Numerical Contractor Renormalization Method for Quantum Spin Models

Abstract

We demonstrate the utility of the numerical Contractor Renormalization (CORE) method for quantum spin systems by studying one and two dimensional model cases. Our approach consists of two steps: (i) building an effective Hamiltonian with longer ranged interactions using the CORE algorithm and (ii) solving this new model numerically on finite clusters by exact diagonalization. This approach, giving complementary information to analytical treatments of the CORE Hamiltonian, can be used as a semi-quantitative numerical method. For ladder type geometries, we explicitely check the accuracy of the effective models by increasing the range of the effective interactions. In two dimensions we consider the plaquette lattice and the kagome lattice as non-trivial test cases for the numerical CORE method. On the plaquette lattice we have an excellent description of the system in both the disordered and the ordered phases, thereby showing that the CORE method is able to resolve quantum phase transitions. On the kagome lattice we find that the previously proposed twofold degenerate S=1/2 basis can account for a large number of phenomena of the spin 1/2 kagome system. For spin 3/2 however this basis does not seem to be sufficient anymore. In general we are able to simulate system sizes which correspond to an 8x8 lattice for the plaquette lattice or a 48-site kagome lattice, which are beyond the possibilities of a standard exact diagonalization approach.

15 pages

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Cited by in corpus (48)

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• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Low energy excitations of the kagome antiferromagnet and the spin gap issue
• The Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A high-order coupled cluster treatment
• Nature of chiral spin liquids on the kagome lattice
• Frustrated three-leg spin tubes: from spin 1/2 with chirality to spin 3/2
• Effective Theory of Magnetization Plateaux in the Shastry-Sutherland Lattice
• Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models
• Frustration and entanglement in the $t_{2g}$ spin--orbital model on a triangular lattice: valence--bond and generalized liquid states
• Dzyaloshinskii-Moriya anisotropy and non-magnetic impurities in the $s=1/2$ kagome system ZnCu_3(OH)_6Cl_2
• A cluster-based mean-field and perturbative description of strongly correlated fermion systems. Application to the 1D and 2D Hubbard model
• Effective models for gapped phases of strongly correlated quantum lattice models
• The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
• Quantum Phase Transition in a Heisenberg Antiferromagnet on a Square Lattice with Strong Plaquette Interactions
• p6 - Chiral Resonating Valence Bonds in the Kagome Antiferromagnet
• Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice
• Effective Spin Couplings in the Mott Insulator of the Honeycomb Lattice Hubbard Model
• A renormalized excitonic method in terms of block excitations. Application to spin lattices
• Temperature dependence of the NMR relaxation rate 1/T_1 for quantum spin chains
• Stability of the spin-$1/2$ kagome ground state with breathing anisotropy
• Mechanisms for Spin-Supersolidity in S=1/2 Spin-Dimer Antiferromagnets
• Microscopic theory of the nearest-neighbor valence bond sector of the spin-1/2 kagome antiferromagnet
• Correlation density matrix: an unbiased analysis of exact diagonalizations
• Bond order wave instabilities in doped frustrated antiferromagnets: "Valence bond solids" at fractional filling
• A contractor-renormalization study of Hubbard plaquette clusters
• Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models
• Spin excitation spectra of the two dimensional $S=1/2$ Heisenberg model with a checkerboard structure
• The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling
• Combined analytical and numerical approach to magnetization plateaux in one-dimensional spin tube antiferromagnets
• Exploring Contractor Renormalization: Tests on the 2-D Heisenberg Antiferromagnet and Some New Perspectives
• Contractor-Renormalization approach to frustrated magnets in magnetic field
• Compass and Kitaev models -- Theory and Physical Motivations
• Optimal inhomogeneity for pairing in Hubbard systems with next-nearest-neighbor hopping
• A continuum of compass spin models on the honeycomb lattice
• Similarity of thermodynamic properties of Heisenberg model on triangular and kagome lattices
• Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition
• Contractor renormalization group theory of the SU($N$) chains and ladders
• Loop-gas description of the localized-magnon states on the kagome lattice with open boundary conditions
• Strong-coupling expansion and effective hamiltonians
• Many-Body Density Matrices On a Two-Dimensional Square Lattice: Noninteracting and Strongly Interacting Spinless Fermions
• Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: A message from spin waves
• Bootstrap Approximations in Contractor Renormalization
• Block Density Matrix Renormalization Group with Effective Interactions
• Local renormalization method for random systems
• Projection Method for Exact Diagonalization in the Strong Coupling Limit for Frustrated Models with Highly Degenerate Ground States
• Real space renormalization group approach to the 2d antiferromagnetic Heisenberg model
• Emergence of magnetic long-range order in kagome quantum antiferromagnets