Lieb-Schultz-Mattis theorem for quasi-topological systems

Freedman, Michael; Nayak, Chetan; Shtengel, Kirill

Lieb-Schultz-Mattis theorem for quasi-topological systems

Authors

Freedman, Michael

Nayak, Chetan

Shtengel, Kirill

Description

In this paper we address the question of the existence of a spectral gap in a class of local Hamiltonians. These Hamiltonians have the following properties: their ground states are known exactly; all equal-time correlation functions of local operators are short-ranged; and correlation functions of certain non-local operators are critical. A variational argument shows gaplessness with $ω\propto k^2$ at critical points defined by the absence of certain terms in the Hamiltonian, which is remarkable because equal-time correlation functions of local operators remain short-ranged. We call such critical points, in which spatial and temporal scaling are radically different, quasi-topological. When these terms are present in the Hamiltonian, the models are in gapped topological phases which are of special interest in the context of topological quantum computation.
v2: The version published in Phys. Rev B. A new section has been added; a gap in the earlier version of the proof has been eliminated