arXiv subjects

Martin Eckstein

Publications and source records attributed to Martin Eckstein.

At least 19 recordsLinked to original sources

arXiv2026

Electronic correlations and fluctuating lattice distortions in vanadium dioxide

Metal-insulator transitions in correlated materials are often accompanied by a change of crystal structure. They are commonly described within a coherent lattice approximation, which combines a correlated treatment of the electrons with a lattice represented by one or a few classical distortion coordinates fixed by minimizing an energy. The structural degrees of freedom then carry no entropy of their own, even though the partition of the transition entropy between electrons and lattice is often what decides the transition temperature. Here we develop a stochastic semiclassical extension of dynamical mean-field theory in which correlated electrons and fluctuating lattice distortions are evolved together, extending previous formulations from linear to nonlinear electron-phonon interactions and from a single to several coupled lattice modes. The resulting non-conservative Langevin equations have deterministic forces, damping, and correlated noise generated self-consistently by the interacting electronic subsystem. Applying the approach to a minimal two-orbital model containing the two symmetry-distinct distortions of the monoclinic phase of vanadium dioxide, we find that the two distortions melt at well separated temperatures, giving an insulating, an intermediate metallic, and a high-symmetry phase. The two transitions have different origins: the melting of the dimerization is driven by the coupling to the correlated electrons and is captured already within the coherent lattice approximation, whereas the restoration of the undistorted structure requires the entropy of the fluctuating lattice. Since the electronic subsystem is treated within nonequilibrium dynamical mean-field theory, the framework can be extended in future work to photoexcited systems with nonthermal electronic distributions.

cond-mat.str-el↗

arXiv2026

Accelerating a Strong-Coupling Non-Equilibrium Steady-State Impurity Solver using (Quantics) Tensor Trains

Including higher order diagrammatic corrections to the strong-coupling expansion is mainly limited by the evaluation of high-dimensional, time-ordered integrals. In this work we present and compare four different parametrizations of the integrands in order to obtain a low-rank (quantics) tensor-train representation using tensor cross interpolation. Particular emphasis is placed on a quantics time-difference formulation in which the required retarded convolutions are performed directly in quantics tensor-train form. Using controlled Gaussian benchmarks, we analyze the accuracy, bond dimensions, and computational scaling of the different approaches. We then validate the most promising formulations in self-consistent equilibrium and nonequilibrium DMFT calculations and demonstrate calculations up to the third order in the strong-coupling expansion. Finally, we extend the solver to impurity models with retarded density-density interactions and apply it within nonequilibrium extended DMFT. Our results show that tensor cross interpolation substantially reduces the cost of evaluating higher-order diagrams and provides a controlled, systematically improvable framework for nonequilibrium quantum impurity calculations.

cond-mat.str-el↗

arXiv2026

Nonperturbative Nonlinear Hall Effect in Nonequilibrium Steady States

The nonlinear Hall effect in quantum materials has attracted broad interest, yet most existing studies focus on the weak-field, perturbative regime. Here we develop a nonperturbative approach based on nonequilibrium steady-state Green's functions for dc-field-driven lattice systems, with dissipation and interactions incorporated through self-energies beyond the constant relaxation-time approximation and interband transitions treated alongside their intraband counterparts. Applied to a two-band semimetal model, our approach provides direct access to the strong-field Hall response beyond the nonperturbative crossover where the edge of the nonequilibrium distribution reaches Berry-curvature hot spots, a regime in which constant relaxation-time estimates and Berry curvature dipole calculations become unreliable. We further demonstrate that interaction and electron-phonon self-energies within dynamical mean-field theory can substantially change the Hall signal. Our framework enables quantitative simulations of nonequilibrium nonlinear Hall phenomena and provides guidance for strong-field transport experiments.

