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We present a general method for simulating lattice gauge theories in low dimensions using infinite matrix product states (iMPS). A central challenge in Hamiltonian formulations of gauge theories is the unbounded local Hilbert space…
Understanding the real-time evolution of many-electron quantum systems is essential for studying dynamical properties in condensed matter, quantum chemistry, and complex materials, yet it poses a significant theoretical and computational…
Tensor network decompositions of path integrals for simulating open quantum systems have recently been proven to be useful. However, these methods scale exponentially with the system size. This makes it challenging to simulate the…
We introduce an algorithm to improve the error scaling of product formulas by randomly sampling the generator of their exact error unitary. Our approach takes an arbitrary product formula of time $t$, $S_k(t)$ with error $O(t^{k+1})$ and…
An acceleration of continuous time quantum Monte Carlo (CTQMC) methods is a potentially interesting branch of work as they are matchless as impurity solvers of a density functional theory in combination with a dynamical mean field theory…
We review recent work on continuous quantum phase transitions in impurity models, both with fermionic and bosonic baths - these transitions are interesting realizations of boundary critical phenomena at zero temperature. The models with…
We explore systems with a large number of fermionic degrees of freedom subject to non-local interactions. We study both vector and matrix-like models with quartic interactions. The exact thermal partition function is expressed in terms of…
This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…
We propose an input sparsity time sampling algorithm that can spectrally approximate the Gram matrix corresponding to the $q$-fold column-wise tensor product of $q$ matrices using a nearly optimal number of samples, improving upon all…
Numerically exact continuous-time Quantum Monte Carlo algorithm for finite fermionic systems with non-local interactions is proposed. The scheme is particularly applicable for general multi-band time-dependent correlations since it does not…
The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…
The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…
We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer…
In this paper, we analyze and provide numerical illustrations for a moving finite element method applied to convection-dominated, time-dependent partial differential equations. We follow a method of lines approach and utilize an underlying…
We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer…
Approximating solutions of non-linear parametrized physical problems by interpolation presents a major challenge in terms of accuracy. In fact, pointwise interpolation of such solutions is rarely efficient and leads generally to incorrect…
We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent variational principle to the set of translational invariant…
We propose a new method for solving quantum mechanical problems, which combines the flexibility of Gaussian basis set methods with the numerical accuracy of the Fourier method. The method is based on the incorporation of periodic boundary…
The investigation of quantum impurity models plays a crucial role in condensed matter physics because of their wide-ranging applications, such as embedding theories and transport problems. Traditional methods often fall short of producing…
We develop analytical tools and numerical methods for time evolving the total density matrix of the finite-size Anderson model. The model is composed of two finite metal grains, each prepared in canonical states of differing chemical…