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Grades |
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Content: |
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-Electronic interaction in solids Single particle representation Fields and interaction Effective models |
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-Exchange interaction Ferromagnetic interacion Anti-ferromagnetic interaction Super-exchange interaction |
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-Hubbard model (Recommended articles: condmat archive 9311033, 9512169, 9712219, 9802240 ) Strong coulomb interaction and t-J model Heisenberg model |
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-Ground state of Hubbard model Variational states Some ground state theorem |
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-Ground state of Heisenberg model Half integer and integer antiferromagnetic Heisenber model Lieb-Schutz-Mattis Theorem |
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-Disorder in low dimension Spontaneously symmetry breaking Marmin-Wagner theorem at zero temperature |
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-Spin representation Holstein-Primakoff bosons Schwinger bosons Spin coherent state representation |
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-Variational state and parent Hamiltonian Valence bond states RVB states Majumdar-Ghosh Hamiltonian AKLT model |
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-Excitations Single mode approximation Goldeston modes Haldane gap |
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-Spine wave theory Ferromagnetic and antiferromagnetic hypercubic lattice |
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-Quantum phase transition Quauntum renormalization group Ising model in transverse field (ITF) Classical approximation Exact solution by Jordan-Wigner transformation (Recommended articles: -- S. L. Sondhi, et.al Rev. Mod. Phys. 69, 315 (1997). -- A. P. Young, "Quantum phase transitions in random systems" (ICTP lecture notes SMR/1003-2, Summer college in condensed matter on ' Statistical physics of frustrated systems'). -- S. Sachdev, "Quantum phase transitions" (Cambridge University Press; 2000) |
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1- Assa Auerbach, "Interacting electrons and quantum magnetism" (Springer-Verlag, New York, Inc 1994) 2- Patrik Fazekas, "Lecture notes on electron correlation and magnetism" (World Scientific Publishing Co. 1999) |
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