Localization of interacting fermions at high temperature

By V. Oganesyan, D. Huse. 2006

1,423 citations recorded by the source corpus.

We suggest that if a localized phase at nonzero temperature $Tg0$ exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and interactions are strong and $T$ is very high. We show that in this high-$T$ regime, the localization transition may be studied numerically through exact diagonalization of small systems. We obtain spectra for one-dimensional lattice models of interacting spinless fermions in a random potential. As expected, the spectral statistics of finite-size samples cross over from those of orthogonal random matrices in the diffusive regime at weak random potential to Poisson statistics in the localized regime at strong randomness. However, these data show deviations from simple one-parameter finite-size scaling: the apparent mobility edge ``drifts'' as the system's size is increased. Based on spectral statistics alone, we have thus been unable to make a strong numerical case for the presence of a many-body localized phase at nonzero $T$.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/f1c1e7846d952d87de2200497cab546d0f9b4f5e

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In Atomic and Molecular Physics, and Optics

1. V. Khemani
2. D. Abanin
3. Maksym Serbyn
4. J. Imbrie
5. D. Huse
6. I. Bloch
7. Tomaz Prosen
8. J. Moore

In Condensed Matter Physics

1. V. Khemani
2. I. Bloch
3. Tomaz Prosen
4. J. Imbrie
5. L. Vidmar
6. Romain Vasseur
7. J. Moore
8. D. Abanin

Citations in the corpus

• Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump (2015, background): “39 [49], while for extended states, rext ≈ 0.”
• Avalanches and many-body resonances in many-body localized systems (2021, background): “…of which has thus far proved to be notoriously elusive: analytical treatments are mainly tractable only under phenomenological frameworks [20–28] and numerical simulations are restricted to very small system sizes that do not exhibit the asymptotic physics of large systems [4,10,29–33].”
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization (2016, methodology): “Further numerical studies [59, 60, 62], mostly restricted to the random-field XXZ Hamiltonian”
• Long-time behavior of macroscopic quantum systems (2010, background): “12 An example of exceptional Hamiltonians that behave differently is provided by the phenomenon of Anderson localization (see in particular [1, 48]): certain physically relevant Hamiltonians possess some eigenfunctions φα that have a spatial energy density function that is macroscopically non-unifor”
• Colloquium : Many-body localization, thermalization, and entanglement (2018, methodology): “Using numerical exact diagonalization of finite-size lattice systems, Oganesyan and Huse (2007) demonstrated signatures of an MBL phase in fermionic spin chains.”
• On Many-Body Localization for Quantum Spin Chains (2014, background): “Indeed, the thermalized phase should have significant level repulsion [23].”
• Colloquium: Nonequilibrium dynamics of closed interacting quantum systems (2010, background): “In many-body disordered systems the emergence of the Wigner-Dyson statistics was argued to be an indicator of the transition between metallic (ergodic) and insulating (non-ergodic) phases (Mukerjee et al., 2006; Oganesyan and Huse, 2007).”