# Theoretical Physics

**6 March 2014**

**Time:**15:00 to 16:00

**Location:**EC Stoner SR 9.90

Sofyan Iblisdir (Barcelona, Spain)

Markov chains for tensor network states

Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation 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 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 the random approximation scheme can be tailored to escape local minima.

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