Titlebook: Introduction to Tensor Network Methods; Numerical simulation Simone Montangero Book 2018 Springer Nature Switzerland AG 2018 computational

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Numerical Renormalization Group Methodsl routinely used to study different phenomena [22, 136, 137], hereafter, we concentrate on its application to numerically attack the many-body quantum problem. To set the stage, we start with the mean-field treatment of the many-body quantum problem and present its application to study the quantum I

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Tensor Network Methodsheir manipulations. Then, we present some of the most successful algorithms developed exploiting tensor networks to study the many-body problem. We first reformulate the mean-field approach using the tensor notation. Then, we introduce the Matrix Product State (MPS) and the reformulation of the DMRG

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Symmetric Tensor Networksrstand the main properties of the systems of interest, simplify their description, and improve the numerical performances of numerical codes employed to describe them. The most straightforward scenario in quantum mechanism – familiar to any physicist – where symmetries can be exploited, is that of a

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Out-of-Equilibrium Processesse equilibrium (dead) state. Indeed, any system in the real world is in contact with the rest (the environment) and subject to changing conditions (temperature, interaction strength, etc.) which drive the system out of its equilibrium state. Moreover, any useful process, from information processing

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Symmetric Tensor Networksto describe them. The most straightforward scenario in quantum mechanism – familiar to any physicist – where symmetries can be exploited, is that of a system described by a Hamiltonian invariant according to a given transformation ..

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