Density Matrix Renormalisation Group Calculations for Two-Dimensional Lattices: An Application to the Spin-Half and Spin-One Square-Lattice Heisenberg Models

TL;DR

This paper introduces a new 2D DMRG method that effectively computes ground-state energies for square-lattice Heisenberg models, outperforming previous approximate techniques.

Contribution

The paper presents a multi-chain-type 2D DMRG approach that utilizes system and environment blocks at all stages, improving accuracy and efficiency for 2D quantum lattice systems.

Findings

Achieved ground-state energy per bond of -0.3321 for spin-half model.

Achieved ground-state energy per bond of -1.1525 for spin-one model.

Method is competitive with previous 2D DMRG and other approximate methods.

Abstract

A new density matrix renormalisation group (DMRG) approach is presented for quantum systems of two spatial dimensions. In particular, it is shown that it is possible to create a multi-chain-type 2D DMRG approach which utilises previously determined system and environment blocks {\it at all points}. One firstly builds up effective quasi-1D system and environment blocks of width $L$ and these quasi-1D blocks are then used to as the initial building-blocks of a new 2D infinite-lattice algorithm. This algorithm is found to be competitive with those results of previous 2D DMRG algorithms and also of the best of other approximate methods. An illustration of this is given for the spin-half and spin-one Heisenberg models on the square lattice. The best results for the ground-state energies per bond of the spin-half and spin-one square-lattice Heisenberg antiferromagnets for the $N = 20 \times 20$ lattice using this treatment are given by $E_g/N_B = -0.3321$ and $E_g/N_B = -1.1525$, respectively.