Zheng-Yuan Wang

Dimerizations in spin-S antiferromagnetic chains with three-spin interaction

We discuss spin-S antiferromagnetic Heisenberg chains with three-spin interactions, next-nearest-neighbor interactions, and bond alternation. First, we prove rigorously that there exist parameter regions of the exact dimerized ground state in this system. This is a generalization of the Majumdar-Ghosh model to arbitrary S. Next, we discuss the ground-state phase diagram of the models by introducing several effective field theories and the universality classes of the transitions are described by the level-2S SU(2) Wess-Zumino-Witten model and the Gaussian model. Finally, we determine the phase diagrams of S = 1 and S = 3/2 systems by using exact diagonalization and level spectroscopy.

Exactly solvable fermion chain describing a ν=1/3 fractional quantum Hall state.

We introduce an exactly solvable fermion chain that describes a ν=1/3 fractional quantum Hall (FQH) state beyond the thin-torus limit. The ground state of our model is shown to be unique for each center-of-mass sector, and it has a matrix product representation that enables us to exactly calculate order parameters, correlation functions, and entanglement spectra. The ground state of our model shows striking similarities with the BCS wave functions and quantum spin-1 chains. Using the variational method with matrix product ansatz, we analytically calculate excitation gaps and vanishing of the compressibility expected in the FQH state. We also show that the above results can be related to a ν=1/2 bosonic FQH state.

One-dimensional lattice model with an exact matrix-product ground state describing the Laughlin wave function

We introduce one-dimensional lattice models with exact matrix-product ground states describing the fractional quantum Hall (FQH) states in Laughlin series (given by filling factors

Beyond the Tao-Thouless limit of the fractional quantum Hall effect: spin chains and Fermi surface deformation

\nu=1/q

Spin-chain description of fractional quantum Hall states in the Jain series

) on torus geometry. Surprisingly, the exactly solvable Hamiltonian has the same mathematical structure as that of the pseudopotential for the Laughlin wave function, and naturally derives the general properties of the Laughlin wave function such as the

Matrix-Product Ansatz for Excited States of Fractional Quantum Hall Systems

Z_2

1D Lattice Models with Exact Ground States Describing Fractional Quantum Hall Systems(Research)

properties of the FQH states and the fermion-boson relation. The obtained exact ground states have high overlaps with the Laughlin states and well describe their properties. Using the matrix product method, density functions and correlation functions are calculated analytically. Especially, obtained entanglement spectra reflects gapless edge states as was discussed by Li and Haldane.

Publisher's Note: Dimerizations in spin-Santiferromagnetic chains with three-spin interaction [Phys. Rev. B88, 224419 (2013)]

We discuss the relationship between the fractional quantum Hall effect in the vicinity of the thin-torus, a.k.a. Tao-Thouless (TT), limit and quantum spin chains. We argue that the energetics of fractional quantum Hall states in Jain sequence at filling fraction ν = p/(2p + 1) (and ν = 1 − p/(2p + 1)) in the lowest Landau level is captured by S = 1 spin chains with p spins in the unit cell. These spin chains naturally arise at sub-leading order in e−2π2 / L21 which serves as an expansion parameter away from the TT limit (L1 → 0). We also corroborate earlier results on the smooth Fermi surface deformation of the gapless state at ν = 1/2, interpolating between a state described by a critical S = 1/2 chain and the bulk.

Dimerizations in spin-

We discuss the relationship between fractional quantum Hall (FQH) states at filling factor

S

\nu=p/(2p+1)