Bootstrap Approximations in Contractor Renormalization
arXiv:0801.0021 · doi:10.1103/PhysRevB.77.155116
Abstract
We propose a bootstrap method for approximating the long-range terms in the Contractor Renormalization (CORE) method. The idea is tested on the 2-D Heisenberg antiferromagnet and the frustrated J_2-J_1 model. We obtain renormalization group flows that directly reveal the Neel phase of the unfrustrated HAF and the existence of a phase transition in the J_2-J_1 model for weak frustration. However, we find that this bootstrap method is dependent on blocking and truncation schemes. For this reason, we discuss these dependencies and unresolved issues that researchers who use this approach must consider.
Some clarifications added for Phys Rev submission
References in corpus (14)
- The density-matrix renormalization group
- Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
- Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions
- Dimer Order with Striped Correlations in the J_1-J_2 Heisenberg Model
- New quantum phase transitions in the two-dimensional J1-J2 model
- Low-energy singlet and triplet excitations in the spin-liquid phase of the two-dimensional J1-J2 model
- CORE Technology and Exact Hamiltonian Real-Space Renormalization Group Transformations
- Numerical Contractor Renormalization Method for Quantum Spin Models
- Core -- a New Computational Technique for Lattice Systems
- Incorporation of Density Matrix Wavefunctions in Monte Carlo Simulations: Application to the Frustrated Heisenberg Model
- Exploring Quantum Phase Transitions with a Novel Sublattice Entanglement Scenario
- Contractor-Renormalization approach to frustrated magnets in magnetic field
- Theoretical studies of the phase transition in the anisotropic 2-D square spin lattice
- Exploring Contractor Renormalization: Tests on the 2-D Heisenberg Antiferromagnet and Some New Perspectives