Thermalization of local observables in small Hubbard lattices
Abstract
We present a study of thermalization of a small isolated Hubbard lattice cluster prepared in a pure state with a well-defined energy. We examine how a two-site subsystem of the lattice thermalizes with the rest of the system as its environment. We explore numerically the existence of thermalization over a range of system parameters, such as the interaction strength, system size, and the strength of the coupling between the subsystem and the rest of the lattice. We find thermalization over a wide range of parameters and that interactions are crucial for efficient thermalization of small systems. We relate this thermalization behavior to the eigenstate thermalization hypothesis and quantify numerically the extent to which eigenstate thermalization holds. We also verify our numerical results theoretically with the help of previously established results from random matrix theory for the local density of states, particularly the finite-size scaling for the onset of thermalization.
- Publication:
-
Physical Review A
- Pub Date:
- August 2012
- DOI:
- 10.1103/PhysRevA.86.023609
- arXiv:
- arXiv:1204.3036
- Bibcode:
- 2012PhRvA..86b3609G
- Keywords:
-
- 03.75.Ss;
- 05.30.Ch;
- 03.65.-w;
- Degenerate Fermi gases;
- Quantum ensemble theory;
- Quantum mechanics;
- Condensed Matter - Quantum Gases;
- Condensed Matter - Mesoscale and Nanoscale Physics;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 22 pages, 23 figures