Related papers: Solving quantum impurity models in the non-equilib…
A general approach based on gauge invariance requirements has been developed for automatic construction of quantum kinetic equation in electron systems, far for equilibrium. Proposed theoretical scheme has high generality and automatism and…
The Schwinger-Keldysh diagram technique is usually involved in the calculation of real-time in-in correlation functions. In the case of a thermal state, one can analytically continue imaginary-time Matsubara correlation functions to real…
We propose a systematic approach to the non-equilibrium dynamics of strongly interacting many-body quantum systems, building upon the standard perturbative expansion in the Coulomb interaction. High order series are derived from the Keldysh…
Solving the Anderson impurity model typically involves a two-step process, where one first calculates the ground state of the Hamiltonian, and then computes its dynamical properties to obtain the Green's function. Here we propose a hybrid…
Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…
For time integration of transient eddy current problems commonly implicit time integration methods are used, where in every time step one or several nonlinear systems of equations have to be linearized with the Newton-Raphson method due to…
The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
Digital quantum computers offer a promising route for studying complex many-body systems that are otherwise inaccessible by their classical counterparts. Capabilities including mid-circuit measurements and feedback allow for simulating the…
We present an efficient separation of variables algorithm for the evaluation of imaginary time Feynman diagrams appearing in the bold pseudo-particle strong coupling expansion of the Anderson impurity model. The algorithm uses a fitting…
On the basis of the method of iterative summation of path integrals (ISPI), we develop a numerically exact transfer-matrix method to describe the nonequilibrium properties of interacting quantum-dot systems. For this, we map the ISPI scheme…
In this manuscript, we introduce the tensor-train reduced basis method, a novel projection-based reduced-order model designed for the efficient solution of parameterized partial differential equations. While reduced-order models are widely…
Motivated by the experiment by M. Budden {\em et al.} [Nature Physics {\bf 17}, 611 (2021)], who observed signatures of long-lived photo-induced superconductivity, we develop an accurate analytical/computational approach to non-equilibrium…
The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. In this paper we focus on nonlinear electronic transport through an interacting…
Exponential integrators based on contour integral representations lead to powerful numerical solvers for a variety of ODEs, PDEs, and other time-evolution equations. They are embarrassingly parallelizable and lead to global-in-time…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional function approximations arising from computational and data sciences. Various sequential and parallel TT decomposition algorithms have…
In this paper, we propose the Coupled Axial and Transverse currents (I) (CATI) method, as an efficient and accurate finite element approach for modelling the electric and magnetic behavior of periodic composite superconducting conductors.…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
Graph autoencoders have gained attention in nonlinear reduced-order modeling of parameterized partial differential equations defined on unstructured grids. Despite they provide a geometrically consistent way of treating complex domains,…
Using the corner-transfer matrix renormalization group to contract the tensor network that describes its partition function, we investigate the nature of the phase transitions of the hard-square model, one of the exactly solved models of…