Theory of a Fermi glass
Abstract
We construct a theory for localized electrons in disordered solids similar in spirit and intent to the Fermiliquid theory of Landau. That is, for low temperatures and excitation energies small compared to the Fermi energy, the electrons may be viewed as forming a gas of localized quasiparticles. The phenomenological theory is presented and applications are made to both equilibrium and time-dependent properties of the glass. A microscopic justification of the quasiparticle picture is made by an examination of the single-particle Green's function of the interacting system. The collective properties of the glass are examined by studing the Bethe-Salpeter equation satisfied by the four-point vertex for particle-hole scattering. This leads to the identification of the phenomenological effective interaction between quasiparticles with a certain limit of the four-point vertex and to a microscopic justification of the phenomenological transport equation used to study time-dependent phenomena.
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The TIM can be solved by using a Jordan-Wigner transformation to a system of non-interacting fermions, and the cost of solving the non-interacting fermion system is the cost of diagonalizing a matrix with rank equal to twice the number of spins in the chain.
“The TIM, in particular, can be solved by using a Jordan-Wigner transformation to a system of non-interacting fermions - and the cost of solving the non-interacting fermion system is the cost of diagonalizing a matrix with rank equal to twice the number of spins in the chain [178].”
From Can one trust quantum simulators? (2012) · cites this paper as [178]
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Boson localization and the superfluid-insulator transition
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Can one trust quantum simulators?
Hauke, P., Cucchietti, F. M., Tagliacozzo, L., Deutsch, I., & Lewenstein, M. (2012) · Reports on Progress in Physics · doi:10.1088/0034-4885/75/8/082401 · Cited by 315 · see citing works
- Authors
- Freedman, R., & Hertz, J. A.
- Affiliations
- University of Chicago (US)
- ORCID
- Hertz, J. A.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1977-02-15
- Volume
- 15
- Issue
- 4
- Pages
- 2384-2398
- ISSN
- 0556-2805 (ISSN-L)
- OpenAlex
- W2041442461
- Cited by
- 36
- References
- 14
- Citations by year
- 2026: 1 · 2024: 2 · 2023: 1 · 2022: 1 · 2021: 3 · 2018: 1 · 2017: 1 · 2016: 1 · 2015: 1 · 2012: 1
- FWCI
- 1.78
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. B, Solid state (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Keywords
- Fermi glass, localized electrons, disordered solids, quasiparticles, Fermi liquid theory, single-particle Green's function, Bethe-Salpeter equation, transport equation, time-dependent transport, low-temperature transport
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