Gapped Hamiltonian: Difference between revisions

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In many-body physics, most commonly within condensed-matter physics, a gapped Hamiltonian is a Hamiltonian for an infinitely large many-body system where there is a finite energy gap separating the (possibly degenerate) ground space from the first excited states. A Hamiltonian that is not gapped is called gapless.

The property of being gapped or gapless is formally defined through a sequence of Hamiltonians on finite lattices in the thermodynamic limit.^[1]

An example is the BCS Hamiltonian in the theory of superconductivity.

In quantum field theory, a continuum limit of many-body physics, a gapped Hamiltonian induces a mass gap.

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 The property of being gapped or gapless is formally defined through a sequence of Hamiltonians on finite [[Lattice model (physics)|lattices]] in the [[thermodynamic limit]].<ref>{{Cite web|url=https://physics.stackexchange.com/questions/4930/what-does-it-mean-for-a-hamiltonian-or-system-to-be-gapped-or-gapless/29166|title=quantum mechanics - What does it mean for a Hamiltonian or system to be gapped or gapless?|website=Physics Stack Exchange|access-date=2019-02-02}}</ref>
-An example is the [[BSC theory|BSC Hamiltonian]] in the theory of superconductivity.
+An example is the [[BCS theory|BCS Hamiltonian]] in the theory of superconductivity.
 In [[quantum field theory]], a continuum limit of many-body physics, a gapped Hamiltonian induces a [[mass gap]].