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The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This…

Strongly Correlated Electrons · Physics 2009-11-10 Ulrich Schollwoeck

Configuration-interaction-type calculations on electronic and vibrational structure are often the method of choice for the reliable approximation of many-particle wave functions and energies. The exponential scaling, however, limits their…

Computational Physics · Physics 2019-05-24 Alberto Baiardi , Christopher J. Stein , Vincenzo Barone , Markus Reiher

We generalize the recently introduced Density-Matrix Renormalization Group (DMRG-X) [Khemani et al, PRL 2016] algorithm to obtain Floquet eigenstates of one-dimensional, periodically driven many-body localized systems. This generalization…

Strongly Correlated Electrons · Physics 2017-09-28 Carolyn Zhang , Frank Pollmann , S. L. Sondhi , Roderich Moessner

We develop a density-matrix renormalization group (DMRG) algorithm for the simulation of quantum circuits. This algorithm can be seen as the extension of time-dependent DMRG from the usual situation of hermitian Hamiltonian matrices to…

Density Matrix Renormalization Group (DMRG) algorithm has been extremely successful for computing the ground states of one-dimensional quantum many-body systems. For problems concerned with mixed quantum states, however, it is less…

Strongly Correlated Electrons · Physics 2022-06-01 Chu Guo

The density matrix renormalization group (DMRG) method generates the low-energy states of linear systems of $N$ sites with a few degrees of freedom at each site by starting with a small system and adding sites step by step while keeping…

Strongly Correlated Electrons · Physics 2016-10-05 Manoranjan Kumar , Dayasindhu Dey , Aslam Parvej , S. Ramasesha , Zoltán G. Soos

The purpose of this paper is (i) to present a generic and fully functional implementation of the density-matrix renormalization group (DMRG) algorithm, and (ii) to describe how to write additional strongly-correlated electron models and…

Strongly Correlated Electrons · Physics 2015-05-13 G. Alvarez

In the numerical analysis of strongly correlated quantum lattice models one of the leading algorithms developed to balance the size of the effective Hilbert space and the accuracy of the simulation is the density matrix renormalization…

Strongly Correlated Electrons · Physics 2015-06-17 Csaba Nemes , Gergely Barcza , Zoltán Nagy , Örs Legeza , Péter Szolgay

Thermalization and its breakdown in interacting quantum many-body systems are governed by mid-spectrum eigenstates, which are typically accessible only in small system sizes amenable to exact diagonalization. Here we demonstrate that the…

Strongly Correlated Electrons · Physics 2026-03-31 Andrew Hallam , Jared Jeyaretnam , Zlatko Papić

We present the theory of a density matrix renormalization group (DMRG) algorithm which can solve for both the ground and excited states of non-Hermitian transcorrelated Hamiltonians, and show applications in \emph{ab initio} molecular…

The Density Matrix Renormalization Group (DMRG) method has become a prominent tool for simulating strongly correlated electronic systems characterized by dominant static correlation effects. However, capturing the full scope of electronic…

Chemical Physics · Physics 2024-11-13 Nicholas Bauman , Libor Veis , Karol Kowalski , Jiri Brabec

The density matrix renormalization group (DMRG) method and its applications to finite temperatures and two-dimensional systems are reviewed. The basic idea of the original DMRG method, which allows precise study of the ground state…

Strongly Correlated Electrons · Physics 2009-11-10 Naokazu Shibata

The density matrix renormalization group (DMRG) approach is arguably the most successful method to numerically find ground states of quantum spin chains. It amounts to iteratively locally optimizing matrix-product states, aiming at better…

Quantum Physics · Physics 2015-06-26 J. Eisert

Understanding the intricate properties of one-dimensional quantum systems coupled to multiple reservoirs poses a challenge to both analytical approaches and simulation techniques. Fortunately, density matrix renormalization group-based…

Quantum Physics · Physics 2021-07-15 Heitor P. Casagrande , Dario Poletti , Gabriel T. Landi

A simplified version of White's Density Matrix Renormalization Group (DMRG) algorithm has been used to find the ground state of the free particle on a tight-binding lattice. We generalize this algorithm to treat the tight-binding particle…

Strongly Correlated Electrons · Physics 2009-10-31 M. A. Martin-Delgado , G. Sierra , R. M. Noack

The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…

Condensed Matter · Physics 2007-05-23 Karen Hallberg

The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…

Strongly Correlated Electrons · Physics 2008-11-26 Karen Hallberg

We have devised and implemented a local ab initio Density Matrix Renormalization Group (DMRG) algorithm to describe multireference nondynamic correlations in large systems. For long molecules that are extended in one of their spatial…

Strongly Correlated Electrons · Physics 2009-11-11 Johannes Hachmann , Wim Cardoen , Garnet Kin-Lic Chan

The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamical…

Condensed Matter · Physics 2007-05-23 Karen Hallberg

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
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