arXiv subjects

Olivier Parcollet

Publications and source records attributed to Olivier Parcollet.

At least 19 recordsLinked to original sources

arXiv2026

Fast Tensor Network Imaginary Time Evolution by Implicit Stepping on Logarithmic Grids

We present a new method for the efficient imaginary time evolution of quantum many-body wavefunctions represented by matrix product states (MPS). We first show that logarithmic time grids are sufficient to resolve long imaginary time dynamics, yielding an exponential reduction in the number of time steps compared with standard approaches. We then show that A-stable implicit time-stepping methods for ordinary differential equations allow stable propagation for any time step size. The resulting scheme requires only matrix-vector products and linear solves, standard operations in the MPS toolbox. We validate our approach with two examples: a Heisenberg spin chain, which we use to demonstrate a speedup of several orders of magnitude over the standard time-dependent variational principle method with uniform time steps, and a single-site Anderson impurity model with a metallic bath, for which propagation to large imaginary times allows one to observe the exponential dependence of the Kondo temperature on the interaction strength.

cond-mat.str-el↗

arXiv2026

Neural-Network Quantum Embedding Solvers for Correlated Materials

Quantum impurity solvers are the computational bottleneck of quantum embedding approaches to correlated materials, such as dynamical mean-field theory (DMFT). We show that neural networks trained on synthetic, material-agnostic data learn the impurity mapping from hybridization functions and local interactions to Green's functions with quantitative accuracy for both model systems and real materials, providing fast solvers for single- and multi-orbital models. Benchmarks against numerically controlled quantum Monte Carlo show that the method reproduces the Mott transition, multi-orbital phase diagrams of Hubbard-Kanamori models, and the electronic properties of SrVO$_3$ and SrMnO$_3$. The learned solvers achieve orders-of-magnitude speedup and can initialize controlled calculations, dramatically accelerating DMFT while preserving accuracy.

cond-mat.str-el↗

arXiv2026

Electronic correlations and dynamical screening with ab initio quantum embedding

First-principles descriptions of correlated quantum materials require a simultaneous treatment of strong local many-body effects and nonlocal dynamical screening. We present an efficient fully self-consistent implementation of $GW$+EDMFT that combines nonlocal effects at the $GW$ level with a non-perturbative treatment of local correlations within extended dynamical mean-field theory (EDMFT), while providing a controlled double-counting prescription. Crucially, self-consistency in both the Green's function and the dynamically screened interaction is essential to achieve a consistent description of screening processes across energy scales. The efficient computation of this self-consistent solution is enabled here by compressing two-particle correlation functions using interpolative separable density fitting (ISDF). Applying the scheme to the Mott insulator SrMnO$_3$ and the correlated metal LaNiO$_3$, we show that full self-consistency resolves the overscreening inherent to constrained-RPA approaches. By suppressing spurious low-energy screening channels, a Mott-insulating state in quantitative agreement with experiment is obtained for SrMnO$_3$. These results establish fully self-consistent $GW$+EDMFT as a predictive ab initio framework for strongly correlated quantum materials.

cond-mat.str-el↗

arXiv2025

Inchworm tensor train hybridization expansion quantum impurity solver

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 accurate results for multi-orbital systems with complex interactions and off-diagonal hybridizations. Recently, tensor-train-based integration and summation techniques have shown promise as effective alternatives. In this study, we use tensor train methods to tackle quantum impurity problems formulated within the imaginary-time inchworm hybridization expansion framework. We identify key challenges in the inchworm expansion itself and its interplay with tensor-train-based methods. We demonstrate the accuracy and versatility of our approach by solving general quantum impurity problems. Our results suggest that tensor-train decomposition schemes offer a viable path toward accurate and efficient multi-orbital impurity solvers.

