Boson topological insulators: A window into highly entangled quantum phases

By Chong Wang, Senthil Todadri. 2013

140 citations recorded by the source corpus.

We study several aspects of the realization of global symmetries in highly entangled phases of quantum matter. Examples include gapped topological ordered phases, gapless quantum spin liquids and non-fermi liquid phases. An insightful window into such phases is provided by recent developments in the theory of short ranged entangled Symmetry Protected Topological (SPT) phases . First they generate useful no-go constraints on how global symmetry may be implemented in a highly entangled phase. Possible symmetry implementation in gapped topological phases and some proposed gapless spin/bose liquids are examined in this light. We show that some previously proposed spin liquid states for 2d quantum magnets do not in fact have consistent symmetry implementation unless they occur as the surface of a 3d SPT phase. A second SPT-based insight into highly entangled states is the development of a view point of such states as SPT phases of one of the emergent excitations. We describe this in the specific context of time reversal symmetric 3d U(1) quantum spin liquids with an emergent photon. Different such spin liquids are shown to be equivalent to different SPT insulating phases of the emergent monopole excitation of such phases. The highly entangled states also in turn enrich our understanding of SPT phases. We use the insights obtained from our results to provide an explicit construction of bosonic SPT phases in 3d in a system of coupled layers. This includes construction of a time reversal symmetric SPT state that is not currently part of the cohomology classification of such states.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/f8378a29e7abb12516ac6c24065125f54034a42e

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Topological Phases Protected by Point Group Symmetry (2016, background): “For bosonic systems with Z2 only or Z T 2 only, the classification of SPT phases is Z2 in d 1⁄4 1 [6,7,10,11] and Z2 × Z2 in d 1⁄4 3 [42,52,53,73].”
Deconfined quantum critical points: symmetries and dualities (2017, unknown): “This property may be altered by shifting θ → θ þ 2π [99,100].”