Introduction to Tensor Network Methods

Numerical simulations of low-dimensional many-body quantum systems

Simone Montangero

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Naturwissenschaften, Medizin, Informatik, Technik / Allgemeines, Lexika


This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter.

The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field. 

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lattice gauge theories simulations, tensor network methods, computational quantum physics textbook, quantum phase transitions, numerical simulations in quantum mechanics, quantum many-body problem, global symmetries, matrix diagonalization