arXiv subjects

Martin Eckstein

Publications and source records attributed to Martin Eckstein.

At least 55 records · Page 3Linked to original sources

arXiv2022

Ultrafast control of spin-orbital separation probed with time-resolved RIXS

Quasi-one-dimensional systems exhibit many-body effects elusive in higher dimensions. A prime example is spin-orbital separation, which has been measured by resonant inelastic X-ray scattering (RIXS) in Sr$_2$CuO$_3$. Here, we theoretically analyze the time-resolved RIXS spectrum of Sr$_2$CuO$_3$ under the action of a time-dependent electric field. We show that the external field can reversibly modify the parameters in the effective $t-J$ model used to describe spinon and orbiton dynamics in the material. For strong driving amplitudes, we find that the spectrum changes qualitatively as a result of reversing the relative spinon to orbiton velocity. The analysis shows that in general, the spin-orbital dynamics in Mott insulators in combination with time-resolved RIXS should provide a suitable platform to explore the reversible control of many-body physics in the solid with strong laser fields.

cond-mat.str-el↗

arXiv2022

Time-resolved photoemission and RIXS study of a site-selective Mott insulator

Inspired by the physics of rare earth nickelates, we study the photoemission (PES) and resonant inelastic X-ray scattering (RIXS) spectra of a correlated electron system with two types of insulating sublattices. Sublattice A is characterized by a hybridization gap and a low-spin state, while sublattice B features a Mott gap and a local magnetic moment. We show how the coupling of these two qualitatively different insulating states affects the dynamics of photo-induced charge carriers and how the nonequilibrium states manifest themselves in the PES and RIXS signals. In particular, we find that charge carriers created on the B sublattice migrate to the A sublattice, where they contribute to the creation of in-gap states in the PES signal, and to characteristic peaks in the nonequilibrium RIXS spectrum. While the contributions from the two sublattices cannot be easily distinguished in the local photoemission spectrum, the weights of the RIXS signals in the two-dimensional $ω_\text{in}$-$ω_\text{out}$ space provide information on the local state evolution on both sublattices.

cond-mat.str-el↗

arXiv2022

Pseudoparticle vertex solver for quantum impurity models

We present a quantum impurity solver based on a pseudo-particle framework, which combines diagrammatic resummations for a three-point vertex with diagrammatic Monte Carlo sampling of a four-point vertex. This recently proposed approach [A. J. Kim et al., arXiv:2112.15549] is generalized here to fermionic impurity problems and we discuss the technical details of the implementation, including the time-stepping approach, the Monte Carlo updates, and the routines for checking the two-particle irreducibility of the four-point vertex. We also explain how the vertex information can be efficiently stored using a Dubiner basis representation. The convergence properties of the algorithm are demonstrated with applications to exactly solvable impurity models and dynamical mean field theory simulations of the single-orbital Hubbard model. It is furthermore shown that the algorithm can handle a two-orbital problem with off-diagonal hybridizations, which would cause a severe sign problem in standard hybridization-expansion Monte Carlo simulations. Since the vertex-based algorithm successfully handles sign oscillating integrals in equilibrium and samples only connected diagrams, it may be a promising approach for real-time simulations.

cond-mat.str-el↗

arXiv2022

Collective theory for an interacting solid in a single-mode cavity

We investigate the control of interacting matter through strong coupling to a single electromagnetic mode, such as the photon mode in a Fabry-Perot or split-ring cavity. For this purpose, we analyze the exact effective theory for the collective light-matter hybrid modes of a generic system of $N$ transition dipoles within an interacting solid. The approach allows to predict properties of the coupled light-matter system from the nonlinear response functions of the uncoupled matter ``outside the cavity''. The limit of large $N$ corresponds to a conventional macroscopic description based on the polarizability of matter. In this limit, the cavity does not affect the static ferroelectric response. Corrections, which are needed to understand finite size systems and to obtain the nonlinear light-matter response, can be obtained from the non-linear susceptibilities of the matter outside the cavity. The theory is benchmarked for the Dicke model, and for a quantum Ising model which serves as a minimal mean-field model for a quantum paraelectric material like SrTiO3.

cond-mat.str-el↗

arXiv2022

Effective theory of lattice electrons strongly coupled to quantum electromagnetic fields

