Surface and bulk critical phenomena in generalized quantum antiferromagnets

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Critical phenomena in the presence of boundaries is a fertile source of interesting physics, which has attracted numerous experimental and theoretical investigations. In the presence of surfaces or, more generally, boundaries, the Renormalization Group predicts that each universality class controlling the bulk critical behavior splits into different surface universality classes, leading to a rich phase diagram. Boundary critical phenomena has recently received a renewed attention, driven by advances in conformal field theory, insights from topological phenomena, as well as results obtained in the previous granting period. Building on these developments, we propose here to continue the investigation of surface critical phenomena in the three-dimensional O(N) universality class, by means of Monte Carlo simulations. A related direction of research concerns the investigation of a symmetry-breaking line defect embedded into a critical three-dimensional bulk, where in the Ising case (N=1) we have previously shown the emergence of a unique critical exponent associated to the defect. Finally, in a third line of research, motivated also by ongoing scanning tunneling microscopy experiments on adatoms, we propose to investigate the critical behavior of a quantum spin chain coupled to a two-dimensional quantum spin model, tuned to its critical point.