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Bulletin of the American Physical Society

Deconfined quantum criticality in bipartite SU($N$) antiferromagnets in two dimensions

Matthew S. Block, Ribhu K. Kaul

Published Mar 22, 2013• 0 citations
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Deconfined quantum criticality in bipartite SU(NNN) antiferromagnets in two dimensions
Deconfined criticality in "easy-plane" SU(NNN) anti-ferromagnets
I will give an overview of unbiased numerical work on the Neelvalence bond solid (VBS) phase transition in d = 2 antiferromagnets. This progress has been possible due to the discovery of a new class of Hamiltonians of SU(N) spins that are free of the sign problem of quantum Monte Carlo. I will show through extensive numerical studies of the quantum phase transition on a variety of bipartite systems: square, rectangular, honeycomb and square bilayer, for a number of values of N (2 ≤ N ≤ 10), that a close to complete picture of an unusual “deconfined critical point” has emerged. Significantly, no direct evidence for first order behavior has been found on the largest simulations with 256 × 256 spins, the crucial role of Berry phases at the critical point has been verified, strong evidence for non-compact CPN−1 universality is evident for a range of N values, the inferred “dangerous” (ir)relevance of lattice anisotropy at the critical point is consistent with various limiting analytic calculations on the CPN−1 field theory and close to the critical point dramatic signatures of the emergent photon excitation have been detected in VBS correlation functions. I will conclude with some open theoretical issues that remain to be resolved and possible experimental realizations.
The antiferromagnetic to valence-bond-solid phase transition in the two-dimensional J-Q model (an S=1/2 Heisenberg model with four-spin interactions) is studied using large-scale quantum Monte Carlo simulations. The results support a continuous transition of the ground state, in agreement with the theory of "deconfined" quantum criticality. There are, however, large corrections to scaling, of logarithmic or very slowly decaying power-law form, which had not been anticipated. This suggests that either the SU(N) symmetric noncompact CP;{N-1} field theory for deconfined quantum criticality has to be revised or that the theory for N=2 (as in the system studied here) differs significantly from N-->infinity (where the field theory is analytically tractable).