Eur. Phys. J. B (2015) 88: 154
https://doi.org/10.1140/epjb/e2015-60188-0

Regular Article

Effective one-dimensional models from matrix product states

Lehrstuhl für Theoretische Physik I, TU Dortmund, Otto-Hahn Straße 4, 44221 Dortmund, Germany

^a e-mail: frederik.keim@tu-dortmund.de

Received: 9 March 2015
Received in final form: 28 April 2015
Published online: 15 June 2015

Abstract

In this paper we present a method for deriving effective one-dimensional models based on the matrix product state formalism. It exploits translational invariance to work directly in the thermodynamic limit. We show, how a representation of the creation operator of single quasi-particles in both real and momentum space can be extracted from the dispersion calculation. The method is tested for the analytically solvable Ising model in a transverse magnetic field. Properties of the matrix product representation of the creation operator are discussed and validated by calculating the one-particle contribution to the spectral weight. Results are also given for the ground state energy and the dispersion.