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We present a study of thermalisation of a small isolated Hubbard latticecluster prepared in a pure state with a well-defined energy. We examine how atwo-site subsystem of the lattice thermalises with the rest of the system asits environment. We explore numerically the existence of thermalisation over arange of system parameters, such as the interaction strength, system size andthe strength of the coupling between the subsystem and the rest of the lattice.We find thermalisation over a wide range of parameters and that interactionsare crucial for efficient thermalisation of small systems. We relate thisthermalisation behaviour to the eigenstate thermalisation hypothesis andquantify numerically the extent to which eigenstate thermalisation holds. Wealso verify our numerical results theoretically with the help of previouslyestablished results from random matrix theory for the local density of states,particularly the finite-size scaling for the onset of thermalisation.

Thermalisation of Local Observables in Small Hubbard Lattices