aqora

Matrix Product States and Density Matrix Renormalization Group Algorithm

Naoki Nakatani

Elsevier eBooksJan 1, 20184 citations

MPS++

The MPS++ computer code simulates models of strongly correlated quantum lattice systems. The algorithm used is the density-matrix renormalization method formulated in the matrix product states language. These models and methods are used to obtain ground state, dynamic, finite temperature and time evolution properties of the underlying materials that are simulated. These materials are usually one- and quasi-one dimensional strongly correlated electronic systems, such as high temperature superconductors, manganites, and other transition metal oxides. This code is (mostly) an implementation of the paper "The density-matrix renormalization group in the age of matrix product states" by U. Schollwoeck, and references therein, found at http://arxiv.org/abs/1008.3477v2 , and that was also published in Annals of Physics 326,96 (2011).The MPS++ computer code simulates models of strongly correlated quantum lattice systems. The algorithm used is the density-matrix renormalization method formulated in the matrix product states language. These models and methods are used to obtain ground state, dynamic, finite temperature and time evolution properties of the underlying materials that are simulated. These materials are usually one- and quasi-one dimensional strongly correlated electronic systems, such as high temperature superconductors, manganites, and other transition metal oxides. This code is (mostly) an implementation of the paper "The density-matrix renormalization group in the age of matrix product states" by U. Schollwoeck, and references therein, found at http://arxiv.org/abs/1008.3477v2 , and that was also published in Annals of Physics 326,96 (2011).

Jul 24, 20180 citations

RECENT PROGRESS IN THE DENSITY-MATRIX RENORMALIZATION GROUP

Ulrich Schollwöck

Sep 1, 20070 citations

Matrix-product-state comparison of the numerical renormalization group and the variational formulation of the density-matrix renormalization group

Hamed Saberi, Andreas Weichselbaum, Jan von Delft

Wilson's numerical renormalization group (NRG) method for solving quantum impurity models yields a set of energy eigenstates that have the form of matrix product states (MPS). White's density-matrix renormalization group (DMRG) for treating quantum lattice problems can likewise be reformulated in terms of MPS. Thus, the latter constitute a common algebraic structure for both approaches. We exploit this fact to compare the NRG approach for the single-impurity Anderson model with a variational matrix product state approach (VMPS), equivalent to single-site DMRG. For the latter, we use an ``unfolded'' Wilson chain, which brings about a significant reduction in numerical costs compared to those of NRG. We show that all NRG eigenstates (kept and discarded) can be reproduced using VMPS, and compare the difference in truncation criteria, sharp vs smooth in energy space, of the two approaches. Finally, we demonstrate that NRG results can be improved upon systematically by performing a variational optimization in the space of variational matrix product states, using the states produced by NRG as input.Wilson's numerical renormalization group (NRG) method for solving quantum impurity models yields a set of energy eigenstates that have the form of matrix product states (MPS). White's density-matrix renormalization group (DMRG) for treating quantum lattice problems can likewise be reformulated in terms of MPS. Thus, the latter constitute a common algebraic structure for both approaches. We exploit this fact to compare the NRG approach for the single-impurity Anderson model with a variational matrix product state approach (VMPS), equivalent to single-site DMRG. For the latter, we use an ``unfolded'' Wilson chain, which brings about a significant reduction in numerical costs compared to those of NRG. We show that all NRG eigenstates (kept and discarded) can be reproduced using VMPS, and compare the difference in truncation criteria, sharp vs smooth in energy space, of the two approaches. Finally, we demonstrate that NRG results can be improved upon systematically by performing a variational optimization in the space of variational matrix product states, using the states produced by NRG as input.

arXiv:0804.0193Physical Review BJul 24, 200856 citations

Theory and Application of the Density-Matrix Renormalization Group

Im Fachbereich Physik

Jan 1, 20020 citations

From density-matrix renormalization group to matrix product states

Ian P. McCulloch

In this paper we give an introduction to the numerical density matrix renormalization group (DMRG) algorithm, from the perspective of the more general matrix product state (MPS) formulation. We cover in detail the differences between the original DMRG formulation and the MPS approach, demonstrating the additional flexibility that arises from constructing both the wavefunction and the Hamiltonian in MPS form. We also show how to make use of global symmetries, for both the Abelian and non-Abelian cases.In this paper we give an introduction to the numerical density matrix renormalization group (DMRG) algorithm, from the perspective of the more general matrix product state (MPS) formulation. We cover in detail the differences between the original DMRG formulation and the MPS approach, demonstrating the additional flexibility that arises from constructing both the wavefunction and the Hamiltonian in MPS form. We also show how to make use of global symmetries, for both the Abelian and non-Abelian cases.

arXiv:cond-mat/0701428Journal of Statistical Mechanics Theory and ExperimentOct 25, 2007459 citations

The density-matrix renormalization group in the age of matrix product states

Related papers

The density-matrix renormalization group in the age of matrix product states

Related papers