Topologically distinct classes of valence bond solid states with their parent Hamiltonians TeX Export

@article{citeulike:4278239, abstract = {In this paper, we introduce a general method to construct one-dimensional translationally invariant valence bond solid states with a built-in Lie group \$G\$ and derive their matrix product representations. The general strategy to find their parent Hamiltonians is provided so that the valence bond solid states are their unique ground states. For quantum integer spin-\$S \$ chains, we discuss two topologically distinct classes of valence bond solid states: One is formed by two virtue SU(2) spin-\$J\$ variables in each site and another is by using two \$SO(2S+1)\$ spinors. Among them, a new spin-\$\% 1\$ fermionic valence bond solid state, its parent Hamiltonian, and its properties are discussed. Moreover, two types of the valence bond solid states with SO(5) symmetry are further generalized and their respective properties are analyzed in detail.}, archivePrefix = {arXiv}, author = {Tu, Hong-Hao and Zhang, Guang-Ming and Xiang, Tao and Liu, Zheng-Xin and Ng, Tai-Kai}, citeulike-article-id = {4278239}, citeulike-linkout-0 = {http://arxiv.org/abs/0904.0550}, citeulike-linkout-1 = {http://arxiv.org/pdf/0904.0550}, day = {3}, eprint = {0904.0550}, keywords = {matrix\_product\_states, topological}, month = {Apr}, posted-at = {2009-04-06 12:32:15}, priority = {2}, title = {Topologically distinct classes of valence bond solid states with their parent Hamiltonians}, url = {http://arxiv.org/abs/0904.0550}, year = {2009} }

TY - JOUR ID - citeulike:4278239 L3 - citeulike-article-id:4278239 N2 - In this paper, we introduce a general method to construct one-dimensional translationally invariant valence bond solid states with a built-in Lie group $G$ and derive their matrix product representations. The general strategy to find their parent Hamiltonians is provided so that the valence bond solid states are their unique ground states. For quantum integer spin-$S $ chains, we discuss two topologically distinct classes of valence bond solid states: One is formed by two virtue SU(2) spin-$J$ variables in each site and another is by using two $SO(2S+1)$ spinors. Among them, a new spin-$% 1$ fermionic valence bond solid state, its parent Hamiltonian, and its properties are discussed. Moreover, two types of the valence bond solid states with SO(5) symmetry are further generalized and their respective properties are analyzed in detail. TI - Topologically distinct classes of valence bond solid states with their parent Hamiltonians KW - matrix_product_states KW - topological AU - Tu, Hong-Hao AU - Zhang, Guang-Ming AU - Xiang, Tao AU - Liu, Zheng-Xin AU - Ng, Tai-Kai PY - 2009/Apr/03/ UR - http://arxiv.org/abs/0904.0550 ER -