cond-mat.str-el↗

arXiv2025

LiV2O4: Hund-Assisted Orbital-Selective Mottness

We show that the remarkably small Fermi-liquid coherence scale and large effective mass observed in LiV$_2$O$_4$ are due to the proximity of a Hund-assisted orbital-selective Mott state. Our work is based on an ab initio dynamical mean-field approach, combining several quantum impurity solvers to capture the physics from high to very low temperature. We find that the Hund coupling plays a crucial role in rearranging the orbital populations and in generating the heavy mass and low coherence scale. The latter is found to be approximately 1-2 Kelvin, even though the most correlated orbital is found to be significantly doped ~10% away from half-filling. A flat quasiparticle band appears near the Fermi level as a result of the strong electronic correlations. Finally, we discuss our results in comparison to experiments.

cond-mat.str-el↗

arXiv2025

Algorithm for computing perturbation series of dynamical mean field theory

We show how to use diagrammatic techniques to compute the weak-coupling perturbation series of the self-consistent solution to a Dynamical Mean Field Theory (DMFT) problem. This approach constitutes an alternative to using diagrammatic techniques directly as an impurity solver. It allows one to bypass the need of multiple perturbative series resummations within the DMFT self-consistency loop. It can be applied at or out of equilibrium, with any diagrammatic formalism, such as real times, imaginary times, or Matsubara frequencies formalisms. As a proof of principle, we illustrate our method with the half-filled Hubbard model on the Bethe lattice in the DMFT approximation, using Quantum Quasi-Monte Carlo (QQMC) to obtain the impurity perturbation series on the real time axis.

cond-mat.str-el↗

arXiv2025

A comprehensive study of out-of-equilibrium Kondo effect and Coulomb blockade

We present a comprehensive set of numerically exact results for the Anderson model of a quantum dot coupled to two electrodes in non-equilibrium regime. We use a high order perturbative expansion in power of the interaction $U$, coupled to a cross-extrapolation method to long time and large interaction. The perturbative series is computed up to $20-25$ orders, using tensor cross-interpolation. We calculate the full Coulomb diamond bias voltage - gate voltage map, including its Kondo ridge, that forms the standard experimental signature of the Coulomb blockage and the Kondo effect. We present current-voltage characteristics that spans three orders of magnitude in bias voltage and display five different regimes of interest from probing the Kondo resonance at small bias to saturation at very high bias. Our technique also naturally produces time-resolved interaction quenches which we use to study the dynamics of the formation of the Kondo cloud. Finally, we predict several qualitatively new physical features that should be within reach of existing or upcoming experiments.

cond-mat.str-el↗

arXiv2025

Hund flat band in a frustrated spinel oxide

Electronic flat bands associated with quenched kinetic energy and heavy electron mass have attracted great interest for promoting strong electronic correlations and emergent phenomena such as high-temperature charge fractionalization and superconductivity. Intense experimental and theoretical research has been devoted to establishing the rich non-trivial metallic and heavy fermion phases intertwined with such localized electronic states. Here, we investigate the transition metal oxide spinel LiV2O4, an enigmatic heavy fermion compound lacking localized f orbital states. We use angle-resolved photoemission spectroscopy and dynamical mean field theory to reveal a new kind of correlation-induced flat band with suppressed inter-atomic electron hopping arising from intra-atomic Hund coupling. The appearance of heavy quasiparticles is ascribed to a proximate orbital-selective Mott state characterized by fluctuating local moments as evidenced by complementary magnetotransport measurements. The spectroscopic fingerprints of long-lived quasiparticles and their disappearance with increasing temperature further support the emergence of a high-temperature bad metal state observed in transport data. This work resolves a long-standing puzzle on the origin of heavy fermion behavior and unconventional transport in LiV2O4. Simultaneously, it opens a new path to achieving flat bands through electronic interactions in d-orbital systems with geometrical frustration, potentially enabling the realization of exotic phases of matter such as the fractionalized Fermi liquids.

