arXiv subjects

Jonas B. Rigo

Publications and source records attributed to Jonas B. Rigo.

9 recordsLinked to original sources

arXiv2026

Geometric inflation of deviations challenges neural quantum states in dynamics of quantum Ising models

Neural quantum states (NQS) have emerged as a powerful framework for simulating non-equilibrium dynamics in strongly correlated quantum systems, offering scalable variational representations of highly entangled states. Yet, accurate NQS simulations have been found to be surprisingly challenging in some physical regimes of limited complexity. Here, we address paradigmatic quench dynamics of a one-dimensional quantum Ising model as a controlled benchmark. Through supervised state reconstruction we establish substantially tighter empirical upper bounds on the required parameter count than previous estimates, ruling out representational limitations as the key obstruction. Instead, we uncover a geometric inflation of small deviations as a hitherto overlooked challenge for accurate solutions of the infinitesimal time-dependent variational principle (TDVP): the dynamical rotation of the kernel of the quantum geometric tensor (QGT) can suddenly lend physical significance to previously irrelevant parameter deviations. The stability of matrix product state solutions of the same TDVP suggests that the non-linearity of the neural network ansatz is the origin of the sensitivity. These results identify QGT-null-space rotation as a geometric diagnostic of sensitive NQS dynamics and as a concrete target for improving TDVP algorithms

quant-ph↗

arXiv2026

Neural quantum states in condensed matter: advances, best practices, and prospects

Neural quantum states provide flexible variational representations of quantum many-body wave functions by combining neural-network parametrizations with Monte Carlo sampling. In this perspective, we review recent advances in their application to condensed-matter systems, focusing on frustrated quantum magnets, interacting lattice fermions, and non-equilibrium dynamics. We discuss the architectures, symmetry constraints, optimization methods, and sampling strategies underlying state-of-the-art calculations, and summarize practical guidelines for reliable simulations. We also examine the principal remaining challenges, including learning non-trivial sign and phase structures, controlling variational bias, enforcing physical symmetries, scaling optimization to large networks, and achieving stable real-time evolution. Finally, we outline promising directions in which neural quantum states may extend the reach of classical simulations of strongly correlated quantum matter.

cond-mat.str-el↗

arXiv2026

Compressed minimum-purity time evolution for late-time quantum dynamics

Unitary time evolution of initially simple quantum many-body states rapidly generates entanglement and complex correlations, which limits direct numerical simulations. The late-time dynamics of physical observables, however, typically exhibits an effective simplicity in the form of hydrodynamics or kinetic theory. This leads to the question whether microscopic equations of motion can remain accurate and tractable up to long time scales by discarding irrelevant information in a controlled manner. Here, we introduce compressed minimum-purity time evolution (CoMPuTE) as an approach to keep track of a consistent set of reduced local density matrices, closing the hierarchical equations of motion using a minimum-purity principle. In benchmark applications we demonstrate (i) accurate description of energy diffusion in the one-dimensional mixed-field Ising model, (ii) the applicability to genuinely out-of-equilibrium Floquet dynamics starting from a pure state, and (iii) the limitations of the local reduced density matrix approximation when describing transport in the XXZ chain at $Δ=1$ that is governed by increasingly non-local integrals of motion. The CoMPuTE method enhances computational efficiency in comparison to the closely related local-information time evolution algorithm, opening a possible route towards an extension to systems in higher spatial dimensions.

cond-mat.stat-mech↗

arXiv2025

Operator Lanczos Approach enabling Neural Quantum States as Real-Frequency Impurity Solvers

To understand the intricate exchange between electrons of different bands in strongly correlated materials, it is essential to treat multi-orbital models accurately. For this purpose, dynamical mean-field theory (DMFT) provides an established framework, whose scope crucially hinges on the availability of efficient quantum impurity solvers. Here we present a real-frequency impurity solver based on neural quantum states (NQS) combined with an operator-Lanczos construction. NQS are an asymptotically unbiased variational ground-state ansatz that employs neural networks to capture long-range correlations on complicated graph structures. We leverage this ability to solve multi-orbital impurity problems using a systematically improvable Segmented Commutator Operator-Lanczos (SCOL) construction. Our benchmarks on both the single-orbital Anderson model and the multi-orbital Hubbard-Kanamori impurity Hamiltonian reveal excellent ground-state precision and the capacity to accurately resolve zero temperature spectral functions and self-energies. These results open avenues for extending DMFT to more challenging problems.