Recent experiments have revealed the tantalizing possibility of fabricating lattice electronic systems strongly coupled to quantum fluctuations of electromagnetic fields, e.g., by means of geometry confinement from a cavity or artificial gauge fields in quantum simulators. In this work, we develop a high-frequency expansion to construct the effective models for lattice electrons strongly coupled to a continuum of off-resonant photon modes with arbitrary dispersion. The theory is nonperturbative in the light-matter coupling strength, and is therefore particularly suitable for the ultrastrong light-matter coupling regime. Using the effective models, we demonstrate how the dispersion and topology of the electronic energy bands can be tuned by the cavity. In particular, quasi-one-dimensional physics can emerge in a two-dimensional square lattice due to a spatially anisotropic band renormalization, and a topologically nontrivial anomalous quantum Hall state can be induced in a honeycomb lattice when the cavity setup breaks time-reversal symmetry. We also demonstrate that the photon-mediated interaction induces an unconventional superconducting paired phase distinct from the pair-density-wave state discussed in models with truncated light-matter coupling. Finally, we study a realistic setup of a Fabry-Pérot cavity. Our work provides a systematic framework to explore the emergent phenomena due to strong light-matter coupling and points out new directions of engineering orders and topological states in solids.

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arXiv2022

Entropy-cooled nonequilibrium states of the Hubbard model

We show that the recently proposed cooling-by-doping mechanism allows to efficiently prepare interesting nonequilibrium states of the Hubbard model. Using nonequilibrium dynamical mean field theory and a particle-hole symmetric setup with dipolar excitations to full and empty bands we produce cold photo-doped Mott insulating states with a sharp Drude peak in the optical conductivity, a superconducting state in the repulsive Hubbard model with an inverted population, and $η$-paired states in systems with a large density of doublons and holons. The reshuffling of entropy into full and empty bands not only provides an efficient cooling mechanism, it also allows to overcome thermalization bottlenecks and slow dynamics that have been observed in systems cooled by the coupling to boson baths.

cond-mat.str-el↗

arXiv2022

Local interpretation of time-resolved X-ray absorption in Mott insulators: Insights from nonequilibrium dynamical mean-field theory

We present a formalism based on nonequilibrium dynamical mean field theory (DMFT) which allows to compute the time-resolved X-ray absorption spectrum (XAS) of photo-excited solids. By applying this formalism to the photo-doped half-filled and quarter-filled two-orbital Hubbard models in the Mott insulating regime we clarify how the time-resolved XAS signal reflects the nonequilibrium population of different local states. Apart from the missing broadening associated with continuum excitations, the atomic XAS spectrum computed with the nonthermal state populations provides a good approximation to the full nonequilibrium DMFT result. This suggest a route to combine the accurate DMFT description of nonequilibrum states of solids with cluster calculations of the XAS signal.

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arXiv2022

Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments

We overview the concept of dynamical phase transitions in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal behaviour on the two sides of a certain dynamical critical point. Dynamical phase transitions are currently mostly understood as long-lived prethermal phenomena in a regime where inelastic collisions are incapable to thermalize the system. The latter enables the dynamics to substain phases that explicitly break detailed balance and therefore cannot be encompassed by traditional thermodynamics. Our presentation covers both cold atoms as well as condensed matter systems. We revisit a broad plethora of platforms exhibiting pre-thermal DPTs, which become theoretically tractable in a certain limit, such as for a large number of particles, large number of order parameter components, or large spatial dimension. The systems we explore include, among others, quantum magnets with collective interactions, $ϕ^4$ quantum field theories, and Fermi-Hubbard models. A section dedicated to experimental explorations of DPTs in condensed matter and AMO systems connects this large variety of theoretical models.

cond-mat.stat-mech↗

arXiv2021

Vertex-based Diagrammatic Treatment of Light-Matter-Coupled Systems

We propose a diagrammatic Monte Carlo approach for general spin-boson models, which can be regarded as a generalization of the strong-coupling expansion for fermionic impurity models. The algorithm is based on a self-consistently computed three-point vertex and a stochastically sampled four-point vertex, and achieves convergence to the numerically exact result in a wide parameter regime. The performance of the algorithm is demonstrated with applications to a spin-boson model representing an emitter in a waveguide. As a function of the coupling strength, the spin exhibits a delocalization-localization crossover at low temperatures, signaling a qualitative change in the real-time relaxation. In certain parameter regimes, the response functions of the emitter coupled to the electromagnetic continuum can be described by an effective Rabi model with appropriately defined parameters. We also discuss the spatial distribution of the photon density around the emitter.

