Cluster property in a classical canonical ensemble

J.L. De Coen, F. Englert, R. Brout

Tomotaka Kuwahara, Keiji Saito

The clustering property of an equilibrium bipartite correlation is one of the most general thermodynamic properties in noncritical many-body quantum systems. Herein, we consider the thermalization properties of a system class exhibiting the clustering property. We investigate two regimes, namely, regimes of high and low density of states corresponding to high- and low-energy regimes, respectively. We show that the clustering property is connected to several properties on the eigenstate thermalization through the density of states. Remarkably, the eigenstate thermalization is obtained in the low-energy regime with a sparse density of states, which is typically seen in gapped systems. For the high-energy regime, we demonstrate the ensemble equivalence between microcanonical and canonical ensembles even for a subexponentially small energy shell with respect to the system size, which eventually leads to the weak version of eigenstate thermalization.

L. J. F. Broer

Wim Magnus, F. Brosens

Deepak Iyer, Mark Srednicki, Marcos Rigol

It is common knowledge that the microcanonical, canonical, and grand-canonical ensembles are equivalent in thermodynamically large systems. Here, we study finite-size effects in the latter two ensembles. We show that contrary to naive expectations, finite-size errors are exponentially small in grand canonical ensemble calculations of translationally invariant systems in unordered phases at finite temperature. Open boundary conditions and canonical ensemble calculations suffer from finite-size errors that are only polynomially small in the system size. We further show that finite-size effects are generally smallest in numerical linked cluster expansions. Our conclusions are supported by analytical and numerical analyses of classical and quantum systems.

Jihyeon Yoon