Symmetry adapted finite-cluster solver for quantum Heisenberg model in two-dimensions: a real-space renormalization approach

TL;DR

This paper introduces a symmetry-adapted real-space renormalization method for solving the 2D quantum Heisenberg model, efficiently incorporating lattice symmetries and SU(2) spin symmetry to improve calculations.

Contribution

It develops a novel finite-cluster solver that combines group-theoretical analysis with exact diagonalization within a real-space renormalization framework for 2D quantum spin systems.

Findings

Successfully applied to spin-half antiferromagnet on a square lattice

Demonstrated accurate calculation of local observables

Verified effectiveness of symmetry-based truncation

Abstract

We present a quantum cluster solver for spin-$S$ Heisenberg model on a two-dimensional lattice. The formalism is based on the real-space renormalization procedure and uses the lattice point group-theoretical analysis and nonabelian SU(2) spin symmetry technique. The exact diagonalization procedure is used twice at each renormalization group step. The method is applied to the spin-half antiferromagnet on a square lattice and a calculation of local observables is demonstrated. A symmetry based truncation procedure is suggested and verified numerically.