Study on Ground States of Quantum Spin Systems by Restructuring Method

TL;DR

This paper introduces a restructuring Monte Carlo method to analyze the ground states of quantum spin systems, enabling efficient simulations and revealing hidden order in ladder spin models.

Contribution

It proposes a novel restructuring technique combined with Monte Carlo methods to study quantum spin ground states more efficiently than previous approaches.

Findings

Successfully determined coefficients in ground state expansions.

Identified hidden order in ladder spin systems with antiferromagnetic rungs.

Challenged previous claims about spin pair states in the ground state.

Abstract

We present a new method to study the ground state of quantum spin systems using the Monte Carlo techniques together with restructured intermediate states which we proposed previously. Our basic idea is to obtain coefficients in the expansion of the ground state from measurements of the normalized frequencies of each state on the boundary in the Trotter direction. The restructuring method we have proposed makes it possible to carry out simulations within available resources of computers. For a concrete example we study ladder spin systems with antiferromagnetic intra-chain nearest neighbor interactions, whose ground states may be equivalent to that of the spin 1 chain. For the ladder with ferromagnetic rungs we successfully show how to determine the magnitudes and relative signs of the coefficients in the expansion. When the ladder has antiferromagnetic rungs we examine White's claim that the diagonally situated pair of spins are mostly triplet states in the ground state. Our results strongly suggest that the system has the hidden order which is constructed by the specially aligned triplet states of diagonal pairs.