Universal Eigenvalue Distribution for Locally Interacting Quantum Systems

Wigner has shown that the eigenvalue distribution of a Gaussian orthogonal or unitary ensemble of random matrices approaches a semicircle in the thermodynamic limit.[1] Here, we show that the joint eigenvalue distribution of locally interacting quantum systems, that is, ensembles of finite dimensional subsystems with local interactions between them, approaches a Gaussian distribution as the number of subsystems is taken to infinity. In the talk, we present our analytical results supported by numerical data and discuss possible implications of a Gaussian density of states for physical problems.