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arXiv:cond-mat/9303010 · Physical review. B, Condensed matter

Phase diagram of theS=1/2 quantum spin chain with bond alternation

Masaru Yamanaka, Yasuhiro Hatsugai, Mahito Kohmoto

Published Oct 1, 1993• 51 citations
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Abstract

We study the ground-state properties of the bond-alternating S=1/2 quantum spin chain whose Hamiltonian is H= ${\mathit{tsum}}_{\mathit{j}}$ (${\mathit{S}}_{2\mathit{j}}^{\mathit{x}}$${\mathit{S}}_{2\mathit{j}+1}^{\mathit{x}}$ +${\mathit{S}}_{2\mathit{j}}^{\mathit{y}}$${\mathit{S}}_{2\mathit{j}+1}^{\mathit{y}}$ +\ensuremath{\lambda}${\mathit{S}}_{2\mathit{j}}^{\mathit{z}}$${\mathit{S}}_{2\mathit{j}+1}^{\mathit{z}}$) +\ensuremath{\beta}t${sum}_{\mathit{j}}$${\mathbf{S}}_{2\mathit{j}\mathrm{\ensuremath{-}}1}$\ensuremath{\cdot}${\mathbf{S}}_{2\mathit{j}}$. When \ensuremath{\beta}=0, the ground state is a collection of local singlets with a finite excitation gap. In the limit of strong ferromagnetic coupling \ensuremath{\beta}\ensuremath{\rightarrow}-\ensuremath{\infty}, this is equivalent to the S=1 XXZ Hamiltonian. It has several ground-state phases in the \ensuremath{\lambda}-\ensuremath{\beta} plane including the Haldane phase which has a finite excitation gap above the ground. They are characterized by a full breakdown, partial breakdowns, and a nonbreakdown of the hidden discrete ${\mathit{Z}}_{2}$\ifmmode\times\else\texttimes\fi{}${\mathit{Z}}_{2}$ symmetry. The ground-state phase diagram is obtained by series expansions.

DOI
10.1103/physrevb.48.9555

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We study the ground-state properties of the bond-alternating S=1/2 quantum spin chain whose Hamiltonian is H= tsumj{\mathit{tsum}}_{\mathit{j}}tsumj​ ({\mathit{S}}_{2\mathit{j}}^{\mathit{x}}$${\mathit{S}}_{2\mathit{j}+1}^{\mathit{x}} +{\mathit{S}}_{2\mathit{j}}^{\mathit{y}}$${\mathit{S}}_{2\mathit{j}+1}^{\mathit{y}} +\ensuremath{\lambda}{\mathit{S}}_{2\mathit{j}}^{\mathit{z}}$${\mathit{S}}_{2\mathit{j}+1}^{\mathit{z}}) +\ensuremath{\beta}t{sum}_{\mathit{j}}$${\mathbf{S}}_{2\mathit{j}\mathrm{\ensuremath{-}}1}\ensuremath{\cdot}S2j{\mathbf{S}}_{2\mathit{j}}S2j​. When \ensuremath{\beta}=0, the ground state is a collection of local singlets with a finite excitation gap. In the limit of strong ferromagnetic coupling \ensuremath{\beta}\ensuremath{\rightarrow}-\ensuremath{\infty}, this is equivalent to the S=1 XXZ Hamiltonian. It has several ground-state phases in the \ensuremath{\lambda}-\ensuremath{\beta} plane including the Haldane phase which has a finite excitation gap above the ground. They are characterized by a full breakdown, partial breakdowns, and a nonbreakdown of the hidden discrete Z2{\mathit{Z}}_{2}Z2​\ifmmode\times\else\texttimes\fi{}Z2{\mathit{Z}}_{2}Z2​ symmetry. The ground-state phase diagram is obtained by series expansions.
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