Simulated annealing for tensor network states

Markov chains for probability distributions related to matrix product states and one-dimensional Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a simulated annealing scheme for ground states of such Hamiltonians. Numerical experiments suggest that a linear, i.e., fast, schedule is possible in non-trivial cases. A natural extension of these chains to two-dimensional settings is next presented and tested. The obtained results compare well with Euclidean evolution. The proposed Markov chains are easy to implement and are inherently sign problem free (even for fermionic degrees of freedom).