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International Journal of Quantum Chemistry

Long-range order for spin pairing in valence bond theory

Daniel Klein

Published Jun 18, 2009• 2 citations
Publisher

Abstract

It is pointed out that on certain extended lattices conventional valence bond wavefunctions exhibit novel types of long-range order (LRO). For the linear chain lattice the LRO might be associated with bond alternation and spin-Peierls transitions. For the graphite lattice the LRO is somewhat more complicated and the physical manifestations are more speculative.

DOI
10.1002/qua.560160830

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•Jan 1, 1995•1 citation
It is pointed out that on certain extended lattices conventional valence bond wavefunctions exhibit novel types of long-range order (LRO). For the linear chain lattice the LRO might be associated with bond alternation and spin-Peierls transitions. For the graphite lattice the LRO is somewhat more complicated and the physical manifestations are more speculative.
Ground-state instability to bond alternation in long linear chains is considered from the point of view of valence-bond (VB) theory. This instability is viewed as the consequence of a long-range order (LRO) which is expected if the ground state is reasonably described in terms of the Kekul\'e states (with nearest-neighbor singlet pairing). It is argued that the bond alternation and associated LRO predicted by this simple, VB picture is retained for certain linear Heisenberg models; many-body VB calculations on spin s=12s=\frac{1}{2}s=21​ and s=1s=1s=1 chains are carried out in a test of this argument.
Quantum spin-lattice systems in low dimensions exhibit a variety of interesting zero-temperature phases, some of which show non-classical (i.e., non-magnetic) long-range orders, such as dimer or trimer valence-bond order. These symmetry-breaking systems with localized valence bonds are referred to as valence-bond lattices (VBL) in this article. A review of our systematic microscopic formalism based on a proper set of composite operators for the ground and excited states of the VBL systems is given. The one-dimensional (1D) spin-121\over221​ frustrated model is investigated in detail. Several possible VBL systems on the 1D spin-1 chains, the 2D square and {\it kagomé} lattices are also discussed. That our microscopic theory guarantees the rotational symmetry of the VBL systems is emphasized.
We propose that a valence-bond-solid (VBS) order can be stabilized in certain two-dimensional antiferromagnets due to spin-lattice coupling. In contrast to the VBS state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) type, the spin-lattice coupling-induced VBS state can occur when 2S2S2S is not an integer multiple of the coordination number zzz. S=2S=2S=2 spins on the triangular lattice with z=6z=6z=6 is discussed as an example. Within the Schwinger boson mean-field theory the ground state is derived as the direct product of states, one of which represents the conventional long-range ordered spins, and the other given by the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ modulation of the valence bond amplitudes. Excitation spectrum for the modulated valence bond state is worked out within the single-mode approximation. The spectrum offers a new collective mode, distinct from the spin wave excitations of the magnetically ordered ground state, and observable in neutron scattering.
Abstract. Quantum spin-lattice systems in low dimensions exhibit a variety of interesting zero-temperature phases, some of which show non-classical (i.e., non-magnetic) long-range orders, such as dimer or trimer valence-bond order. These symmetry-breaking systems with localized valence bonds are referred to as valence-bond lattices (VBL) in this article. A review of our systematic microscopic formalism based on a proper set of composite operators for the ground and excited states of the VBL systems is given. The onedimensional (1D) spin-1 2 frustrated model is investigated in detail. Several possible VBL systems on the 1D spin-1 chains, the 2D square and kagomé lattices are also discussed. That our microscopic theory guarantees the rotational symmetry of the VBL systems is emphasized. 1.