# Ergodicity breaking and wave-function statistics in disordered interacting systems

## Abstract

We present the study of the structure of many-body eigenfunctions in a one-dimensional disordered spin chain. We discuss the choice of an appropriate basis in the Hilbert space, where the problem can be seen as an Anderson model defined on a high-dimensional non-trivial graph, determined by the many-body Hamiltonian. The comparison with the usual behavior of wave-functions in finite dimensional Anderson localization allows us to put in light the main differences of the many-body case. At high disorder, the typical eigenfunctions do not seem to localize though they occupy a infinitesimal portion of the Hilbert space in the thermodynamic limit. We perform a detailed analysis of the distribution of the wave-function coefficients and their peculiar scaling in the small and large disorder phase. We propose a criterion to identify the position of the transition by looking at the long tails of these distributions. The results coming from exact diagonalization show signs of breaking of ergodicity when the disorder reaches a critical value that agrees with the estimation of the many-body localization transition in the same model.

- Authors:

- Laboratoire de Physique Théorique de l'ENS and Institut de Physique Theorique Philippe Meyer (France)

- Publication Date:

- OSTI Identifier:
- 22308267

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1610; Journal Issue: 1; Conference: TIDS15: 15. international conference on transport in interacting disordered systems, Sant Feliu de Guixols (Spain), 1-5 Sep 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENFUNCTIONS; HAMILTONIANS; HILBERT SPACE; MANY-BODY PROBLEM; SPIN; STATISTICS; WAVE FUNCTIONS

### Citation Formats

```
De Luca, Andrea.
```*Ergodicity breaking and wave-function statistics in disordered interacting systems*. United States: N. p., 2014.
Web. doi:10.1063/1.4893516.

```
De Luca, Andrea.
```*Ergodicity breaking and wave-function statistics in disordered interacting systems*. United States. doi:10.1063/1.4893516.

```
De Luca, Andrea. Wed .
"Ergodicity breaking and wave-function statistics in disordered interacting systems". United States.
doi:10.1063/1.4893516.
```

```
@article{osti_22308267,
```

title = {Ergodicity breaking and wave-function statistics in disordered interacting systems},

author = {De Luca, Andrea},

abstractNote = {We present the study of the structure of many-body eigenfunctions in a one-dimensional disordered spin chain. We discuss the choice of an appropriate basis in the Hilbert space, where the problem can be seen as an Anderson model defined on a high-dimensional non-trivial graph, determined by the many-body Hamiltonian. The comparison with the usual behavior of wave-functions in finite dimensional Anderson localization allows us to put in light the main differences of the many-body case. At high disorder, the typical eigenfunctions do not seem to localize though they occupy a infinitesimal portion of the Hilbert space in the thermodynamic limit. We perform a detailed analysis of the distribution of the wave-function coefficients and their peculiar scaling in the small and large disorder phase. We propose a criterion to identify the position of the transition by looking at the long tails of these distributions. The results coming from exact diagonalization show signs of breaking of ergodicity when the disorder reaches a critical value that agrees with the estimation of the many-body localization transition in the same model.},

doi = {10.1063/1.4893516},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1610,

place = {United States},

year = {Wed Aug 20 00:00:00 EDT 2014},

month = {Wed Aug 20 00:00:00 EDT 2014}

}