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We present a refinement of the Spectral Method by incorporating an optimization method into it and generalize it to two space dimensions. We then apply this Refined Spectral Method as an extremely accurate technique for finding the bound…

Mathematical Physics · Physics 2007-05-23 P. Pedram , M. Mirzaei , S. S. Gousheh

We present a detailed study of the real-time dynamics and spectral properties of the one-dimensional fermionic Hubbard model at infinite temperature. Using tensor network simulations in Liouville space, we compute the single-particle…

Strongly Correlated Electrons · Physics 2025-09-26 Cătălin Paşcu Moca , Ovidiu I. Patu , Balázs Dóra , Gergely Zaránd

This paper presents a novel approach to rigorously solving initial value problems for semilinear parabolic partial differential equations (PDEs) using fully spectral Fourier-Chebyshev expansions. By reformulating the PDE as a system of…

Analysis of PDEs · Mathematics 2025-03-03 Matthieu Cadiot , Jean-Philippe Lessard

Chebyshev expansion coefficients can be computed efficiently by using the FFT, and for smooth functions the resulting approximation is close to optimal, with computations that are numerically stable. Given sufficiently accurate function…

Numerical Analysis · Mathematics 2015-03-30 Haiyong Wang , Daan Huybrechs

Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…

Numerical Analysis · Mathematics 2019-01-21 Kevin W. Aiton , Tobin A. Driscoll

We present a numerical spectral method to solve systems of differential equations on an infinite interval $y\in (-\infty, \infty)$ in presence of linear differential operators of the form $Q(y) \left(\partial/\partial_y\right)^b$ (where…

Fluid Dynamics · Physics 2017-10-11 Benjamin Miquel , Keith Julien

The transmission coefficient for a one dimensional system is given in terms of Chebyshev polynomials using the tight-binding model. This result is applied to a system composed of two impurities located between $N$ sites of a host lattice.…

Disordered Systems and Neural Networks · Physics 2009-11-07 P. Ojeda , R. Huerta Quintanilla , M. Rodriguez-Achach

A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of…

Symbolic Computation · Computer Science 2014-07-11 Alexandre Benoit , Mioara Joldes , Marc Mezzarobba

In this work we outline a simple and numerically inexpensive approach to describe the spectral features of the single-impurity Anderson model. The method combines aspects of the density matrix embedding theory (DMET) approach with a…

Strongly Correlated Electrons · Physics 2017-04-12 Soumyodipto Mukherjee , David R. Reichman

The quality of numerically simulated spectra using real-time evolution methods for strongly correlated systems is affected by both the length of simulation time and the system size, limiting resolution in both frequency and momentum. In…

Strongly Correlated Electrons · Physics 2025-09-22 Ta Tang , Chunjing Jia , Brian Moritz , Thomas P. Devereaux

We present a tensor network especially suited for multi-orbital Anderson impurity models and as an impurity solver for multi-orbital dynamical mean-field theory (DMFT). The solver works directly on the real-frequency axis and yields very…

Strongly Correlated Electrons · Physics 2017-07-26 Daniel Bauernfeind , Manuel Zingl , Robert Triebl , Markus Aichhorn , Hans Gerd Evertz

A dynamic density-matrix renormalisation group approach to the spectral properties of quantum impurity problems is presented. The method is demonstrated on the spectral density of the flat-band symmetric single-impurity Anderson model. We…

Strongly Correlated Electrons · Physics 2007-05-23 Satoshi Nishimoto , Eric Jeckelmann

We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…

Computational Physics · Physics 2009-10-31 Bogdan Mihaila , Ioana Mihaila

We consider discrete linear Chebyshev approximation problems in which the unknown parameters of linear function are fitted by minimizing the maximum absolute deviation of errors. Such problems find application in the solution of…

Optimization and Control · Mathematics 2020-12-22 Nikolai Krivulin

This work explores the representation of univariate and multivariate functions as matrix product states (MPS), also known as quantized tensor-trains (QTT). It proposes an algorithm that employs iterative Chebyshev expansions and Clenshaw…

This article focuses on the calculation of spectral functions for single- and multi-impurity models using the density matrix renormalization group (DMRG). To calculate spectral functions from DMRG, the correction vector method is presently…

Strongly Correlated Electrons · Physics 2015-03-19 Robert Peters

We extend a previously proposed rotation and truncation scheme to optimize quantum Anderson impurity calculations with exact diagonalization [PRB 90, 085102 (2014)] to density-matrix renormalization group (DMRG) calculations. The method…

Strongly Correlated Electrons · Physics 2019-10-02 Y. Lu , X. Cao , P. Hansmann , M. W. Haverkort

We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity…

Strongly Correlated Electrons · Physics 2009-11-10 Satoshi Nishimoto , Florian Gebhard , Eric Jeckelmann

We implement the recently developed influence functional matrix product states approach as impurity solver in equilibrium and nonequilibrium dynamical mean field theory (DMFT) calculations of the single-band Hubbard model. The method yields…

Strongly Correlated Electrons · Physics 2025-07-02 Mithilesh Nayak , Julian Thoenniss , Michael Sonner , Dmitry A. Abanin , Philipp Werner

We study the limits of the energy resolution that can be achieved in the calculations of spectral functions of quantum impurity models using the numerical renormalization group (NRG) technique with interleaving (z-averaging). We show that…

Strongly Correlated Electrons · Physics 2009-03-05 Rok Zitko , Thomas Pruschke