Multivariate functions of continuous variables arise in countless branches science. Numerical computations with such typically involve a compromise between two contrary desiderata: accurate resolution the functional dependence, versus parsimonious memory usage. Recently, promising strategies have emerged for satisfying both requirements: (i) The quantics representation, which expresses as multi-index tensors, each index representing one bit binary encoding variables; and (ii) tensor cross...

The tensor cross interpolation (TCI) algorithm is a rank-revealing for decomposing low-rank, high-dimensional tensors into trains/matrix product states (MPS). TCI learns compact MPS representation of the entire object from tiny training data set. Once obtained, large existing toolbox provides exponentially fast algorithms performing set operations. We discuss several improvements and variants TCI. In particular, we show that replacing by partially LU decomposition yields more stable flexible...

We use tensor network techniques to obtain high-order perturbative diagrammatic expansions for the quantum many-body problem at very high precision. The approach is based on a train parsimonious representation of sum all Feynman diagrams, obtained in controlled and accurate way with cross interpolation algorithm. It yields full time evolution physical quantities presence any arbitrary time-dependent interaction. Our benchmarks Anderson impurity problem, within real-time nonequilibrium...

The simulation of strongly correlated quantum impurity models is a significant challenge in modern condensed matter physics that has multiple important applications. Thus far, the most successful methods for approaching this involve Monte Carlo techniques accurately and reliably sample perturbative expansions to any order. However, cost obtaining high precision through these high. Recently, tensor train decomposition have been developed as an alternative integration. In study, we apply...

We present a general-purpose algorithm to extrapolate low-rank function of two variables from small domain larger one. It is based on the cross-interpolation formula. apply it reconstruct physical quantities in some quantum many-body perturbative expansions real-time Keldysh formalism, considered as time $t$ and interaction $U$. These functions are remarkably low rank. This property, combined with convergence expansion $U$ both at finite (for any $U$), $t$), sufficient for our quantity long...

The tensor cross interpolation (TCI) algorithm is a rank-revealing for decomposing low-rank, high-dimensional tensors into trains/matrix product states (MPS). TCI learns compact MPS representation of the entire object from tiny training data set. Once obtained, large existing toolbox provides exponentially fast algorithms performing set operations. We discuss several improvements and variants TCI. In particular, we show that replacing by partially LU decomposition yields more stable flexible...

A repulsive Coulomb interaction between electrons in different orbitals correlated materials can give rise to bound quasiparticle states. We study the non-hybridized two-orbital Hubbard model with intra (inter)-orbital $U$ ($U_{12}$) and band widths using an improved dynamical mean field theory numerical technique which leads reliable spectra on real energy axis directly at zero temperature. find that a finite density of states Fermi one is emergence well defined excited energies...

The dynamical mean-field theory (DMFT) has become a standard technique for the study of strongly correlated models and materials overcoming some limitations density functional approaches based on local approximations. An important step in this method involves calculation response functions multiorbital impurity problem which is related to original model. Recently there been considerable progress development techniques matrix renormalization group (DMRG) product states (MPS) implying...

We study the electronic spectral properties at zero temperature of one-dimensional (1D) version degenerate two-orbital Kanamori-Hubbard model, one well-established frameworks to transition metal compounds, using state-of-the-art numerical techniques based on density matrix renormalization group. While system is Mott insulating for half-filled case, as expected an interacting 1D system, we find interesting and rich structures in single-particle states (DOS) hole-doped system. In particular,...

We calculate and resolve with unprecedented detail the local density of states (DOS) momentum-dependent spectral functions at zero temperature one key models for strongly correlated electron materials, degenerate two-orbital Kanamori-Hubbard model, by means dynamical mean-field theory, which uses matrix renormalization group as impurity solver. When system is hole doped in presence a finite interorbital Coulomb interaction, we find emergence novel holon-doublon in-gap subband split Hund's...

Starting from \textit{ab-initio} calculations, we derive a five-band Hubbard model to describe the CuO$_2$ chains of LiCu$_2$O$_2$. This is further simplified low-energy effective Heisenberg with nearest-neighbor (NN) $J_1$, and next-nearest-neighbor (NNN) $J_2$ interactions, combining perturbation theory, exact diagonalization calculations Density Matrix Renormalization Group results. For realistic parameters find corresponding values these interactions. The obtained consistent...

We present a general-purpose algorithm to extrapolate low rank function of two variables from small domain larger one. It is based on the cross-interpolation formula. apply it reconstruct physical quantities in some quantum many-body perturbative expansions real time Keldysh formalism, considered as $t$ and interaction $U$. These functions are remarkably rank. This property, combined with convergence expansion $U$ both at finite (for any $U$), $t$), sufficient for our quantity long time,...

A zero-site density matrix renormalization algorithm (DMRG0) is proposed to minimize the energy of product states (MPSs). Instead site tensors themselves, we propose optimize sequentially ``message'' between neighbor sites, which contain singular values bipartition. This leads a local minimization step that independent physical dimension site. Conceptually, it separates optimization and decimation steps in DMRG. Furthermore, introduce two global perturbations based on optimal low-rank...

In this work we study the two-orbital Hubbard model on a square lattice in presence of hybridization between nearest-neighbor orbitals and crystal-field splitting. We use highly reliable numerical technique based density matrix renormalization group to solve dynamical mean field theory self-consistent impurity problem. find that orbital mixing always leads finite local states at Fermi energy both when least one band is metallic. When doped, chemical potential lies bands other band, coherent...

We use tensor network techniques to obtain high order perturbative diagrammatic expansions for the quantum many-body problem at very precision. The approach is based on a train parsimonious representation of sum all Feynman diagrams, obtained in controlled and accurate way with cross interpolation algorithm. It yields full time evolution physical quantities presence any arbitrary dependent interaction. Our benchmarks Anderson impurity problem, within real non-equilibrium Schwinger-Keldysh...