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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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