Dynamics in the planar pyrochlore lattice: bow-tie flat band and mixed 't Hooft anomaly

TL;DR

This paper investigates the quantum phase transition on the planar pyrochlore lattice, revealing flat band structures, topological excitations, and the role of mixed 't Hooft anomalies in deconfinement phenomena.

Contribution

It proposes a 2+1D Abelian-Higgs model with mixed 't Hooft anomaly to explain deconfinement at the transition, supported by numerical simulations and spectral analysis.

Findings

Observation of bow-tie flat bands in both phases

Identification of continuous, gapless spectra at transition

Detection of domain walls with symmetry anomalies

Abstract

The quantum phase transition between $\mathbb{Z}_{2}$ plaquette valence bound solid (PVBS) and superfluid (SF) phases on the planar pyrochlore lattice (square ice) is under debate, because the conventional deconfined theory does not support continuous one, but the numerical evidence is still not solid. Here, we propose the system can be effectively described by a 2+1 dimensional Abelian-Higgs model which may host the mixed 't Hooft anomaly, so that the deconfinement can exist on the domain walls at the transition point. To verify it, we study the spin excitation spectra by combining stochastic analytic continuation and quantum Monte Carlo simulation. In both PVBS and SF phases, a flat band with bow-tie structure is observed and can be explained by group theoretic analysis. At the transition point, the spectra turn to be continuous and gapless, which indicates the topological excitations. From the snapshot of the spin configuration in real space, we found the existence of the domain wall in which the symmetries satisfy the anomaly. Meanwhile, a Luttinger liquid like continuum implies additional domain walls (point-defect) can emerge in the domain walls (line-defect) and take the role of deconfinement at transition point, as prediction of mixed 't Hooft anomaly. Our work can build a new bridge between the topological gauge field theory and a strongly correlated system.