Emergent symmetry causes effective two-dimensional behavior.

Dimensional reduction occurs at the quantum critical point due to frustration.

Abstract

We show that the spatial dimensionality of the quantum critical point associated with Bose--Einstein condensation at T=0 is reduced when the underlying lattice comprises a set of layers coupled by a frustrating interaction. For this purpose, we use an heuristic mean field approach that is complemented and justified by a more rigorous renormalization group analysis. Due to the presence of an emergent symmetry, i.e. a symmetry of the ground state that is absent in the underlying Hamiltonian, a three--dimensional interacting Bose system undergoes a chemical potential tuned quantum phase transition that is strictly two dimensional. Our theoretical predictions for the critical temperature as a function of the chemical potential correspond very well with recent measurements in BaCuSi$_{2}$O$_{6}$.