Related papers: A hybrid approach to Fermi operator expansion
We propose and investigate two new methods to approximate $f({\bf A}){\bf b}$ for large, sparse, Hermitian matrices ${\bf A}$. The main idea behind both methods is to first estimate the spectral density of ${\bf A}$, and then find…
Approximation theorem is one of the most important aspects of numerical analysis that has evolved over the years with many different approaches. Some of the most popular approximation methods include the Lebesgue approximation theorem, the…
Simulating strongly-correlated quantum many-body systems at finite temperatures is a significant challenge in computational physics. In this work, we present a scalable finite-temperature tensor network algorithm for two-dimensional quantum…
We present a general formalism that allows for the computation of large-order renormalized expansions in the spacetime representation, effectively doubling the numerically attainable perturbation order of renormalized Feynman diagrams. We…
We introduce a method "DMT" for approximating density operators of 1D systems that, when combined with a standard framework for time evolution (TEBD), makes possible simulation of the dynamics of strongly thermalizing systems to arbitrary…
In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative operators in the sense that the tempered fractional derivative…
The recursive polynomial expansion for construction of a density matrix approximation with rigorous error control [J. Chem. Phys. 128, 074106 (2008)] is implemented in the quantum chemistry program Ergo [SoftwareX 7, 107 (2018)] using the…
A novel method to determine the density and temperature of a system is proposed based on quantum fluctuations typical of Fermions in the limit where the reached temperature T is small compared to the Fermi energy $\epsilon_f$ at a given…
We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms…
We present a quantum Monte Carlo method capable of sampling the full density matrix of a many-particle system at finite temperature. This allows arbitrary reduced density matrix elements and expectation values of complicated non-local…
We introduce a novel method to bootstrap crossing equations in Conformal Field Theory and apply it to finite temperature theories on $S^1\times \mathbb{R}^{d-1}$. The proposed approach does not rely on positivity constraints and does not…
Quantum statistical mechanics allows us to extract thermodynamic information from a microscopic description of a many-body system. A key step is the calculation of the density of states, from which the partition function and all…
We employ the generalized Remez algorithm, initially suggested by P. T. P. Tang, to perform an experimental study of Chebyshev polynomials in the complex plane. Our focus lies particularly on the examination of their norms and zeros. What…
We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (> 1000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham…
We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev…
We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz…
Finite-temperature transport properties of one-dimensional systems can be studied using the time dependent density matrix renormalization group via the introduction of auxiliary degrees of freedom which purify the thermal statistical…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
Over the last decades the 'fixed-node method' has been used for a numerical treatment of thermodynamic properties of strongly correlated Fermi systems. In this work correctness of the 'fixed -node method' for ideal Fermi systems has been…
We propose a density matrix renormalization group (DMRG) technique at finite temperatures. As is the case of the ground state DMRG, we use a single-target state that is calculated by making use of a regulated polynomial expansion. Both…