Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states

By D. Basko, I. Aleiner, B. L. Altshuler. 2005

1,829 citations recorded by the source corpus.

Abstract We consider low-temperature behavior of weakly interacting electrons in disordered conductors in the regime when all single-particle eigenstates are localized by the quenched disorder. We prove that in the absence of coupling of the electrons to any external bath dc electrical conductivity exactly vanishes as long as the temperature T does not exceed some finite value Tc. At the same time, it can be also proven that at high enough T the conductivity is finite. These two statements imply that the system undergoes a finite temperature metal-to-insulator transition, which can be viewed as Anderson-like localization of many-body wave functions in the Fock space. Metallic and insulating states are not different from each other by any spatial or discrete symmetries. We formulate the effective Hamiltonian description of the system at low energies (of the order of the level spacing in the single-particle localization volume). In the metallic phase quantum Boltzmann equation is valid, allowing to find the kinetic coefficients. In the insulating phase, T

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Electronic, Optical and Magnetic Materials

View Paper: https://www.semanticscholar.org/paper/90c64c5f5cc14758af75f6ea48574e5319c5a0e9

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In Atomic and Molecular Physics, and Optics

1. D. Abanin
2. V. Khemani
3. I. Bloch
4. J. Imbrie
5. Maksym Serbyn
6. V. Ros
7. A. Nahum
8. Antonello Scardicchio

In Condensed Matter Physics

1. I. Bloch
2. J. Imbrie
3. L. Vidmar
4. D. Abanin
5. Tomaz Prosen
6. Antonello Scardicchio
7. V. Ros
8. J. Moore

In Electronic, Optical and Magnetic Materials

1. Antonello Scardicchio
2. V. Ros
3. J. Imbrie
4. D. Abanin
5. A. Mirlin
6. Maksym Serbyn
7. F. Evers
8. I. Bloch

Citations in the corpus

• Many-body localization: An introduction and selected topics (2017, neutral): “It is equivalent, via a Jordan–Wigner transformation, to the interacting spinless fermionic model i , c i creation and annihilation operators, n i c i c i occupation operator at site i (open boundary conditions are assumed to make a strict correspondence with H XXZ ).”
• Many-body energy localization transition in periodically driven systems (2012, background): “Moreover, using the example of the many-body localization transition, it has been convincingly argued that disordered interacting systems can behave non-ergodically [16, 17] and the standard assumption that the interacting non-integrable system can serve as its own bath can fail.”
• Colloquium : Many-body localization, thermalization, and entanglement (2018, methodology): “The possibility of localization in an interacting setting was established for a zero-dimensional case of a quantum dot (Altshuler et al., 1997), and in higher-dimensional systems with local interactions (Basko et al., 2006; Gornyi et al., 2005).”