Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain

TL;DR

This paper analyzes the thermodynamic limit of the density matrix renormalization group (DMRG) for the spin-1 Heisenberg chain, showing that fixed points can be represented by product states with elementary excitations, and introduces a variational approach.

Contribution

It demonstrates that in the thermodynamic limit, DMRG fixed points can be described by simple product states and elementary excitations, providing a new variational method.

Findings

States can be represented by product ground states with Bloch excitations.

The variational ansatz reproduces DMRG results without renormalization.

Method successfully applied to the spin-1 Heisenberg model.

Abstract

The density matrix renormalization group (``DMRG'') discovered by White has shown to be a powerful method to understand the properties of many one dimensional quantum systems. In the case where renormalization eventually converges to a fixed point we show that quantum states in the thermodynamic limit with periodic boundary conditions can be simply represented by a special type of product ground state with a natural description of Bloch states of elementary excitations that are spin-1 solitons. We then observe that these states can be rederived through a simple variational ansatz making no reference to a renormalization construction. The method is tested on the spin-1 Heisenberg model.