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The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as…

We introduce a general model of stochastically generated matrix product states (MPS) in which the local tensors share a common distribution and form a strictly stationary sequence, without requiring spatial independence. Under natural…

Quantum Physics · Physics 2026-01-27 Lubashan Pathirana , Albert H. Werner

The adaptive Thouless--Anderson--Palmer (TAP) mean-field approximation is one of the advanced mean-field approaches, and it is known as a powerful accurate method for Markov random fields (MRFs) with quadratic interactions (pairwise MRFs).…

Disordered Systems and Neural Networks · Physics 2020-03-10 Chako Takahashi , Muneki Yasuda , Kazuyuki Tanaka

We apply the Matrix Product Ansatz to study the Totally Asymmetric Simple Exclusion Process on a ring with a generalized discrete-time dynamics depending on two hopping probabilities, $p$ and $\tilde{p}$. The model contains as special cases…

Mathematical Physics · Physics 2016-10-06 Boyka Aneva , Jordan Brankov

We present a low-scaling algorithm for the random phase approximation (RPA) with \textbf{k}-point sampling in the framework of tensor hypercontraction (THC) for electron repulsion integrals (ERIs). The THC factorization is obtained via a…

Materials Science · Physics 2023-12-01 Chia-Nan Yeh , Miguel A. Morales

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…

Strongly Correlated Electrons · Physics 2009-11-13 Hamed Saberi , Andreas Weichselbaum , Jan von Delft

Recently, Tao and Mo proposed an accurate meta-generalized gradient approximation for the exchange-correlation energy. The exchange part is derived from the density matrix expansion, while the correlation part is obtained by improving the…

Chemical Physics · Physics 2017-10-11 Yuxiang Mo , Guocai Tian , Jianmin Tao

Continuous tensor network gives a variational ansatz for the ground state of the quantum field theories (QFTs). The notable examples are the continuous matrix product state (cMPS) and the continuous multiscale entanglement renormalization…

High Energy Physics - Theory · Physics 2023-11-23 Niloofar Vardian

Out-of-equilibrium dynamics of non-integrable Hamiltonian many-body quantum systems are characterized by highly entangled wave functions. Near-maximal entanglement arises in systems exhibiting thermalization or pre-thermalization, where the…

The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the…

Strongly Correlated Electrons · Physics 2011-01-04 Ulrich Schollwoeck

Matrix product state methods are known to be efficient for computing ground states of local, gapped Hamiltonians, particularly in one dimension. We introduce the multi-targeted density matrix renormalization group method that acts on a…

Strongly Correlated Electrons · Physics 2023-06-29 Thomas E. Baker , Alexandre Foley , David Sénéchal

Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for…

Quantum Physics · Physics 2025-11-27 Karan Tiwana , Antoine Tilloy

The familiar unrestricted Hartree-Fock variational principle is generalized to include quasi-free states. As we show, these are in one-to-one correspondence with the one-particle density matrices and these, in turn provide a convenient…

Condensed Matter · Physics 2009-10-22 Volker Bach , Elliott H. Lieb , Jan philip Solovej

We solve the nonequilibrium dynamical mean-field theory (DMFT) using matrix product states (MPS). This allows us to treat much larger bath sizes and by that reach substantially longer times (factor $\sim$ 2 -- 3) than with exact…

Strongly Correlated Electrons · Physics 2014-12-22 F. Alexander Wolf , Ian P. McCulloch , Ulrich Schollwöck

This work presents a comparative study of new and existing optimization and diagonalization methods for solving time-independent partial differential equations (PDEs) using matrix product states (MPS) in the quantized tensor-train formalism…

Quantum Physics · Physics 2026-02-17 Paula García-Molina , Luca Tagliacozzo , Juan José García-Ripoll

Constructing matrix product operators (MPO) is at the core of the modern density matrix renormalization group (DMRG) and its time dependent formulation. For DMRG to be conveniently used in different problems described by different…

Chemical Physics · Physics 2020-09-01 Jiajun Ren , Weitang Li , Tong Jiang , Zhigang Shuai

Given in the title are two algorithms to compute the extreme eigenstate of a high-dimensional Hermitian matrix using the tensor train (TT) / matrix product states (MPS) representation. Both methods empower the traditional alternating…

Numerical Analysis · Mathematics 2014-12-02 Sergey V. Dolgov , Dmitry V. Savostyanov

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional…

High Energy Physics - Lattice · Physics 2015-11-16 Boye Buyens , Karel Van Acoleyen , Jutho Haegeman , Frank Verstraete

Matrix product states (MPS) and matrix product operators (MPOs) are one dimensional tensor networks that underlie the modern density matrix renormalization group (DMRG) algorithm. The use of MPOs accounts for the high level of generality…

Strongly Correlated Electrons · Physics 2020-05-27 Matthew J. O'Rourke , Garnet Kin-Lic Chan

For hamiltonian lattice gauge theory, we introduce the matrix product anzats inspired from density matrix renormalization group. In this method, wavefunction of the target state is assumed to be a product of finite matrices. As a result,…

High Energy Physics - Lattice · Physics 2009-11-10 Takanori Sugihara