Work

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

Year: 2009

Type: article

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.

Source: Physical Review B

DOI: 10.1103/physrevb.80.014401

Authors: Hong-Hao Tu, Guang-Ming Zhang, Tao Xiang, Zheng-Xin Liu, Tai-Kai Ng

Institutions: Tsinghua University, Chinese Academy of Sciences, Institute of Theoretical Physics, Institute of Physics, Hong Kong University of Science and Technology

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

OpenAlex ID: W2068469669

FWCI: 2.964

Cites: 54

Cited by: 36

Related to: 10