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Quantum Many-Body Physics
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The book starts by explaining in detail the idea of the effective Hamiltonian, and explains how renormalization can be used to understand the difference between hydrogen and oxygen molecules concerning magnetism, before addressing more sophisticated uses of renormalization for Kondo systems and superconductivity, including multiple bands and with repulsive interactions.§§Emphasis is also placed on one-dimensional systems, which include Kondo impurity systems via certain mapping. The book then presents a self-contained description of the method of bosonization and re-fermionization, providing a clear understanding of nonperturbative correlation effects. It also explains the first quantization approach that extends to finite temperatures. With only a minimum of mathematics involved, readers will recognize how the quasi-particles obeying fractional statistics appear in low-dimensional systems.§
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