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

TL;DR

This work presents a detailed study of finite-temperature properties near a quantum Lifshitz transition between two valence bond solid phases in two dimensions, described by a free Gaussian height-field theory with dynamic exponent $z=2$. The authors exactly compute the finite-$T$ autocorrelation function of monopole-like operators and demonstrate $\omega/T$ scaling in the temporal sector while spatial correlations vanish in the scaling limit, i.e., correlations are purely local in space at scaling, due to a high density of soft modes. Spatial structure reappears only when including formally irrelevant operators (e.g., the marginal quartic term) or gapped spinons, yielding a crossover length $\xi_T$ and, at large distances, a power-law with a temperature-dependent exponent or an exponential decay if spinons proliferate. The results provide a concrete, analytically tractable example of local quantum criticality and offer quantitative predictions for numerical tests in quantum dimer models and related systems.

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 $ω/T$ 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.

Figures (1)

• Figure 1: The scaling part of the spectral function, defined in Eqn (\ref{['scalingdefn']}) associated with the monopole operator autocorrelation function plotted for two different values of $K$ (and hence $\eta$, the scaling dimension of the monopole operator). The value $\eta=1$ corresponds to the scaling dimension of the monopole operator at the square lattice RK point. The value $\eta=9/2$ corresponds to a point on the stable fixed line that controls the transition between VBS phases of a bilayer honeycomb quantum magnet.