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Abstract
A deeper understanding of the density matrix renormalization group (DMRG) method has been achieved, thanks to DMRG’s developments and insights from quantum information theory (QIT) in recent years. For example, DMRG’s great success is ascribed to its efficient compression and localized representation of quantum states in its wavefunction’s entangled matrix product state (MPS) formulation or the equivalent tensor train structure in mathematical language. In this chapter, we start by presenting the necessary fundamentals of tensor decompositions for quantum many-body wavefunction and principles of an efficient Schmidt decomposition from a QIT perspective. The concepts of MPS and matrix product operators for large quantum systems are discussed. Finally, we introduce detailed algorithms for ground state calculations by variationally optimizing MPS.
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