Ground state properties of the bond alternating spin-1/2 anisotropic Heisenberg chain

Paul Paul,Ghosh Ghosh

doi:10.5488/cmp.20.23701

Abstract

Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-$\frac{1}{2}$ anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases. The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains. Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization. Dispersion relations, spin gap and several ground state orders have been obtained. Dimer order and string orders are found to coexist in the ground state. Spin gap is found to develop as soon as the non-uniformity in alternating bond strength is introduced in the AFM-AFM chain which further remains non-zero for the AFM-FM chain. This spin gap along with the string orders attribute to the Haldane phase. The Haldane phase is found to exist in most of the anisotropic region similar to the isotropic point.

Highlights

The spin-Heisenberg chains with an energy gap just above the ground state attract immense interest since they give rise to many exotic properties in the ground state
Dispersion relations, dimer order and spin gap are obtained by using the bond operator formalism
For fixed values of J1, J2 and ∆, the six self-consistent solutions are obtained from equations (3.7) and are employed to determine the dispersion relations, ground state energy, spin gap and dimer order

Summary

Introduction

Heisenberg chains with an energy gap (spin gap) just above the ground state attract immense interest since they give rise to many exotic properties in the ground state. The Haldane phase can be characterized by the finite value of string order parameter [3, 4] The existence of this spin gap can be explained from the incongruousness of this system with the Lieb-Schultz-Mattis (LSM) theorem [5]. LSM theorem though the system has global U(1) symmetry From this point of view, a gap in the spin excitation may appear in the bond alternating chain. Dispersion relations, dimer order and spin gap are obtained by using the bond operator formalism. All those properties in addition to string orders have been separately estimated by using exact diagonalization method.

Four-site bond alternating anisotropic Heisenberg plaquette

Jordan-Wigner representation

Exact diagonalization results

Ground state properties

Findings

Conclusions