An Ising spin system which is situated on a two-dimensional square or a three-dimensional simple cubic lattice is considered. If there is a spin-lattice coupling and the lattice has no translational symmetry, there appears effectively a long range four-spin interaction in which the four spins are on a same axis. The ground state of the spin system is represented by using the ground state of a one-dimensional system where only the interactions along one axis are considered. The devil's staircase which has recently been shown to exist in such a one-dimensional system is wholly reproduced in a system on a two-dimensional square or a three-dimensional simple cubic lattice.An Ising spin system which is situated on a two-dimensional square or a three-dimensional simple cubic lattice is considered. If there is a spin-lattice coupling and the lattice has no translational symmetry, there appears effectively a long range four-spin interaction in which the four spins are on a same axis. The ground state of the spin system is represented by using the ground state of a one-dimensional system where only the interactions along one axis are considered. The devil's staircase which has recently been shown to exist in such a one-dimensional system is wholly reproduced in a system on a two-dimensional square or a three-dimensional simple cubic lattice.

Journal of the Physical Society of JapanJan 15, 19863 citations

Theory of valence-bond lattice on spin-lattices

Yang Xian

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.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.

Jan 1, 19951 citation

Quantum Spin Systems

Ola Bratteli, Derek W. Robinson

Springer eBooksJan 1, 19970 citations

On a one-dimensional spin system

Stanislav Alekseevich Molchanov, Nguyen The Long

Theoretical and Mathematical PhysicsOct 1, 19750 citations

Theory of Valence-Bond Lattice on Spin Lattice

Yang Xian

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- $1\over2$ 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.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-$1\over2$ 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.

arXiv:cond-mat/9407117Jul 29, 19940 citations

1\over2

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.