Ground state of an $S=1/2$ distorted diamond chain - model of $\mathrm{C}{\mathrm{u}}_3\mathrm{C}{\mathrm{l}}_6({\mathrm{H}}_2\mathrm{O}{)}_2\cdot 2{\mathrm{H}}_8{\mathrm{C}}_4\mathrm{S}{\mathrm{O}}_2$

Abstract

We study the ground state of the model Hamiltonian of the trimerized $S=1/2$ quantum Heisenberg chain $\mathrm{C}{\mathrm{u}}_3\mathrm{C}{\mathrm{l}}_6({\mathrm{H}}_2\mathrm{O}{)}_2\cdot 2{\mathrm{H}}_8{\mathrm{C}}_4\mathrm{S}{\mathrm{O}}_2$ in which the non-magnetic ground state is observed recently. This model consists of stacked trimers and has three kinds of coupling constants between spins; the intra-trimer coupling constant $J_1$ and the inter-trimer coupling constants $J_2$ and $J_3$. All of these constants are assumed to be antiferromagnetic. By use of the analytical method and physical considerations, we show that there are three phases on the ${\tilde{J}}_2-{\tilde{J}}_3$ plane (${\tilde{J}}_2\equiv J_2/J_1$, ${\tilde{J}}_3\equiv J_3/J_1$), the dimer phase, the spin fluid phase and the ferrimagnetic phase. The dimer phase is caused by the frustration effect. In the dimer phase, there exists the excitation gap between the two-fold degenerate ground state and the first excited state, which explains the non-magnetic ground state observed in $\mathrm{C}{\mathrm{u}}_3\mathrm{C}{\mathrm{l}}_6({\mathrm{H}}_2\mathrm{O}{)}_2\cdot 2{\mathrm{H}}_8{\mathrm{C}}_4\mathrm{S}{\mathrm{O}}_2$. We also obtain the phase diagram on the ${\tilde{J}}_2-{\tilde{J}}_3$ plane from the numerical diagonalization data for finite systems by use of the Lanczos algorithm.

LaTeX2e, 15 pages, 21 eps figures, typos corrected, slightly detailed explanation added

References in corpus (3)

• Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
• Ground states with cluster structures in a frustrated Heisenberg chain
• Plateau of the Magnetization Curve of the S=1/2 Ferromagnetic-Ferromagnetic-Antiferromagnetic Spin Chain

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