cond-mat.str-el↗

arXiv2026

NESSi 2.0: The Non-Equilibrium Systems Simulation package version 2.0

Nonequilibrium Green's functions provide a powerful framework for studying quantum many-body dynamics including the laser-induced dynamics in solids. The Non-Equilibrium Systems Simulation package (NESSi) offers an efficient platform for such simulations, ranging from perturbative approaches like nonequilibrium $GW$ to nonequilibrium dynamical mean-field theory. However, simulations based on nonequilibrium Green's functions become computationally demanding when the dynamics span a large temporal range, such as from sub-femtosecond electron dynamics to the picosecond dynamics of collective modes. Due to the memory integral in the Kadanoff-Baym equations, which serve as equations of motion for nonequilibrium Green's functions, the computational cost scales as $\mathcal{O}(N_t^3)$ with the number of timesteps $N_t$, and the memory requirement scales as $\mathcal{O}(N_t^2)$. In this work, we extend NESSi by incorporating techniques that aim to overcome this bottleneck: (i) By truncating the memory integrals in the KBE to a maximum of $N_c$ timesteps, the computational complexity is reduced to $\mathcal{O}(N_tN_c^2)$, and the memory requirement to $\mathcal{O}(N_c^2)$. Provided that the results converge with respect to the cutoff $N_c$, memory truncation allows to extend the simulations to significantly longer times. (ii) We introduce functionalities to describe nonequilibrium steady states, i.e. time-translationally invariant nonequilibrium states. Such states are relevant for transport settings, and they provide an approximate description of slowly evolving (prethermal) nonequilibrium states.

cond-mat.str-el↗

arXiv2026

Fluctuation engineering in cavity quantum materials

Coupling tailored electromagnetic fluctuations to materials provides a resource for controlling correlated quantum matter. By structuring the frequency, spatial, and modal distribution of fluctuations through a new generation of cavity quantum materials, vacuum and thermal spectra can shift phase boundaries and stabilize or suppress orders. This review organizes the field around a fluctuation-focused perspective, surveying a practical design toolbox and recent milestones, and outlining theory-experiment challenges in realistic, multimode, beyond-long-wavelength regimes. We highlight photonic observables and map opportunities for equilibrium and driven control across superconducting, magnetic, moire, and topological platforms.

cond-mat.mes-hall↗

arXiv2026

Floquet X-Ray Scattering as a Probe of Hidden Electronic Orders

We develop a theoretical framework for Floquet resonant X-ray scattering, using Floquet theory combined with the ultrashort core-hole lifetime expansion. We obtain a compact expression for the Floquet components of the resonant inelastic X-ray scattering operator, which shows that Floquet X-ray scattering provides direct access to bond and current correlations that do not directly produce charge Bragg peaks in conventional diffraction. Applying this framework to charge-ordered states on the Kagome lattice, we demonstrate that different symmetry-breaking orders exhibit distinct polarization fingerprints in the Floquet Bragg peaks. Moreover, the relative weight of bond and current contributions can be tuned through the drive frequency. These results establish Floquet X-ray scattering as a symmetry-resolved probe of hidden electronic order or fluctuations in quantum materials.

cond-mat.str-el↗

arXiv2026

Dynamical instability in a Floquet-Driven Dissipative System

We analyse the magnon spectrum and distribution function of the antiferromagnetic phase of the Floquet-driven Hubbard model. Above a critical drive strength, we find a dynamical instability, resulting from a change in sign of the magnon damping at a non-zero wavevector. The change in sign means that infinitesimal fluctuations grow with time, corresponding to an instability of the driven state. Implications for the nonequilibrium distribution function and the strong drive nonlinear dynamics are discussed.

cond-mat.str-el↗

arXiv2025

Variational Time Evolution Compression for Solving Impurity Models on Quantum Hardware

Dynamical mean-field theory (DMFT) is a useful tool to analyze models of strongly correlated fermions like the Hubbard model. In DMFT, the lattice of the model is replaced by a single impurity site embedded in an effective bath. The resulting single impurity Anderson model (SIAM) can then be solved self-consistently with a quantum-classical hybrid algorithm. This procedure involves repeatedly preparing the ground state on a quantum computer and evolving it in time to measure the Greens function. We here develop an approximation of the time evolution operator for this setting by training a Hamiltonian variational ansatz. The parameters of the ansatz are obtained via a variational quantum algorithm that utilizes a small number of time steps, given by the Suzuki-Trotter expansion of the time evolution operator, to guide the evolution of the parameters. The resulting circuit has a fixed depth for the time evolution depending on the size of the bath and is significantly shallower than a comparable Suzuki-Trotter expansion.

quant-ph↗

arXiv2025

Stochastic resonance in disordered charge-density-wave systems

Ultrafast disordering observed after photo-excitation challenges the conventional picture of photo-induced transitions where symmetry-breaking takes place along a single collective coordinate. We propose that key spectroscopic signatures of these transient disordered states can be revealed through stochastic resonance, a hallmark of nonlinear stochastic dynamics. Studying the disordered phase of Holstein model we show that, at given frequency, the linear response as a function of temperature has a peak, which indicates enhanced coherent switching between metastable configurations. From this resonance, we extract the intrinsic stochastic transition timescale and energy barrier separating equivalent local minima. This mechanism offers a new perspective to identify and characterize hidden disordered phases in driven many-body systems.