cond-mat.str-el↗

arXiv2024

Unsupervised Learning of Effective Quantum Impurity Models

Generalized quantum impurity models -- which feature a few localized and strongly-correlated degrees of freedom coupled to itinerant conduction electrons -- describe diverse physical systems, from magnetic moments in metals to nanoelectronics quantum devices such as quantum dots or single-molecule transistors. Correlated materials can also be understood as self-consistent impurity models through dynamical mean field theory. Accurate simulation of such models is challenging, especially at low temperatures, due to many-body effects from electronic interactions, resulting in strong renormalization. In particular, the interplay between local impurity complexity and Kondo physics is highly nontrivial. A common approach, which we further develop in this work, is to consider instead a simpler effective impurity model that still captures the low-energy physics of interest. The mapping from bare to effective model is typically done perturbatively, but even this can be difficult for complex systems, and the resulting effective model parameters can anyway be quite inaccurate. Here we develop a non-perturbative, unsupervised machine learning approach to systematically obtain low-energy effective impurity-type models, based on the renormalization group framework. The method is shown to be general and flexible, as well as accurate and systematically improvable. We benchmark the method against exact results for the Anderson impurity model, and provide an outlook for more complex models beyond the reach of existing methods.

cond-mat.str-el↗

arXiv2022

Two-channel charge-Kondo physics in graphene quantum dots

Nanoelectronic quantum dot devices exploiting the charge-Kondo paradigm have been established as versatile and accurate analog quantum simulators of fundamental quantum impurity models. In particular, hybrid metal-semiconductor dots connected to two metallic leads realize the two-channel Kondo (2CK) model, in which Kondo screening of the dot charge pseudospin is frustrated. Here, we consider theoretically a two-channel charge-Kondo device made instead from graphene components, realizing a pseudogapped version of the 2CK model. We solve the model using Wilson's Numerical Renormalization Group method, and uncover a rich phase diagram as a function of dot-lead coupling strength, channel asymmetry, and potential scattering. The complex physics of this system is explored through its thermodynamic properties, scattering T-matrix, and experimentally measurable conductance. We find that the strong coupling pseudogap Kondo phase persists in the channel-asymmetric two-channel context, while in the channel-symmetric case frustration results in a novel quantum phase transition. Remarkably, despite the vanishing density of states in the graphene leads at low energies, we find a finite linear conductance at zero temperature at the frustrated critical point, which is of non-Fermi liquid type. Our results suggest that the graphene charge-Kondo platform offers a unique possibility to access multichannel pseudogap Kondo physics.

cond-mat.str-el↗

arXiv2022

Linear response quantum transport through interacting multi-orbital nanostructures

Nanoelectronics devices, such as quantum dot systems or single-molecule transistors, consist of a quantum nanostructure coupled to a macroscopic external electronic circuit. Thermoelectric transport between source and drain leads is controlled by the quantum dynamics of the lead-coupled nanostructure, through which a current must pass. Strong electron interactions due to quantum confinement on the nanostructure produce nontrivial conductance signatures such as Coulomb blockade and Kondo effects, which become especially pronounced at low temperatures. In this work we first provide a modern review of standard quantum transport techniques, focusing on the linear response regime, and highlight the strengths and limitations of each. In the second part, we develop an improved numerical scheme for calculation of the ac linear electrical conductance through generic interacting nanostructures, based on the numerical renormalization group (NRG) method, and explicitly demonstrate its utility in terms of accuracy and efficiency. In the third part we derive low-energy effective models valid in various commonly-encountered situations, and from them we obtain simple analytical expressions for the low-temperature conductance. This indirect route via effective models, although approximate, allows certain limitations of conventional methodologies to be overcome, and provides physical insights into transport mechanisms. Finally, we apply and compare the various techniques, taking the two-terminal triple quantum dot and the serial multi-level double dot devices as nontrivial benchmark systems.

cond-mat.str-el↗

arXiv2022

Automatic Differentiable Numerical Renormalization Group

Machine learning techniques have recently gained prominence in physics, yielding a host of new results and insights. One key concept is that of backpropagation, which computes the exact gradient of any output of a program with respect to any input. This is achieved efficiently within the differentiable programming paradigm, which utilizes automatic differentiation (AD) of each step of a computer program and the chain rule. A classic application is in training neural networks. Here, we apply this methodology instead to the numerical renormalization group (NRG), a powerful technique in computational quantum many-body physics. We demonstrate how derivatives of NRG outputs with respect to Hamiltonian parameters can be accurately and efficiently obtained. Physical properties can be calculated using this differentiable NRG scheme--for example, thermodynamic observables from derivatives of the free energy. Susceptibilities can be computed by adding source terms to the Hamiltonian, but still evaluated with AD at precisely zero field. As an outlook, we briefly discuss the derivatives of dynamical quantities and a possible route to the vertex.

cond-mat.str-el↗

arXiv2020

Machine learning effective models for quantum systems

The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We propose a machine learning approach that optimizes an effective model based on an estimation of its partition function. The success of the method is demonstrated by application to the single impurity Anderson model and double quantum dots, where non-perturbative results are obtained for the old problem of mapping to effective Kondo models. For quantum impurity parent Hamiltonians, we derive an alternative approach based on learning from observables. When mapping to minimal effective models, emergent scales may not be captured by observable learning, while partition function learning may not reproduce all observables.

cond-mat.str-el↗