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Density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. In this work, we develop a perturbation theory of DMRG (PT-DMRG) to largely increase its accuracy in an extremely…

Strongly Correlated Electrons · Physics 2017-03-01 Emanuele Tirrito , Shi-Ju Ran , Andrew J. Ferris , Ian P. McCulloch , Maciej Lewenstein

Estimating ground state energies of many-body Hamiltonians is a central task in many areas of quantum physics. In this work, we give quantum algorithms which, given any $k$-body Hamiltonian $H$, compute an estimate for the ground state…

A new approach to derivation of various effective-field approximation for lattice spin models is presented. It is shown that it can give a number of methods, including the DMRG method, that can be used to find generally inhomogeneous…

Statistical Mechanics · Physics 2007-05-23 A. Surda

We quantify how well matrix product states approximate exact ground states of 1-D quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also investigate the convex set of local reduced density…

Strongly Correlated Electrons · Physics 2007-05-23 F. Verstraete , J. I. Cirac

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

We introduce a generic method for computing groundstates that is applicable to a wide range of spatially anisotropic 2D many-body quantum systems. By representing the 2D system using a low-energy 1D basis set, we obtain an effective 1D…

Strongly Correlated Electrons · Physics 2025-10-27 Sam Mardazad , Nicolas Laflorencie , Johannes Motruk , Adrian Kantian

Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which…

Quantum Physics · Physics 2024-04-10 Danial Motlagh , Modjtaba Shokrian Zini , Juan Miguel Arrazola , Nathan Wiebe

The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough paper [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)], provides a powerful variational ansatz for the ground state of…

Strongly Correlated Electrons · Physics 2017-06-07 Martin Ganahl , Julian Rincon , Guifre Vidal

Stabilizer states, which are also known as the Clifford states, have been commonly utilized in quantum information, quantum error correction, and quantum circuit simulation due to their simple mathematical structure. In this work, we apply…

Quantum Physics · Physics 2025-06-26 Jiace Sun , Lixue Cheng , Shi-Xin Zhang

For many systems with quenched disorder the study of ground states can crucially contribute to a thorough understanding of the physics at play, be it for the critical behavior if that is governed by a zero-temperature fixed point or for…

Disordered Systems and Neural Networks · Physics 2020-06-12 Manoj Kumar , Martin Weigel

We determine the computational difficulty of finding ground states of one-dimensional (1D) Hamiltonians which are known to be Matrix Product States (MPS). To this end, we construct a class of 1D frustration free Hamiltonians with unique MPS…

Quantum Physics · Physics 2009-11-13 Norbert Schuch , Ignacio Cirac , Frank Verstraete

Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding…

Quantum Physics · Physics 2024-10-18 Laura Lewis , Hsin-Yuan Huang , Viet T. Tran , Sebastian Lehner , Richard Kueng , John Preskill

We present a simple and stable numerical method to approximate the ground state of a quantum many-body system by multiple determinant states. This method searches these determinant states one by one according to the matching pursuit…

Strongly Correlated Electrons · Physics 2009-11-13 Quanlin Jie

Minimizing the energy of an $N$-electron system as a functional of a two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions (conditions for the 2-RDM to represent an ensemble $N$-electron…

Chemical Physics · Physics 2016-06-21 Nicholas C. Rubin , David A. Mazziotti

A momentum-space approach of the density-matrix renormalization-group (DMRG) method is developed. Ground state energies of the Hubbard model are evaluated using this method and compared with exact diagonalization as well as quantum…

Condensed Matter · Physics 2009-10-28 T. Xiang

We give a new proof for the area law for general 1D gapped systems, which exponentially improves Hastings' famous result \cite{ref:Has07}. Specifically, we show that for a chain of d-dimensional spins, governed by a 1D local Hamiltonian…

Quantum Physics · Physics 2013-01-08 Itai Arad , Alexei Kitaev , Zeph Landau , Umesh Vazirani

We devise a quasilinear quantum algorithm for generating an approximation for the ground state of a quantum field theory (QFT). Our quantum algorithm delivers a super-quadratic speedup over the state-of-the-art quantum algorithm for…

We use matrix product techniques to investigate the performance of two algorithms for obtaining the ground state of a quantum many-body Hamiltonian $H = H_A + H_B$ in infinite systems. The first algorithm is a generalization of the quantum…

Strongly Correlated Electrons · Physics 2022-11-30 Ruoshui Wang , Timothy H. Hsieh , Guifre Vidal

The density matrix renormalization group (DMRG) is a numerical method that optimizes a variational state expressed by a tensor product. We show that the ground state is not fully optimized as far as we use the standard finite system…

Statistical Mechanics · Physics 2010-05-20 H. Takasaki , T. Hikihara , T. Nishino

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