On the Optimal Layout of Two-Dimensional Lattices for Density Matrix Renormalization Group

TL;DR

This paper investigates optimal two-dimensional lattice layouts for density matrix renormalization group (DMRG) to improve accuracy and convergence, proposing a Hamiltonian path-based approach and applying it to various spin models.

Contribution

It introduces a geometric cost function to find optimal lattice layouts, enhancing DMRG performance for 2D quantum spin models.

Findings

Optimal layouts reduce variational energy and truncation error.

Hamiltonian path conjecture improves DMRG efficiency.

Applications to square and triangular lattices demonstrate effectiveness.

Abstract

For quantum spin models defined on a two-dimensional lattice, we look for the best numbering of the lattice sites (a layout) that, at fixed bond dimension and other parameters of the density matrix renormalization group (DMRG) algorithm, gives the lowest value of the variational energy, maximum entropy and truncation error. We consider the conjecture that the optimal layout is a Hamiltonian path, and that it optimizes a simply computable geometric cost function. Finding the minimum of such a function, which is a variant of the minimum linear arrangement problem, provides the DMRG with an efficient layout of the lattice and improves both accuracy and convergence time. We present applications to the antiferromagnetic and spin glass spin-1/2 models on the square and triangular lattices.