cond-mat.str-el↗

arXiv2025

Nonlocal Correlation Effects in dc and Optical Conductivity of the Hubbard Model

Conductivity is one of the most direct probes of electronic systems, yet its theoretical description remains challenging in the presence of strong non-local correlations. In this Letter, we analyze the conductivity of the half-filled single-band Hubbard model and identify the role of spatial correlations across the Mott transition. We show that in the correlated metallic regime, an accurate description of the conductivity requires not only the correct spectral function but also the inclusion of complex multi-electron processes encoded in vertex corrections. The crossover to the Mott insulating regime is marked by a vanishing contribution of vertex corrections to the DC conductivity. However, in the Mott insulating case, vertex corrections remain significant for the optical conductivity.

cond-mat.str-el↗

arXiv2025

Ultrafast Electronic Structure Engineering in 1$T$-TaS$_2$: Role of Doping and Amplitude Mode Dynamics

In strongly correlated transition metal dichalcogenides, an intricate interplay of polaronic distortions, stacking arrangement, and electronic correlations determines the nature of the insulating state. Here, we study the response of the electronic structure to optical excitations to reveal the effect of chemical electron doping on this complex interplay. Transient changes in pristine and electron-doped 1$T$ -TaS$_2$ are measured by femtosecond time-resolved photoelectron spectroscopy and compared to theoretical modeling based on non-equilibrium dynamical mean-field theory and density functional theory. The fine changes in the oscillatory signal of the charge density wave amplitude mode indicate phase-dependent modifications in the Coulomb interaction and the hopping. Furthermore, we find an enhanced fraction of monolayers in the doped system. Our work demonstrates how the combination of time-resolved spectroscopy and advanced theoretical modeling provides insights into the physics of correlated transition metal dichalcogenides.

cond-mat.str-el↗

arXiv2025

Electron-magnon dynamics triggered by an ultrashort laser pulse: A real-time Dual $GW$ study

Ultrafast irradiation of correlated electronic systems triggers complex dynamics involving quasi-particle excitations, doublons, charge carriers, and spin fluctuations. To describe these effects, we develop an efficient non-equilibrium approach, dubbed D-$GW$, that enables a self-consistent treatment of local correlations within dynamical mean-field theory (DMFT) and spatial charge and spin fluctuations, that are accounted for simultaneously within a diagrammatic framework. The method is formulated in the real-time domain and provides direct access to single- and two-particle momentum- and energy-dependent response functions without the need for analytical continuation, which is required in Matsubara frequency-based approaches. We apply the D-$GW$ method to investigate the dynamics of a photo-excited extended Hubbard model, the minimal system that simultaneously hosts strong charge and spin fluctuations. Focusing on the challenging parameter regime near the Mott transition, we demonstrate that correlated metals and narrow-gap Mott insulators undergo distinct thermalization processes involving complex energy transfer between single-particle and collective electronic excitations.

cond-mat.str-el↗

arXiv2025

Tracking the photoinduced dynamics of a dark excitonic state in single-layer WS$_2$ via resonant Autler-Townes splitting

Excitons in a monolayer transition metal dichalcogenide (1L-TMD) are highly bound states characterized by a Rydberg-like spectrum of discrete energy levels. Among these, states with odd-parity are known as dark excitons due to selection rules, which make their stationary and transient characterization challenging using linear optical techniques. Here, we demonstrate that the dynamics of a 2p dark excitonic state in 1L-WS$_2$ can be directly retrieved by measuring the Autler-Townes splitting of bright states in a three-pulse experiment. The splitting of the bright 1s excitonic state, observed by detuning a mid-infrared control field across the 1s-2p transition, provides an accurate characterization of the 2p state. Following carrier photoinjection, we observe a qualitatively different dynamics of the 1s and 2p levels, which is indicative of symmetry-dependent screening and exciton-exciton interactions. These findings provide new insights into many-body effects in TMDs, offering potential avenues for advancing the next generation optoelectronics.

cond-mat.mes-hall↗

arXiv2025

The 2025 Roadmap to Ultrafast Dynamics: Frontiers of Theoretical and Computational Modelling

