Tensor network states: matrix product states and relatives

Glen Evenbly, Guifré Vidal

Anders W. Sandvik, Guifré Vidal

We show that the formalism of tensor-network states, such as the matrix-product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of this approach by explicit MPS calculations for the transverse Ising chain with up to N=256 spins at criticality, using periodic boundary conditions and D x D matrices with D up to 48. The computational cost of our scheme formally scales as ND3, whereas standard MPS approaches and the related density matrix renormalization group method scale as ND5 and ND6, respectively, for periodic systems.

Boye Buyens

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems.The matrix product states (MPS) are one particular class of TNS and are used for the simulation of (1+1)-dimensional systems.In this proceeding we use MPS to determine the elementary excitations of the Schwinger model in the presence of an electric background field.We obtain an estimate for the value of the background field where the oneparticle excitation with the largest energy becomes unstable and decays into two other elementary particles with smaller energy.

Teresa Dimitra Karanikoulaou

Román Orús

Karel Van Acoleyen

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems.The matrix product states (MPS) are one particular class of TNS and are used for the simulation of 1+1 dimensional systems.In this proceeding we use MPS to determine the elementary excitations of the Schwinger model in the presence of an electric background field.We obtain an estimate for the value of the background field where the oneparticle excitation with the largest energy becomes unstable and decays into two other elementary particles with smaller energy.