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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…

强关联电子 · 物理学 2009-11-13 Ian P. McCulloch

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…

强关联电子 · 物理学 2022-06-01 Chu Guo

We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix…

强关联电子 · 物理学 2025-08-11 Ting-Tung Wang , Xiaoxue Ran , Zi Yang Meng

We present an implementation of the relativistic quantum-chemical density matrix renormalization group (DMRG) approach based on a matrix-product formalism. Our approach allows us to optimize matrix product state (MPS) wave functions…

化学物理 · 物理学 2017-10-24 Stefano Battaglia , Sebastian Keller , Stefan Knecht

In the past two decades, the density matrix renormalization group (DMRG) has emerged as an innovative new method in quantum chemistry relying on a theoretical framework very different from that of traditional electronic structure…

计算物理 · 物理学 2020-02-18 Alberto Baiardi , Markus Reiher

The Density Matrix Renormalization Group (DMRG) is a state-of-the-art numerical technique for a one dimensional quantum many-body system; but calculating accurate results for a system with Periodic Boundary Condition (PBC) from the…

强关联电子 · 物理学 2016-11-29 Dayasindhu Dey , Debasmita Maiti , Manoranjan Kumar

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…

强关联电子 · 物理学 2009-11-10 Ulrich Schollwoeck

In this paper recent substantial progress in applying the density-matrix renormalization-group (DMRG) to the simulation of the time-evolution of strongly correlated quantum systems in one dimension is reviewed. Various approaches to…

强关联电子 · 物理学 2015-06-25 Ulrich Schollwoeck

Density Matrix Renormalization Group (DMRG) or Matrix Product States (MPS) are widely acknowledged as highly effective and accurate methods for solving one-dimensional quantum many-body systems. However, the direct application of DMRG to…

强关联电子 · 物理学 2024-11-25 Xiangjian Qian , Jiale Huang , Mingpu Qin

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…

强关联电子 · 物理学 2008-11-26 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…

凝聚态物理 · 物理学 2007-05-23 Karen Hallberg

The density matrix renormalization group (DMRG) is a celebrated tensor network algorithm, which computes the ground states of one-dimensional quantum many-body systems very efficiently. Here we propose an improved formulation of continuous…

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…

凝聚态物理 · 物理学 2007-05-23 Karen Hallberg

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…

量子物理 · 物理学 2021-07-15 Heitor P. Casagrande , Dario Poletti , Gabriel T. Landi

The density matrix renormalization group (DMRG) algorithm is a cornerstone computational method for studying quantum many-body systems, renowned for its accuracy and adaptability. Despite DMRG's broad applicability across fields such as…

计算物理 · 物理学 2026-03-24 Per Sehlstedt , Jan Brandejs , Paolo Bientinesi , Lars Karlsson

The Density Matrix Renormalization Group (DMRG) was introduced by Steven White in 1992 as a method for accurately describing the properties of one-dimensional quantum lattices. The method, as originally introduced, was based on the…

介观与纳米尺度物理 · 物理学 2011-05-12 Jorge Dukelsky , Stuart Pittel

A new density matrix renormalisation group (DMRG) approach is presented for quantum systems of two spatial dimensions. In particular, it is shown that it is possible to create a multi-chain-type 2D DMRG approach which utilises previously…

强关联电子 · 物理学 2009-11-10 Damian J. J. Farnell

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…

During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of…

化学物理 · 物理学 2014-09-25 Sebastian Wouters , Dimitri Van Neck

The density-matrix renormalization group (DMRG) method, which can deal with a large active space composed of tens of orbitals, is nowadays widely used as an efficient addition to traditional complete active space (CAS)-based approaches. In…

强关联电子 · 物理学 2016-11-06 Yingjin Ma , Jing Wen , Haibo Ma
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