skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Topologically distinct classes of valence-bond solid states with their parent Hamiltonians

Abstract

We present 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 strategies to find their parent Hamiltonians are 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 consists of two virtual SU(2) spin-J variables in each site and another is formed by using two SO(2S+1) spinors. Among them, a spin-1 fermionic valence-bond solid state, its parent Hamiltonian, and its properties are discussed in detail. Moreover, two types of valence-bond solid states with SO(5) symmetries are further generalized and their respective properties are analyzed as well.

Authors:
; ; ; ;  [1]
  1. Department of Physics, Tsinghua University, Beijing 100084 (China)
Publication Date:
OSTI Identifier:
21287037
Resource Type:
Journal Article
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 80; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevB.80.014401; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1098-0121
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FERMIONS; GROUND STATES; HAMILTONIANS; ONE-DIMENSIONAL CALCULATIONS; SO GROUPS; SO-5 GROUPS; SOLIDS; SPIN; SPINORS; SU-2 GROUPS; SYMMETRY; VALENCE

Citation Formats

Honghao, Tu, Guangming, Zhang, Tao, Xiang, Zhengxin, Liu, Taikai, Ng, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, and Department of Physics, Hong Kong University of Science and Technology, Kowloon, Hong Kong. Topologically distinct classes of valence-bond solid states with their parent Hamiltonians. United States: N. p., 2009. Web. doi:10.1103/PHYSREVB.80.014401.
Honghao, Tu, Guangming, Zhang, Tao, Xiang, Zhengxin, Liu, Taikai, Ng, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, & Department of Physics, Hong Kong University of Science and Technology, Kowloon, Hong Kong. Topologically distinct classes of valence-bond solid states with their parent Hamiltonians. United States. https://doi.org/10.1103/PHYSREVB.80.014401
Honghao, Tu, Guangming, Zhang, Tao, Xiang, Zhengxin, Liu, Taikai, Ng, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, and Department of Physics, Hong Kong University of Science and Technology, Kowloon, Hong Kong. 2009. "Topologically distinct classes of valence-bond solid states with their parent Hamiltonians". United States. https://doi.org/10.1103/PHYSREVB.80.014401.
@article{osti_21287037,
title = {Topologically distinct classes of valence-bond solid states with their parent Hamiltonians},
author = {Honghao, Tu and Guangming, Zhang and Tao, Xiang and Zhengxin, Liu and Taikai, Ng and Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190 and Department of Physics, Hong Kong University of Science and Technology, Kowloon, Hong Kong},
abstractNote = {We present 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 strategies to find their parent Hamiltonians are 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 consists of two virtual SU(2) spin-J variables in each site and another is formed by using two SO(2S+1) spinors. Among them, a spin-1 fermionic valence-bond solid state, its parent Hamiltonian, and its properties are discussed in detail. Moreover, two types of valence-bond solid states with SO(5) symmetries are further generalized and their respective properties are analyzed as well.},
doi = {10.1103/PHYSREVB.80.014401},
url = {https://www.osti.gov/biblio/21287037}, journal = {Physical Review. B, Condensed Matter and Materials Physics},
issn = {1098-0121},
number = 1,
volume = 80,
place = {United States},
year = {2009},
month = {7}
}