Relaxation mechanisms in a disordered system with the Poisson level statistics

Janez Bonča1,2 and Marcin Mierzejewski3

1Department of Physics, Faculty of Mathematics and Physics,

University of Ljubljana, SI-1000 Ljubljana, Slovenia

2Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia

3Department of Theoretical Physics, Faculty of Fundamental Problems of Technology,

Wrocław University of Science and Technology, 50-370 Wrocław, Poland

I will discuss the interplay between many-body localization and spin-symmetry. I will present the time evolution of several observables in the anisotropic t − J model. Like the Hubbard chain, the studied model contains charge and spin degrees of freedom. Yet, it has a smaller Hilbert space and thus allows for numerical studies of larger systems. I will compare the field disorder that breaks the Z2 spin symmetry and a potential disorder that preserves the latter symmetry. In the former case, sufficiently strong disorder leads to localization of all studied observables, at least for the studied system sizes. However, in the case of symmetry-preserving disorder, we observe that odd operators under the Z2 spin transformation relax towards the equilibrium value at relatively short time scales that grow only polynomially with the disorder strength. On the other hand, the dynamics of even operators and the level statistics within each symmetry sector are consistent with localization. Our results indicate that localization exists within each symmetry sector for symmetry preserving disorder. Odd operators’ apparent relaxation is due to their time evolution between various symmetry sectors.

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