Diverging equilibration times in long-range quantum spin models

Abstract

The approach to equilibrium is studied for long-range quantum Ising models where the interaction strength decays like r^{-α} at large distances r with an exponent $\alpha$ not exceeding the lattice dimension. For a large class of observables and initial states, the time evolution of expectation values can be calculated. We prove analytically that, at a given instant of time t and for sufficiently large system size N, the expectation value of some observable <A>(t) will practically be unchanged from its initial value <A>(0). This finding implies that, for large enough N, equilibration effectively occurs on a time scale beyond the experimentally accessible one and will not be observed in practice.

4+ pages, 1 figure

References in corpus (6)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Breakdown of thermalization in finite one-dimensional systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Quasi-stationary states and the range of pair interactions
• Relaxation to thermal equilibrium in the self-gravitating sheet model