TY - JOUR

T1 - Lieb-Schultz-Mattis theorem and its generalizations from the perspective of the symmetry-protected topological phase

AU - Jian, Chao Ming

AU - Bi, Zhen

AU - Xu, Cenke

N1 - Funding Information:
Z. Bi and C. Xu are supported by the David and Lucile Packard Foundation and NSF Grant No. DMR-1151208. C.-M. Jian's research at the KITP is funded by the Gordon and Betty Moore Foundation's EPiQS Initiative through Grant No. GBMF4304. We thank Y.-Z. You for helpful discussions.
Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/2/12

Y1 - 2018/2/12

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevB.97.054412

DO - 10.1103/PhysRevB.97.054412

M3 - Article

AN - SCOPUS:85042203047

VL - 97

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 2469-9950

IS - 5

M1 - 054412

ER -