cond-mat.str-el↗

arXiv2025

Enhanced Strange Metallicity due to Hubbard-U Coulomb Repulsion

We solve a model of electrons with Hubbard-$U$ Coulomb repulsion and a random Yukawa coupling to a two-dimensional bosonic bath, using an extended dynamical mean field theory scheme. Our model exhibits a quantum critical point, at which the repulsive component of the electron interactions strongly enhances the effects of the quantum critical bosonic fluctuations on the electrons, leading to a breakdown of Fermi liquid physics and the formation of a strange metal with `Planckian' ($\mathcal{O}(k_B T/\hbar)$) quasiparticle decay rates at low temperatures $T\rightarrow 0$. Furthermore, the eventual Mott transition that occurs as the repulsion is increased seemingly bounds the maximum decay rate in the strange metal. Our results provide insight into low-temperature strange metallicity observed in proximity to a Mott transition, as is observed, for instance, in recent experiments on certain moiré materials.

cond-mat.str-el↗

arXiv2024

Learning tensor networks with tensor cross interpolation: new algorithms and libraries

The tensor cross interpolation (TCI) algorithm is a rank-revealing algorithm for decomposing low-rank, high-dimensional tensors into tensor trains/matrix product states (MPS). TCI learns a compact MPS representation of the entire object from a tiny training data set. Once obtained, the large existing MPS toolbox provides exponentially fast algorithms for performing a large set of operations. We discuss several improvements and variants of TCI. In particular, we show that replacing the cross interpolation by the partially rank-revealing LU decomposition yields a more stable and more flexible algorithm than the original algorithm. We also present two open source libraries, xfac in Python/C++ and TensorCrossInterpolation.jl in Julia, that implement these improved algorithms, and illustrate them on several applications. These include sign-problem-free integration in large dimension, the superhigh-resolution quantics representation of functions, the solution of partial differential equations, the superfast Fourier transform, the computation of partition functions, and the construction of matrix product operators.

physics.comp-ph↗

arXiv2024

Variational Benchmarks for Quantum Many-Body Problems

The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems, identifying cases where state-of-the-art numerical approaches show limited accuracy, and future algorithms or computational platforms, such as quantum computing, could provide improved accuracy. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems, especially in regimes where classical verifiability is impossible.

quant-ph↗

arXiv2024

Exact numerical solution of the fully-connected classical and quantum Heisenberg spin glass

We present the mean field solution of the quantum and classical Heisenberg spin glasses, using the combination of a high precision numerical solution of the Parisi full replica symmetry breaking equations and a continuous time Quantum Monte Carlo. We characterize the spin glass order and its low-energy excitations down to zero temperature. The Heisenberg spin glass has a rougher energy landscape than its Ising analogue, and exhibits a very slow temperature evolution of its dynamical properties. We extend our analysis to the doped, metallic Heisenberg spin glass, which displays an unexpectedly slow spin dynamics reflecting the proximity to the melting quantum critical point and its associated Sachdev-Ye-Kitaev Planckian dynamics.

cond-mat.dis-nn↗

arXiv2024

Discrete Lehmann representation of three-point functions

We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time and Matsubara frequency. The representation takes the form of a linear combination of judiciously chosen exponentials in imaginary time, and products of simple poles in Matsubara frequency, which are universal for a given temperature and energy cutoff. We present a systematic algorithm to generate compact sampling grids, from which the coefficients of such an expansion can be obtained by solving a linear system. We show that the explicit form of the representation can be used to evaluate diagrammatic expressions involving infinite Matsubara sums, such as polarization functions or self-energies, with controllable, high-order accuracy. This collection of techniques establishes a framework through which methods involving three-point objects can be implemented robustly, with a substantially reduced computational cost and memory footprint.

