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Viewpoint: The universal behavior of a disordered system

Gil Refael

The presence of disorder in a quantum many-body system may appear to make an already difficult problem nearly impossible to solve. However, scientists show that the details of the disorder often do not matter, allowing them to describe realistic systems from magnets to superconductors.

Jan 5, 20090 citations

Many-body localization properties of disordered interacting fermionic systems

Kanabet Yapara, E. N. Djoukouo, Celsus Bouri +2 more

Indian Journal of PhysicsSep 8, 20240 citations

The fate of states of fermionic systems submitted to a disordered potentialunder Many-Body Localization}

M. H. B. Mackongo, Kanabet Yapara, Celsus Bouri +1 more

Jan 1, 20260 citations

Details of Disorder Matter in 2D d -Wave Superconductors

W. A. Atkinson, P. J. Hirschfeld, Allan H. MacDonald +1 more

Within numerically exact solutions of the Bogoliubov-de Gennes equations, we demonstrate that discrepancies between predicted low-energy quasiparticle properties in disordered 2D d-wave superconductors occur because of the unanticipated importance of disorder model details and normal state particle-hole symmetry. For the realistic case, which is best described by a binary alloy model without particle-hole symmetry, we predict density-of-state suppression below an energy scale which appears to be correlated with the corresponding single impurity resonance.Within numerically exact solutions of the Bogoliubov-de Gennes equations, we demonstrate that discrepancies between predicted low-energy quasiparticle properties in disordered 2D d-wave superconductors occur because of the unanticipated importance of disorder model details and normal state particle-hole symmetry. For the realistic case, which is best described by a binary alloy model without particle-hole symmetry, we predict density-of-state suppression below an energy scale which appears to be correlated with the corresponding single impurity resonance.

arXiv:cond-mat/0005487Physical Review LettersOct 30, 200066 citations

Quasi-Particle Density of States and Thouless Conductance of Disorderedd-wave Superconductors

Bodo Huckestein, Alexander Altland

Disorder in electronic systems suppresses diffusion and can lead to localization. The origin of this behavior is enhanced backscattering due to quantum interference. In addition, disorder leads to a broadening of the density of states (DoS). However, the localization properties of a disordered system are usually not discernible from a study of the DoS. It is necessary to calculate two-particle properties or consider the influence of boundary conditions on energy eigenvalues as in the study of Thouless numbers to obtain information about localization. Another feature of disordered systems is the independence of their localization properties from details of the disorder in the system. For example, the range of the disorder affects non-universal quantities like the mean-free path but does not influence whether or not the system shows localization at all. Recently, new symmetry classes came into focus that do not conform to the standard expectations about disordered systems outlined above. As we will show in this contribution, details of disorder do matter for these systems and localization properties leave their mark on the DoS. In particular, we look at a system that presents an idealization of a disordered d-wave superconductor. In our study we neglect effects of self-consistency and concentrate on the d-wave symmetry and influence of different kinds of disorder. We consider the lattice quasi-particle HamiltonianDisorder in electronic systems suppresses diffusion and can lead to localization. The origin of this behavior is enhanced backscattering due to quantum interference. In addition, disorder leads to a broadening of the density of states (DoS). However, the localization properties of a disordered system are usually not discernible from a study of the DoS. It is necessary to calculate two-particle properties or consider the influence of boundary conditions on energy eigenvalues as in the study of Thouless numbers to obtain information about localization. Another feature of disordered systems is the independence of their localization properties from details of the disorder in the system. For example, the range of the disorder affects non-universal quantities like the mean-free path but does not influence whether or not the system shows localization at all. Recently, new symmetry classes came into focus that do not conform to the standard expectations about disordered systems outlined above. As we will show in this contribution, details of disorder do matter for these systems and localization properties leave their mark on the DoS. In particular, we look at a system that presents an idealization of a disordered d-wave superconductor. In our study we neglect effects of self-consistency and concentrate on the d-wave symmetry and influence of different kinds of disorder. We consider the lattice quasi-particle Hamiltonian

Journal of the Physical Society of JapanJan 3, 20030 citations

Universal Features of the Nonequilibrium Dynamics of Many-Body Quantum Systems

Léa Ferreira dos Santos, Eduardo Jonathan Torres-Herrera

Bulletin of the American Physical SocietyJun 4, 20140 citations

The universal behavior of a disordered system

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The universal behavior of a disordered system

Abstract

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