The exploration of ultrafast phenomena is a frontier of condensed matter research, where the interplay of theory, computation, and experiment is unveiling new opportunities for understanding and engineering quantum materials. With the advent of advanced experimental techniques and computational tools, it has become possible to probe and manipulate nonequilibrium processes at unprecedented temporal and spatial resolutions, providing insights into the dynamical behavior of matter under extreme conditions. These capabilities have the potential to revolutionize fields ranging from optoelectronics and quantum information to catalysis and energy storage. This Roadmap captures the collective progress and vision of leading researchers, addressing challenges and opportunities across key areas of ultrafast science. Contributions in this Roadmap span the development of ab initio methods for time-resolved spectroscopy, the dynamics of driven correlated systems, the engineering of materials in optical cavities, and the adoption of FAIR principles for data sharing and analysis. Together, these efforts highlight the interdisciplinary nature of ultrafast research and its reliance on cutting-edge methodologies, including quantum electrodynamical density-functional theory, correlated electronic structure methods, nonequilibrium Green's function approaches, quantum and ab initio simulations.

cond-mat.mtrl-sci↗

arXiv2025

High order strong-coupling expansion for X-ray absorption on a dynamically screened impurity

Time-resolved X-ray absorption can reveal the dynamical screening of the local Coulomb interaction in strongly correlated photo-excited materials. Here, we focus on the theoretical prediction of X-ray absorption in the presence of dynamical screening using the strong coupling expansion, i.e., an expansion around the isolated absorption site in terms of the retarded interaction. The evaluation of higher order diagrams is made numerically feasible by an approach based on the decomposition of the retarded interaction into complex exponentials. With this, we evaluate the strong coupling series to third order on an electron-boson model of Holstein type. We demonstrate that in relevant coupling regimes, even low orders of the strong coupling expansion can give a significant correction over the previously used lowest order approximation.

cond-mat.str-el↗

arXiv2024

Role of phonon coupling in driving photo-excited Mott insulators towards a transient superconducting steady state

Understanding light-induced hidden orders is relevant for nonequilibrium materials control and future ultrafast technologies. Hidden superconducting order, in particular, has been a focus of recent experimental and theoretical efforts. In this study, we investigate the stability of light-induced $\eta$ pairing. Using a memory truncated implementation of nonequilibrium dynamical mean field theory (DMFT) and entropy cooling techniques, we study the long-time dynamics of the photoinduced superconducting state. In the presence of coupling to a cold phonon bath, the photodoped system reaches a quasi-steady state, which can be sustained over a long period of time in large-gap Mott insulators. We show that this long-lived prethermalized state is well described by the nonequilibrium steady state implementation of DMFT.

cond-mat.str-el↗

arXiv2024

Nonthermal order by disorder

The quench dynamics of systems exhibiting cooperative or almost competitive orders in equilibrium are explored using Ginzburg-Landau theory plus fluctuations. We show that when the renormalization of the free energy by fluctuations is taken into account, anisotropic stiffnesses and relaxation rates of the order parameters can lead to a stabilization of ordered states at transient free energy minima which are distinct from any (global or local) minima of the equilibrium free energy. This theory demonstrates that nonequilibrium fluctuations play a pivotal role in forming nonthermal orders. As nonthermal order and nonthermal fluctuations mutually stabilize each other over some time, this mechanism could be seen as a nonequilibrium variant of the order-by-disorder phenomenon. We discuss the potential relevance of these findings for systems with intertwined orders, such as superconductivity and density wave orders, relevant for high-temperature superconductors and the kagome metals, as well as for systems that show orbital ordering.

cond-mat.str-el↗

arXiv2024

Solving quantum impurity models in the non-equilibrium steady state with tensor trains

We discuss the evaluation of the integrals for intermediate-order diagrams in the self-consistent strong-coupling expansion on the Keldysh contour using Tensor Cross Interpolation (TCI). TCI is used to factorize the nested parts of the integrand, allowing the integral to be computed as a recursion of convolution integrals, which are efficiently evaluated using the Fast Fourier Transform. The evaluation of diagrams where all vertices lie on one branch of the Keldysh contour resembles the structure of the imaginary-time formalism. For diagrams with time arguments on both contour branches, we find that it can be advantageous to parametrize the integrals in terms of physical time arguments with an additional sum over Keldysh indices. We benchmark the solution in relevant test cases, including the single impurity Anderson model and an exactly solvable electron-boson model. While the bond dimension increases with diagram order, the TCI-based integration efficiently handles low-order diagrams, making it a promising approach to go beyond the non-crossing approximation in steady-state non-equilibrium dynamical mean-field theory simulations.

cond-mat.str-el↗