DMRG Studies of the Spin-Half Heisenberg System with Dimerization and Frustration

TL;DR

This study uses the density matrix renormalization group method to analyze the phase diagram and low-energy properties of a frustrated, dimerized spin-half chain, revealing critical points, gap behaviors, and phase transitions.

Contribution

It provides a detailed phase diagram of the frustrated dimerized spin-half chain, including critical points, gap scaling, and the identification of disorder lines and phase boundaries.

Findings

The system is gapless for J2 < J2c and gapped for J2 > J2c.

The gap scales as δ^0.667 at the critical point J2c.

A disorder line separates Neel and spiral phases in the phase diagram.

Abstract

Using the density matrix renormalization group technique, we study the ground state phase diagram and other low-energy properties of an isotropic antiferromagnetic spin-half chain with both dimerization and frustration, i.e., an alternation $\delta$ of the nearest neighbor exchanges and a next-nearest-neighbor exchange $J_2~$. For $\delta = 0$, the system is gapless for $J_2 < J_{2c} ~$ and has a gap for $J_2 > J_{2c} ~$ where $J_{2c}~$ is about $0.241$. For $J_2 = J_{2c}$, the gap above the ground state grows as $\delta$ to the power $0.667 \pm 0.001$. In the $J_2 - \delta$ plane, there is a disorder line $2 J_2 + \delta = 1$. To the left of this line, the peak in the static structure factor $S(q)$ is at $q_{max} = \pi$ (Neel phase), while to the right of the line, $q_{max}$ decreases from $\pi$ to $\pi / 2$ as $J_2$ is increased to large values (spiral phase). For $\delta = 1$, the system is equivalent to two coupled chains as on a ladder and it is gapped for all values of the interchain coupling.