Ground State Properties of an S=1/2 Distorted Diamond Chain

TL;DR

This paper studies the ground state phases and magnetization properties of a distorted S=1/2 diamond chain model relevant to a specific copper compound, using numerical methods to identify phase boundaries and magnetization plateaus.

Contribution

It provides a detailed phase diagram of the model and reveals the emergence of a 2/3 magnetization plateau, which is associated with spontaneous translational symmetry breaking.

Findings

Identification of dimerized, spin fluid, and ferrimagnetic phases.

Discovery of a 2/3 magnetization plateau in certain parameter regimes.

Good agreement between perturbation theory and numerical results for phase boundaries.

Abstract

We investigate the ground state properties of an S=1/2 distorted diamond chain described by the Hamiltonian ${\cal H}=J_1\sum_\ell\bigl\{\bigl(\vecS_{3\ell-1}\cdot\vecS_{3\ell} +\vecS_{3\ell}\cdot\vecS_{3\ell+1}\bigr)+J_2\vecS_{3\ell-2}\cdot\vecS_{3\ell-1} +J_3\bigl(\vecS_{3\ell-2}\cdot\vecS_{3\ell}+\vecS_{3\ell}\cdot\vecS_{3\ ell+2}\bigr)-H S_{\ell}^z\bigr\}$ ($J_1,~J_2,~J_3\geq0$), which models well a trimerized S=1/2 spin chain system Cu$_3$Cl$_6$(H$_2$O)$_2$$\cdot$2H$_8$C$_4$SO$_2$. Using an exact diagonalization method by means of the Lancz\"os technique, we determine the ground state phase diagram in the H=0 case, composed of the dimerized, spin fluid, and ferrimagnetic phases. Performing a degenerate perturbation calculation, we analyze the phase boundary line between the latter two phases in the $J_2,~J_3\llJ_1$ limit, the result of which is in good agreement with the numerical result. We calculate, by the use of the density matrix renormalization group method, the ground state magnetization curve for the case (a) where $J_1=1.0$, $J_2=0.8$, and $J_3=0.5$, and the case (b) where $J_1=1.0$, $J_2=0.8$, and $J_3=0.3$. We find that in the case (b) the 2/3-plateau appears in addition to the 1/3-plateau which also appears in the case (a). The translational symmetry of the Hamiltonian $\cal H$ is spontaneously broken in the 2/3-plateau state as well as in the dimerized state.