nLab gapped Hamiltonian

Idea

In solid state physics a material is said to have a gapped Hamiltonian if in the thermodynamic limit of infinite volume its Hamiltonian has a spectral gap over the ground state.

Related concepts

• confinement

• topological phase of matter

• tensor network

• mass term

• mass gap problem in Yang-Mills theory/QCD

References

General

See also

• Wikipedia, Gapped Hamiltonian

K-Theory classification of topological phases of matter

topological phases of matter via K-theory – references

Classification of condensed matter with gapped Hamiltonians (topological insulators, topological phases of matter) by twisted equivariant topological K-theory:

• Alexei Kitaev, Periodic table for topological insulators and superconductors, talk at: L.D.Landau Memorial Conference “Advances in Theoretical Physics”, June 22-26, 2008, In:AIP Conference Proceedings 1134, 22 (2009) (arXiv:0901.2686, doi:10.1063/1.3149495)

• Daniel Freed, Gregory Moore, Twisted equivariant matter, Ann. Henri Poincaré (2013) 14: 1927 (arXiv:1208.5055)

• Guo Chuan Thiang, On the K-theoretic classification of topological phases of matter, Annales Henri Poincare 17(4) 757-794 (2016) (arXiv:1406.7366)

• Guo Chuan Thiang, Topological phases: isomorphism, homotopy and K-theory, Int. J. Geom. Methods Mod. Phys. 12 1550098 (2015) (arXiv:1412.4191)

• Ralph M. Kaufmann, Dan Li, Birgit Wehefritz-Kaufmann, Topological insulators and K-theory (arXiv:1510.08001, spire:1401095/)

• Daniel Freed, Michael Hopkins, Reflection positivity and invertible topological phases (arXiv:1604.06527)

• Daniel Freed, Lectures on field theory and topology (cds:2699265)

• Charles Zhaoxi Xiong, Classification and Construction of Topological Phases of Quantum Matter (arXiv:1906.02892)