Thermodynamic limit of density matrix renormalization.

By S. Östlund, S. Rommer. 1995

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “In this area, the term matrix product state (MPS) representation for the decomposition (5) has been established [218].”
Entanglement in many-body systems (2007, background): “MPS, first discussed in (Fannes et al., 1992), appear naturally in the Density Matrix Renormalization Group (DMRG) (Ostlund and Rommer, 1995).”
Geometry of Quantum States: Index (2007, background): “The link to MPS was forged by Östlund and Rommer (1995) [709].”
Constructive Representation of Functions in Low-Rank Tensor Formats (2012, background): “A tensor A is said to be in the TT-format (also known in other research areas as Matrix Product States (MPS) [32]) if its elements satisfy [27, 29] where G k (i k ) are r k − 1 × r k matrices for each ﬁxed i k .”
Fast adaptive interpolation of multi-dimensional arrays in tensor train format (2011, methodology): “The idea of the Density Matrix Renormalization Group (DMRG), proposed by White [22] was only later realized as an idea of constrained optimization in the matrix product state [30].”
Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, methodology): “[36, 26] for the ground state problem in Quantum Physics.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, background): “In [Östlund and Rommer, 1995] pointed out that the wave function generated by the DMRG iteration is a matrix product state.”
Efficient quantum state tomography. (2010, methodology): “For this task standard methods have been developed in condensed matter physics [13, 29] for which the number of parameters scale polynomially in the system size and converge rapidly [30, 31] to the optimal MPS approximation.”
DMRG+QTT approach to computation of the ground state for the molecular Schrödinger operator (2010, methodology): “3) are used for quite a long time [45, 8].”