Lieb-Schultz-Mattis theorem for quasi-topological systems

Details Lieb-Schultz-Mattis theorem for quasi-topological systems Lieb-Schultz-Mattis theorem for quasi-topological systems

2005-08-22

arxiv.org/abs/cond-mat/0508508v2

Phys. Rev. B 78, 174411 (2008)

Physics

Condensed Matter

Strongly Correlated Electrons

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 eli

Scientific paper

10.1103/PhysRevB.78.174411

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 $\omega \propto k^2$ 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.

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