Quantum Criticality and Deconfinement in Phase Transitions Between Valence Bond Solids

TL;DR

This paper investigates quantum phase transitions between valence bond solid phases in two-dimensional spin-half antiferromagnets, revealing deconfined critical points with emergent fractional excitations and complex phase structures.

Contribution

It demonstrates the existence of continuous deconfined quantum critical points between VBS phases, with variable critical exponents and intricate phase diagrams, including a 'devil's staircase' structure.

Findings

Deconfined quantum critical points with emergent spinons.

Variable critical exponents along fixed lines.

Complex phase structure with closely spaced transitions.

Abstract

We consider spin-half quantum antiferromagnets in two spatial dimensions in the quantum limit, where the spins are in a valence bond solid (VBS) phase. The transitions between two such VBS phases is studied. In some cases, an interesting second order transition controlled by a fixed line with varying critical exponents if found. A specific example is provided by an antiferromagnetically coupled bilayer system on the honeycomb lattice where a continuous quantum phase transition can generically exist between two VBS phases. Furthermore, these critical points are deconfined, in the sense that gapped spin-1/2 spinon excitations emerge right at the transition. The low energy physics of this critical point (upto marginally irrelevant interactions) contains just a free quadratically dispersing `photon'. The phase structure on one side of this continuous transition is very intricate consisting of a series of infinitely closely spaced further transitions in a `devil's staircase' form. Analogies with previous examples of deconfined quantum criticality are emphasized. Closely related transitions in single layer systems are explored. These are second order only at some multicritical points. The solvable Rokshar-Kivelson point of quantum dimer models of single layer systems is found to correspond to a very special non-generic multicritical point