arXiv subjects
Publications and source records attributed to Z. Shuai.
The symmetric two-layer Ising model (TLIM) is studied by the corner transfer matrix renormalisation group method. The critical points and critical exponents are calculated. It is found that the TLIM belongs to the same universality class as the Ising model. The shift exponent is calculated to be 1.773, which is consistent with the theoretical prediction 1.75 with 1.3% deviation.
The symmetrized density matrix renormalization group approach is applied within the extended Hubbard-Peierls model (with parameters U/t, V/t, and bond alternation δ) to study the ordering of the lowest one-photon (1^{1}B^{-}_u) and two-photon (2^{1}A^{+}_g) states in one- dimensional conjugated systems with chain lengths, N, up to N=80 sites. Three different types of crossovers are studied, as a function of U/t, δ, and N. The U-crossover emphasizes the larger ionic character of the 2A_g state compared to the lowest triplet excitation. The δcrossover shows strong dependence on both N and U/t. The N-crossover illustrates the more localized nature of the 2A_g excitation relative to the 1B_u excitation at intermediate correlation strengths.
A symmetrized Density Matrix Renormalization Group procedure together with the correction vector approach is shown to be highly accurate for obtaining dynamic linear and third order polarizabilities of one-dimensional Hubbard and $U-V$ models. The $U-V$ model is seen to show characteristically different third harmonic generation response in the CDW and SDW phases. This can be rationalized from the excitation spectrum of the systems.
We extend the symmetrized density matrix renormalization group (SDMRG) method to compute the dynamic nonlinear optic coefficients for long chains. By computing correction vectors in the appropriate symmetry subspace we obtain the dynamic polarizabilities, $α_{ij}(ω)$, and third-order polarizabilities $γ_{ijkl}(ω,ω,ω)$ of the Hubbard and "$U-V$" chains in an $all-trans$ polyacetylene geometry, with and without dimerization. We rationalize the behavior of $\barα$ and $\barγ$ on the basis of the low-lying excitation gaps in the system. This is the first study of the dynamics of a fermionic system within the DMRG framework.
We extend the density matrix renormalization group method to exploit Parity, $C_2$ (rotation by $π$) and electron-hole symmtries of model Hamiltonians. We demonstrate the power of this method by obtaining the lowest energy states in all the eight symmetry subspaces of Hubbard chains with upto 50 sites. The ground-state energy, optical gap and spin gap of regular $U=4t$ and $U=6t$ Hubbard chains agree very well with exact results. This development extends the scope of the DMRG method and allows future applications to study of optical properties of low-dimensional conjugated polymeric systems.