A class of ansatz wave functions for 1D spin systems and their relation to DMRG

TL;DR

This paper explores the connection between DMRG and matrix product states in 1D spin systems, providing a simple variational ansatz and methods to construct and analyze these states.

Contribution

It introduces a straightforward variational ansatz for DMRG ground states and details how to construct and analyze matrix product states for 1D spin systems.

Findings

DMRG ground states can be expressed as matrix product states

A simple variational ansatz reproduces DMRG results

Methods to compute properties and excitation spectra of matrix product states

Abstract

We investigate the density matrix renormalization group (DMRG) discovered by White and show that in the case where the renormalization eventually converges to a fixed point the DMRG ground state can be simply written as a ``matrix product'' form. This ground state can also be rederived through a simple variational ansatz making no reference to the DMRG construction. We also show how to construct the ``matrix product'' states and how to calculate their properties, including the excitation spectrum. This paper provides details of many results announced in an earlier letter.