Tensor Product State Formulation for the Spin 1/2 Antiferromagnetic XXZ Model on the Checkerboard Lattice
arXiv:cond-mat/0404556 · doi:10.1143/JPSJ.73.60
Abstract
Vertical density matrix algorithm (VDMA), a tensor product state formulation of the ``higher-dimensional'' density matrix renormalization group, is applied to the spin 1/2 antiferromagnetic XXZ model on the checkerboard lattice. The VDMA was, in the preceding study, applied to the transverse field Ising model on the square lattice and the three-dimensional classical Ising model. In the present paper, its implementation procedure is modified in order to apply the VDMA to the XXZ model. Numerical accuracy of the VDMA is investigated for the XXZ model on the square lattice, which shows that the method gives reliable results for the ground state energy. In the frustrated region, VDMA results are compared with a simple calculation based on a magnetically disordered state. It is found that the weakly frustrated region is in the Néel ordered phase, while in the strongly frustrated region the realized phase cannot be identified clearly by the obtained results.
9 pages, 11 figures
References in corpus (21)
- Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
- Corner Transfer Matrix Renormalization Group Method
- Density Matrix Renormalization Group Method for 2D Classical Models
- Two-Dimensional Tensor Product Variational Formulation
- Singlet Excitations in Pyrochlore: A Study of Quantum Frustration
- Quantum phase transition in spin-3/2 systems on the hexagonal lattice - optimum ground state approach
- A Density Matrix Algorithm for 3D Classical Models
- Self-Consistent Tensor Product Variational Approximation for 3D Classical Models
- A two-dimensional algorithm of the density matrix renormalization group
- Vertical Density Matrix Algorithm: A Higher-Dimensional Numerical Renormalization Scheme based on the Tensor Product State Ansatz
- Numerical Renormalization Approach to Two-Dimensional Quantum Antiferromagnets with Valence-Bond-Solid Type Ground State
- From the Square Lattice to the Checkerboard Lattice : Spin Wave and Large-n Analysis
- Planar pyrochlore: a strong-coupling analysis
- Quantum disorder in the two-dimensional pyrochlore Heisenberg antiferromagnet
- Spinons in a Crossed-Chains Model of a 2D Spin Liquid
- 1-Dimensional behavior and sliding Luttinger liquid phase in a frustrated spin-1/2 crossed chain model: contribution of exact diagonalizations
- Kramers-Wannier Approximation for 3D Ising Model
- Stripe Ansatzs from Exactly Solved Models
- A Two-dimensional Infinte System Density Matrix Renormalization Group Algorithm
- 2D XXZ Model ground state Properties using an analytic Lanczos Expansion
- Single-Block Renormalization Group: Quantum Mechanical Problems
Cited by in corpus (6)
- Symmetry protected topological orders and the group cohomology of their symmetry group
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
- Tensor product representation of topological ordered phase: necessary symmetry conditions
- Variational treatment of the Shastry-Sutherland antiferromagnet using Projected Entangled Pair States (PEPS)
- Finite-size-scaling analysis of the XY universality class between two and three dimensions: An application of Novotny's transfer-matrix method