Geometric Frustration and Dimensional Reduction at a Quantum Critical Point

TL;DR

This paper demonstrates that geometric frustration in layered lattices reduces the effective spatial dimensionality at quantum critical points, with theoretical predictions aligning well with experimental data on BaCuSi2O6.

Contribution

It introduces a theoretical framework showing dimensional reduction at quantum critical points due to frustration, validated by experimental agreement.

Findings

Critical temperature dependence matches experiments in BaCuSi2O6

Dimensionality is effectively reduced at the quantum critical point

Frustrating interactions influence quantum phase transitions

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. Our theoretical predictions for the critical temperature as a function of the chemical potential correspond very well with recent measurements in BaCuSi$_{2}$O$_{6}$ [S. E. Sebastian \textit{et al}, Nature \textbf{411}, 617 (2006)].