Condensed Matter Theory

Abstract:

August 1972 saw the publication of Philip Anderson’s essay ‘More is different’. In it, he crystallized the idea of emergence, arguing that “at each level of complexity entirely new properties appear” — that is, although, for example, chemistry is subject to the laws of physics, we cannot infer the field of chemistry from our knowledge of physics. Fifty years on from this landmark publication, eight scientists describe the most interesting phenomena that emerge in their fields.

Abstract:

We present microscopic models of spin ladders which exhibit continuous critical surfaces whose properties and existence, unusually, cannot be inferred from those of the flanking phases. These models exhibit either “multiversality”—the presence of different universality classes over finite regions of a critical surface separating two distinct phases—or its close cousin, “unnecessary criticality”—the presence of a stable critical surface within a single, possibly trivial, phase. We elucidate these properties using Abelian bosonization and density-matrix renormalization-group simulations, and attempt to distill the key ingredients required to generalize these considerations.

Abstract:

We consider fractional quantum Hall states in systems where two flat Chern number C=±1 bands are labeled by an approximately conserved 'valley' index and interchanged by time reversal symmetry. At filling factor ν = 1 this setting admits an unusual hierarchy of correlated phases of excitons, neutral particle-hole pair excitations of a fully valley-polarized 'orbital ferromagnet’ parent state where all electrons occupy a single valley. Excitons experience an effective magnetic field due to the Chern numbers of the underlying bands. This obstructs their condensation in favor of a variety of crystalline orders and gapped and gapless liquid states. All these have the same quantized charge Hall response and are electrically incompressible, but differ in their edge structure, orbital magnetization, and hence valley and thermal responses. We explore the relevance of this scenario for moir'e heterostructures of bilayer graphene on a hexagonal boron nitride substrate.