Effective One-Dimensional Models from Matrix Product States

TL;DR

This paper introduces a method to derive effective one-dimensional models using matrix product states, leveraging translational invariance and applicable in the thermodynamic limit, with validation on the Ising model.

Contribution

The paper presents a novel approach to extract effective 1D models and quasi-particle creation operators directly from matrix product states, enhancing analysis of many-body systems.

Findings

Validated method on the Ising model in a transverse field

Calculated ground state energy and dispersion relations

Analyzed properties of matrix product representations

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.