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Using truncated conformal field theory (CFT), we present the formalism necessary to obtain exact matrix product state (MPS) representations for any fractional quantum hall model state which can be written as an expectation value of primary…

Strongly Correlated Electrons · Physics 2013-11-14 B. Estienne , N. Regnault , B. A. Bernevig

In these lecture notes, we present a pedagogical review of a number of related {\it numerically exact} approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix…

Strongly Correlated Electrons · Physics 2007-05-23 Reinhard M. Noack , Salvatore R. Manmana

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…

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

We investigate the use of matrix product states (MPS) to approximate ground states of critical quantum spin chains with periodic boundary conditions (PBC). We identify two regimes in the (N,D) parameter plane, where N is the size of the…

Statistical Mechanics · Physics 2013-02-08 B. Pirvu , G. Vidal , F. Verstraete , L. Tagliacozzo

We present a construction of a matrix product state (MPS) that approximates the largest-eigenvalue eigenvector of a transfer matrix T, for the purpose of rapidly performing the infinite system density matrix renormalization group (DMRG)…

Statistical Mechanics · Physics 2010-05-20 Kouji Ueda , Tomotoshi Nishino , Kouichi Okunishi , Yasuhiro Hieida , Rene Derian , Andrej Gendiar

We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…

Quantum Physics · Physics 2014-09-11 Andrew Critch , Jason Morton

We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall (FQH) Hamiltonian. To find the set of degenerate ground states, we employ the infinite density…

Strongly Correlated Electrons · Physics 2013-06-19 Michael P. Zaletel , Roger S. K. Mong , Frank Pollmann

We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS), which are quantum states of low entanglement with an efficient classical description. Our algorithm represents a near-term…

Quantum Physics · Physics 2026-04-15 Refik Mansuroglu , Norbert Schuch

Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact Matrix Product States…

Strongly Correlated Electrons · Physics 2018-05-02 Valentin Crepel , Benoit Estienne , B. Andrei Bernevig , Philippe Lecheminant , Nicolas Regnault

In this note, we describe a method for reconstructing matrix product states from a small number of efficiently-implementable measurements. Our method is exponentially faster than standard tomography, and it can also be used to certify that…

Quantum Physics · Physics 2010-02-26 Olivier Landon-Cardinal , Yi-Kai Liu , David Poulin

Accurate electronic structure calculations are essential in modern materials science, but strongly correlated systems pose a significant challenge due to their computational cost. Traditional methods, such as complete active space…

Chemical Physics · Physics 2024-12-11 Pavlo Golub , Chao Yang , Vojtěch Vlček , Libor Veis

Encoding classical data in a quantum state is a key prerequisite of many quantum algorithms. Recently matrix product state (MPS) methods emerged as the most promising approach for constructing shallow quantum circuits approximating input…

Google's Tensor Processing Units (TPUs) are integrated circuits specifically built to accelerate and scale up machine learning workloads. They can perform fast distributed matrix multiplications and therefore be repurposed for other…

Strongly Correlated Electrons · Physics 2023-06-27 Martin Ganahl , Jackson Beall , Markus Hauru , Adam G. M. Lewis , Jae Hyeon Yoo , Yijian Zou , Guifre Vidal

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

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…

Systems of correlated quantum matter can be a steep challenge to any would-be method of solution. Matrix-product state (MPS)-based methods can describe 1D systems quasiexactly, but often struggle to retain sufficient bipartite entanglement…

Strongly Correlated Electrons · Physics 2024-11-04 Gunnar Bollmark , Sam Mardazad , Johannes S. Hofmann , Adrian Kantian

While general quantum many-body systems require exponential resources to be simulated on a classical computer, systems of non-interacting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of…

Strongly Correlated Electrons · Physics 2019-12-18 Norbert Schuch , Bela Bauer

We combine the Density Matrix Renormalization Group (DMRG) with Matrix Product State tangent space concepts to construct a variational algorithm for finding ground states of one dimensional quantum lattices in the thermodynamic limit. A…

Quantum Physics · Physics 2019-04-22 V. Zauner-Stauber , L. Vanderstraeten , M. T. Fishman , F. Verstraete , J. Haegeman

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