Ground State Properties of One Dimensional S=1/2 Heisenberg Model with Dimerization and Quadrumerization

TL;DR

This paper investigates the ground state phases of a one-dimensional S=1/2 Heisenberg model with dimerization and quadrumerization, revealing a rich phase diagram including Haldane and dimer states through numerical and analytical methods.

Contribution

It provides a comprehensive phase diagram for the model using numerical exact diagonalization and analytical solutions, highlighting the variety of ground states and critical exponents.

Findings

Identified ground states including S=1 Haldane, S=1 dimer, and S=1/2 dimer states.

Calculated the gap exponent $ u$, matching the dimerization transition of the isotropic chain.

Derived the phase diagram analytically in the XY limit and compared with the isotropic case.

Abstract

The one dimensional S=1/2 Heisenberg model with dimerization and quadrumerization is studied by means of the numerical exact diagonalization of finite size systems. Using the phenomenological renormalization group and finite size scaling law, the ground state phase diagram is obtained in the isotropic case. It exhibits a variety of the ground states which contains the S=1 Haldane state, S=1 dimer state and S=1/2 dimer state as limiting cases. The gap exponent $\nu$ is also calculated which coincides with the value for the dimerization transition of the isotropic Heisenberg chain. In the XY limit, the phase diagram is obtained analytically and the comparison is made with the isotropic case.