Aneesur Rahman Prize for Computational Physics (2021): Lattice models of deconfined quantum criticality and related phenomena

The quantum phase transition between an antiferromagnet and dimerized state in two-dimensional quantum magnets can be studied within a class of J-Q models, where the Heisenberg exchange J competes with Q terms inducing correlated local singlets. This type of transition is associated with spinon deconfinement and emergent symmetry. Though the ultimate nature of the transition - continuous or very weakly first-order - is still controversial, it is by now clear that the signatures of deconfinement are manifested up to very large length scales and the phenomenology of deconfinement applies. I will here discuss a number of extensions of the original J-Q model which allow access to phenomena related to deconfined criticality but that were not part of the original scenario. (1) Emergent O(4) and O(5) symmetry can appear even when the transition is clearly first-order. (2) The dimerized phase develops into a helical (winding) phase in the presence of certain spatial modulation of the J interactions. (3) In the presence of coupling disorder the dimerized phase develops into a critical random-singlet phase with universal static correlations and varying dynamic exponent. I will illustrate these cases with quantum Monte Carlo results and also connect with recent experiments on frustrated quasi-2D quantum magnets.