Studies on a frustrated Heisenberg spin chain with alternating ferromagnetic and antiferromagnetic exchanges

TL;DR

This paper investigates a frustrated Heisenberg spin chain with alternating ferromagnetic and antiferromagnetic interactions, revealing its phase diagram, ground states, and a magnetization jump, combining analytical and numerical methods.

Contribution

It provides the first comprehensive analysis of a frustrated alternating Heisenberg chain, including exact ground states and phase diagram characterization.

Findings

Exact ground state along a specific parameter line

Identification of phase boundaries and quantum phases

Observation of a magnetization jump under magnetic field

Abstract

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ($J_1^F$) and antiferromagnetic ($J_1^A$) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction ($J_2^F$). In this model frustration is present due to the non-zero $J_2^F$. The model with site spin $s$ behaves like a Haldane spin chain with site spin 2$s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$. We show that the exact ground state of the model can be found along a line in the parameter space. For fixed $J_1^F$, the phase diagram in the space of $J_1^A-J_2^F$ is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.