Matrix product states approach to the Heisenberg ferrimagnetic spin chains

TL;DR

This paper introduces a generalized matrix product states method for quantum spin chains, enabling the description of systems with nonzero total spin and broken rotational symmetry, demonstrated on ferrimagnetic chains with strong agreement to numerical data.

Contribution

A novel matrix product states approach that constructs states with specific total spin, extending previous methods to describe ferrimagnetic chains with broken symmetry.

Findings

Accurate ground state energy calculations for ferrimagnetic chains.

Good agreement with quantum Monte Carlo data on correlation functions.

Method generalizes previous MP wavefunctions for integer-spin chains.

Abstract

We propose a new version of the matrix product (MP) states approach to the description of quantum spin chains, which allows one to construct MP states with certain total spin and its z-projection. We show that previously known MP wavefunctions for integer-spin antiferromagnetic chains and ladders correspond to some particular cases of our general ansatz. Our method allows to describe systems with spontaneously broken rotational symmetry, like quantum ferrimagnetic chains whose ground state has nonzero total spin. We apply this approach to describe the ground state properties of the isotropic ferrimagnetic Heisenberg chain with alternating spins 1 and 1/2 and compare our variational results with the high-precision numerical data obtained by means of the quantum Monte Carlo (QMC) method. For both the ground state energy and the correlation functions we obtain very good agreement between the variational results and the QMC data.