Quantum Magnetism and Quantum Entanglement

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Jahanfar Abouie Adv Cond Mat Smr School 2012-IPM 41/ Heisenberg spin models-energy gap Numerical method: DMRG: Steven R. White, PRL 69 2863 (1992) Exact diagonalization Lanczos method Field theory: Nonlinear Sigma model 1983 Haldane: AF spin-s Heisenberg chain → O(3) NLSM F. D. M. Haldane, Phys. Lett. A, 93, 464 (1983); F. D. M. Haldane, Phys. Rev. Lett. 59, 1153 (1983). 1990 (LSM) Demonstrate: Integer spin → NLSM → gapped Conjecture: Half-integer → NLSM+ topological Berry phase → gapless Spin systems <strong>Quantum</strong> Hall Effect Topological insulators Tunneling effects
Jahanfar Abouie Adv Cond Mat Smr School 2012-IPM 42/ Heisenberg spin models-NLSM Mapping: • Generalizing the Hubbard-Stratonovich formula in the partition function, • Applying gradient expansions in the Hamiltonian formalism, • Using spin coherent states in the path integral formalism. One spin systems Partition function <strong>and</strong> spin coherent state Classical Hamiltonian Berry phase Geometrical Berry phase
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Page 85: Thanks for your attentions

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