Physics:Gapped Hamiltonian
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][unreliable source?]
An example is the BCS Hamiltonian in the theory of superconductivity.
In quantum many-body systems, ground states of gapped Hamiltonians have exponential decay of correlations.[2][3][4]
In quantum field theory, a continuum limit of many-body physics, a gapped Hamiltonian induces a mass gap.
References
- ↑ "quantum mechanics - What does it mean for a Hamiltonian or system to be gapped or gapless?". https://physics.stackexchange.com/questions/4930/what-does-it-mean-for-a-hamiltonian-or-system-to-be-gapped-or-gapless/29166.
- ↑ Nachtergaele, Bruno; Sims, Robert (22 March 2006). "Lieb-Robinson Bounds and the Exponential Clustering Theorem". Communications in Mathematical Physics 265 (1): 119–130. doi:10.1007/s00220-006-1556-1. Bibcode: 2006CMaPh.265..119N.
- ↑ Hastings, Matthew B.; Koma, Tohru (22 April 2006). "Spectral Gap and Exponential Decay of Correlations". Communications in Mathematical Physics 265 (3): 781–804. doi:10.1007/s00220-006-0030-4. Bibcode: 2006CMaPh.265..781H.
- ↑ Gosset, David; Huang, Yichen (3 March 2016). "Correlation Length versus Gap in Frustration-Free Systems". Physical Review Letters 116 (9): 097202. doi:10.1103/PhysRevLett.116.097202. PMID 26991196. Bibcode: 2016PhRvL.116i7202G.
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