Kagome Spin Liquid戈薇自旋液体.pptVIP

Kagome Spin Liquid Classical Heisenberg AFM Experiments S=1/2 Kagome: Numerical Results RVB on the Kagome Mambrini Mila, EPJB 2000 Contractor Renormalization (CORE) Kagome CORE step 1 Triangles on a triangular superlattice Dominant range 2 interactions Range 3 corrections Effective Bond Interactions Variational theory Energies of dimer configurations Quantum Dimer Model Long Wavelength GL Theory The triangular Heisenberg Antiferromagnet Iterated Core Transformations Second Renormalization Proposed RG flow Conclusions Contractor Renormalization (CORE) CORE Step II: The Effective Hamiltonian on a particular cluster CORE Step III: The Cluster Expansion 2 CORE Steps to Ground State Hexagons Versus Supertetrahedra The Checkerboard Geometrical Frustration on Pyrochlores Interactions between pseudospins Spin-? Pyrochlore Antiferromagnet * Assa Auerbach Ranny Budnik Erez Berg Macroscopic degeneracy Kagome O(3)xO(2)/O(2) - O(4) critical pt Three sublattice N’eel state Huse, Singh Triangular a c b a b c a b b Strong quantum spin fluctuations (spin gap?) S=3/2 layered Kagome ‘90 ‘90 However: Large low T specific heat 1. Short range spin correlations : Zheng Elser ’90; Chalker Eastmond ‘92 Spin gap 0.06J 2. Finite spin gap E(Smin+1)-E(Smin)= Lots of Low Energy Singlets Mambrini Mila Finite T=0 entropy? energy Log (# states) Number of sites MisguichLhuillier Log (# states) Massless nonmagnetic modes? S=0 S=1 E Weak bonds strong bonds 6-site singlet “dimer” Perturbation theory in weak/strong bonds. 1. Number of dimer coverings is 2. Dimers (10-5 of all singlets N=36) exhaust low energy spectrum. C.Morningstar, M.Weinstein, PRD 54, 4131 (1996). E. Altman and A. A, PRB 65, 104508, (2002). Details: Ehud Altmans Ph.D. Thesis. Truncate small longer range interactions 2. Interactions range N From exact diagonalization of clusters 2. Effective Hamiltonian (exact) States of 2 triangles Heisenberg Dimerization field TEST Supertriangle has 4-fold degenera