Type of communication: Oral
Submitted by:IBLISDIR, Sofyan
University of Barcelona

Markov chains for tensor network states

Sofyan Iblisdir

Markov chains for probability distributions related to matrix product states and 1-dimensional 
quantum 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 2-dimensional quantum Hamiltonians is next presented and tested. This 
extension is stable by construction and the obtained results compare well with euclidean evolution. 
The proposed Markov chains are inherently sign problem free (even for fermionic degrees of 
freedom), and can be tailored to escape local minima.