physics.comp-ph↗

arXiv2024

Embedded multi-boson exchange: A step beyond quantum cluster theories

We introduce a diagrammatic multi-scale approach to the Hubbard model based on the interaction-irreducible (multi-boson) vertex of a small cluster embedded in a self-consistent medium. The vertex captures short-ranged correlations up to the length scale of the cluster, while long-ranged correlations are recovered from a set of diagrammatic equations for the Hedin three-leg vertex. By virtue of the crossing symmetry, the Fierz decoupling ambiguity of the Hubbard interaction is resolved exactly. Our benchmarks for the half-filled Hubbard model on the square lattice are in very good agreement with numerically exact diagrammatic Monte Carlo simulations.

cond-mat.str-el↗

arXiv2024

Dynamical correlation functions from complex time evolution

We present an approach to tame the growth of entanglement during time evolution by tensor network methods. It combines time evolution in the complex plane with a perturbative and controlled reconstruction of correlation functions on the real-time axis. We benchmark our approach on the single impurity Anderson model. Compared to purely real-time evolution, the complex time evolution significantly reduces the required bond dimension to obtain the spectral function. Notably, our approach yields self-energy results with high precision at low frequencies, comparable to numerical renormalization group (NRG) results, and it successfully captures the exponentially small Kondo energy scale.

cond-mat.str-el↗

arXiv2024

Finite Temperature Minimal Entangled Typical Thermal States Impurity Solver

We present a minimally entangled typical thermal state (METTS) quantum impurity solver for general multi-orbital systems at finite temperatures. We introduce an improved estimator for the single-particle Green's function that strongly reduces the large fluctuations at long imaginary time and low temperature, which were a severe limitation of the original algorithm. In combination with the fork tensor product states ansatz, we obtain a dynamical mean field theory (DMFT) quantum impurity solver, which we benchmark for single and three-band models down to low temperatures, including the effect of spin-orbit coupling in a realistic DMFT computation for the Hund's metal Sr$_2$RuO$_4$ down to low temperatures.

cond-mat.str-el↗

arXiv2024

Cross-extrapolation reconstruction of low-rank functions and application to quantum many-body observables in the strong coupling regime

We present a general-purpose algorithm to extrapolate a low rank function of two variables from a small domain to a larger one. It is based on the cross-interpolation formula. We apply it to reconstruct physical quantities in some quantum many-body perturbative expansions in the real time Keldysh formalism, considered as a function of time $t$ and interaction $U$. These functions are of remarkably low rank. This property, combined with the convergence of the perturbative expansion in $U$ both at finite $t$ (for any $U$), and small $U$ (for any $t$), is sufficient for our algorithm to reconstruct the physical quantity at long time, strong coupling regime. Our method constitutes an alternative to standard resummation techniques in perturbative methods, such as diagrammatic Quantum Monte Carlo. We benchmark it on the single impurity Anderson model and show that it is successful even in some regime where standard conformal mapping resummation techniques fail.

cond-mat.str-el↗

arXiv2023

Frequency-Dependent Superconducting States From the Two-Time Linear Response Theory: Application To Sr$_2$RuO$_4$

We investigate the possible superconducting instabilities of strongly correlated electron materials using a generalization of linear response theory to external pairing fields depending on frequency. We compute a pairing susceptibility depending on two times, allowing us to capture dynamical pairing and in particular odd-frequency solutions. We first benchmark this method on the attractive one-band Hubbard model and then consider the superconductivity of strontium ruthenate Sr$_2$RuO$_4$ within single-site dynamical mean-field theory, hence restricting ourselves to pairing states which are momentum independent in the orbital basis. The symmetry of the superconducting order parameter of this material is still debated, and local odd-frequency states have been proposed to explain some experimental discrepancies. In the temperature range studied, we find that the leading eigenvectors are odd-frequency intra-orbital spin-triplet states, while the eigenvectors with the highest predicted transition temperature correspond to even-frequency intra-orbital spin-singlet states. The latter include a state with $d$-wave symmetry when expressed in the band basis.

cond-mat.supr-con↗