Finite temperature properties of quantum Lifshitz transitions between valence bond solid phases: An example of `local' quantum criticality

TL;DR

This paper investigates the finite temperature behavior of quantum Lifshitz transitions between valence bond solid phases, revealing local quantum criticality characterized by purely local spatial correlations and ω/T scaling in certain operators.

Contribution

It provides an exact analysis of local correlations at finite temperature near a quantum Lifshitz transition, illustrating a microscopic example of local quantum criticality.

Findings

Correlation functions show ω/T scaling at T>0

Correlators are purely local in space at finite temperature

Exact autocorrelation functions are calculated in the scaling limit

Abstract

We study the finite temperature properties of quantum magnets close to a continuous quantum phase transition between two distinct valence bond solid phases in two spatial dimension. Previous work has shown that such a second order quantum `Lifshitz' transition is described by a free field theory and is hence tractable, but is nevertheless non-trivial. At $T>0$, we show that while correlation functions of certain operators exhibit $\omega/T$ scaling, they do not show analogous scaling in space. In particular, in the scaling limit, all such correlators are purely {\em local} in space, although the same correlators at T=0 decay as a power law. This provides a valuable microscopic example of a certain kind of `local' quantum criticality. The local form of the correlations arise from the large density of soft modes present near the transition that are excited by temperature. We calculate exactly the autocorrelation function for such operators in the scaling limit. Going beyond the scaling limit by including irrelevant operators leads to finite spatial correlations which are also obtained.