Alioscia Hamma, Perimeter Institute
Abstract
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body system are not physically accessible. We define physical ensembles of states by acting on random factorized states by a circuit of length $k$ of random and independent unitaries with local support. This simulates an evolution for finite time $k$ generated by a local (time-dependent) Hamiltonian. We apply group theoretic methods to study these statistical ensembles. In particular, we study the typicality of entanglement by means of the purity of the reduced state. We find that for a time $k=O(1)$ the typical purity obeys the area law, while for a time $k\sim O(L)$ the purity obeys a volume law, with $L$ the linear size of the system. Moreover, we show that for large values of $k$ the reduced state becomes very close to the completely mixed state.