Lieb-Schultz-Mattis theorem and its generalizations from the perspective of the symmetry-protected topological phase

Chao Ming Jian, Zhen Bi, Cenke Xu

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21 Scopus citations

Abstract

We ask whether a local Hamiltonian with a featureless (fully gapped and nondegenerate) ground state could exist in certain quantum spin systems. We address this question by mapping the vicinity of certain quantum critical point (or gapless phase) of the d-dimensional spin system under study to the boundary of a (d+1)-dimensional bulk state, and the lattice symmetry of the spin system acts as an onsite symmetry in the field theory that describes both the selected critical point of the spin system and the corresponding boundary state of the (d+1)-dimensional bulk. If the symmetry action of the field theory is nonanomalous, i.e., the corresponding bulk state is a trivial state instead of a bosonic symmetry-protected topological (SPT) state, then a featureless ground state of the spin system is allowed; if the corresponding bulk state is indeed a nontrivial SPT state, then it likely excludes the existence of a featureless ground state of the spin system. From this perspective, we identify the spin systems with SU(N) and SO(N) symmetries on one-, two-, and three-dimensional lattices that permit a featureless ground state. We also verify our conclusions by other methods, including an explicit construction of these featureless spin states.

Original languageEnglish (US)
Article number054412
JournalPhysical Review B
Volume97
Issue number5
DOIs
StatePublished - Feb 12 2018

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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