No abstract

We show the boundedness of entanglement entropy for (bipartite) pure states of quantum spin chains implies split property of subsystems. As a corollary the infinite volume ground states for 1-dim spin chains with the spectral gap between the ground state energy and the rest of spectrum have the split property. We see gapless excitation exists for the spinless Fermion on Z if the ground state is non-trivial and translationally invariant and the U (1) gauge symmetry is unbroken. Here we do not assume uniqueness of ground states for all finite volume Hamiltonians.Keywords: quantum spin chain, spectral gap, split property, boundedness of entanglement entropy.

We consider an infinite spin chain as a bipartite system consisting of the left and right half-chain and analyze entanglement properties of pure states with respect to this splitting. In this context we show that the amount of entanglement contained in a given state is deeply related to the von Neumann type of the observable algebras associated to the halfchains. Only the type I case belongs to the usual entanglement theory which deals with density operators on tensor product Hilbert spaces, and only in this situation separable normal states exist. In all other cases the corresponding state is infinitely entangled in the sense that one copy of the system in such a state is sufficient to distill an infinite amount of maximally entangled qubit pairs. We apply this results to the critical XY model and show that its unique ground state ϕS provides a particular example for this type of entanglement. * Electronic

For an infinitely extended system consisting of a finite subsystem and several reservoirs, the time evolution of states is studied. Initially, the reservoirs are prepared to be in equilibrium with different temperatures and chemical potentials. If the time evolution is L 1-asymptotic abelian, (i) steady states exist, (ii) they and their relative entropy production are independent of the way of division into a subsystem and reservoirs, and (iii) they are stable against local perturbations. The explicit expression of the relative entropy production and a KMS characterization of the steady states are given. And a rigorous definition of MacLennan-Zubarev ensembles is proposed. A noncommutative analog to the fluctuation theorem is derived provided that the evolution and an initial state are time reversal symmetric.

We prove the central limit theorem for Gibbs states and ground states of quasifree Fermions (bilinear Hamiltonians) and those of the off critical XY model on a onedimensional integer lattice.