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Indentation test is used with growing popularity for the characterization of various materials on different scales. Developed methods are combining the test with computer simulation and inverse analyses to assess material parameters…
We consider quantum entanglement in strongly correlated quantum impurity systems for states manifesting interesting properties such as multi-level Kondo effect and dual nature between itineracy and localization etc.. For this purpose, we…
The entanglement quantification and classification of multipartite quantum states are two important research fields in quantum information. In this work, we study the entanglement of arbitrary-dimensional multipartite pure states by looking…
We present a new method to solve nonlinear Hammerstein equations with weakly singular kernels. The process to approximate the solution, followed usually, consists in adapting the discretization scheme from the linear case in order to obtain…
We apply a two-particle semi-analytic approach to a single Anderson impurity attached to two biased metallic leads. The theory is based on reduced parquet equations justified in critical regions of singularities in the Bethe-Salpeter…
Quantum entanglement is a particularly useful characterization of topological orders which lack conventional order parameters. In this work, we study the entanglement in topologically ordered states between two arbitrary spatial regions,…
We explore two complementary modifications of the hybridization-expansion continuous-time Monte Carlo method, aiming at large multi-orbital quantum impurity problems. One idea is to compute the imaginary-time propagation using a matrix…
We construct the boundary conformal field theory that describes the low-temperature behavior of the two-channel Anderson impurity model. The presence of an exactly marginal operator is shown to generate a line of stable fixed points…
We propose a discrete time formulation of the semi-martingale optimal transport problem based on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by [17],…
A versatile and efficient variational approach is developed to solve in- and out-of-equilibrium problems of generic quantum spin-impurity systems. Employing the discrete symmetry hidden in spin-impurity models, we present a new canonical…
We investigate the single-impurity Anderson model by means of the recently introduced modified perturbation theory. This approximation scheme yields reasonable results away from the symmetric case. The agreement with exactly known results…
Finding ways to transform a quantum state to another is fundamental to quantum information processing. In this paper, we apply the sparse matrix approach to the quantum state transformation problem. In particular, we present a new approach…
We introduce a novel quantum computing heuristic for solving the irregular strip packing problem, a significant challenge in optimizing material usage across various industries. This problem involves arranging a set of irregular polygonal…
A new method is presented which allows time averaged density matrices of closed quantum systems to be computed via a constraint overlap maximization. Due to its simplicity, this method can be combined with algorithms based on tensor…
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…
We simulate the nonequilibrium dynamics of two generic many-body quantum impurity models by employing the recently developed iterative influence-functional path integral method [Phys. Rev. B {\bf 82}, 205323 (2010)]. This general approach…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…
We give an exact solution to the nonlinear optimization problem of approximating a Hermitian matrix by positive semi-definite matrices. Our algorithm was then used to judge whether a quantum state is entangled or not. We show that the exact…
We present a method to quantify entanglement in mixed states of highly symmetric systems. Symmetry constrains interactions between parts and predicts the degeneracies of the states. While symmetry alone produces entangled eigenstates, the…
Affine matrix rank minimization problem is a fundamental problem with a lot of important applications in many fields. It is well known that this problem is combinatorial and NP-hard in general. In this paper, a continuous promoting low rank…