Tensor Product Variational Formulation for Quantum Systems

TL;DR

This paper introduces a variational approach using tensor product states and CTMRG to analyze 2D quantum spin models, providing a new method to approximate their ground states and energies.

Contribution

It presents a novel variational formulation for 2D quantum systems employing tensor product states and CTMRG, extending DMRG techniques to infinite 2D models.

Findings

Upper bounds for variational energy are obtained.

The method effectively approximates ground states of 2D quantum models.

The approach bridges DMRG and tensor network methods for 2D systems.

Abstract

We consider a variational problem for the two-dimensional (2D) Heisenberg and XY models, using a trial state which is constructed as a 2D product of local weights. Variational energy is calculated by use of the the corner transfer matrix renormalization group (CTMRG) method, and its upper bound is surveyed. The variational approach is a way of applying the density matrix renormalization group method (DMRG) to infinite size 2D quantum systems.