cond-mat.str-el↗

arXiv2021

Non-equilibrium evolution of the optical conductivity of the weakly interacting Hubbard model: Drude response and $π$-ton type vertex corrections

The optical conductivity contains information about energy absorption and the underlying physical processes. In finite-dimensional systems, vertex corrections to the bare bubble need to be considered, which is a computationally challenging task. Recent numerical studies showed that in the weak coupling limit, near an ordering instability with wave vector $π$, $π$-tons (or Maki-Thompson diagrams) yield the most relevant vertex corrections. This provides a route for including vertex corrections into, for example, dynamical mean field theory estimates of the optical conductivity. By implementing calculations on the Kadanoff-Baym contour, we reveal the characteristic spectral signatures of the $π$-tons and their evolution under non-equilibrium conditions. We consider interaction quenches of the weakly-correlated Hubbard model near the antiferromagnetic phase boundary, and analyze the evolution of the Drude and $π$-ton features. While the bubble contribution to the optical conductivity is found to thermalize rapidly, after some oscillations with frequencies related to the local spectral function, the $π$-ton contribution exhibits a slower evolution. We link this observation to the prethermalization phenomenon which has been previously studied in weakly interacting, quenched Hubbard models.

cond-mat.str-el↗

arXiv2021

Memory truncated Kadanoff-Baym equations

The Keldysh formalism for nonequilibrium Green's functions is a powerful theoretical framework for the description of the electronic structure, spectroscopy, and dynamics of strongly correlated systems. However, the underlying Kadanoff-Baym equations (KBE) for the two-time Keldysh Green's functions involve a memory kernel which results in a high computational cost for long simulation times $t_\text{max}$, with a cubic scaling of the computation time with $t_\text{max}$. Truncation of the memory kernel can reduce the computational cost to linear scaling with $t_\text{max}$, but the required memory times will depend on the model and the diagrammatic approximation to the self-energy. We explain how a truncation of the memory kernel can be incorporated into the time-propagation algorithm to solve the KBE, and investigate the systematic truncation of the memory kernel for the Hubbard model in different parameter regimes, and for different diagrammatic approximations. The truncation is easier to control within dynamical mean-field solutions, where it is applied to a momentum-independent self-energy. Here, simulation times up to two orders of magnitude longer are accessible both in the weak and strong coupling regime, allowing for a study of long-time phenomena such as the crossover between pre-thermalization and thermalization dynamics.

cond-mat.str-el↗

arXiv2021

Nonequilibrium RIXS study of an electron-phonon model

We use the nonequilibrium dynamical mean field theory formalism to compute the equilibrium and nonequilibrium resonant inelastic X-ray scattering (RIXS) signal of a strongly interacting fermionic lattice model with a coupling of dispersionless phonons to the total charge on a given site. In the atomic limit, this model produces phonon subbands in the spectral function, but not in the RIXS signal. Electron hopping processes however result in phonon-related modifications of the charge excitation peak. We discuss the equilibrium RIXS spectra and the characteristic features of nonequilibrium states induced by photo-doping and by the application of a static electric field. The latter produces features related to Wannier-Stark states, which are dressed with phonon sidebands. Thanks to the effect of field-induced localization, the phonon features can be clearly resolved even in systems with weak electron-phonon coupling.

cond-mat.str-el↗

arXiv2021

Ultrafast metal-to-insulator switching in a strongly correlated system

Light-manipulation of correlated electronic phases in solids offers the tantalizing prospect of realizing electronic devices operating at the ultrafast time-scale. In this context, the experimental realization of non-equilibrium transitions from a metal to a band or Mott insulator has shown to be particularly elusive. Using dynamical mean-field theory, we study a simple model representing the main physical properties of the oxygen-enriched compound LaTiO$_{3+x}$. By properly optimizing the photo-doping of electrons from a low-energy band into the valence states of the system, we show it is possible to induce a valence transition from a correlated metallic state to a Mott insulator at ultrashort time scales and to contain the heating during this process, with the final non-thermal valence insulator having almost the same effective temperature of the starting metal.

cond-mat.str-el↗

arXiv2021

Fluctuation control of non-thermal orbital order

Orbitally ordered states exhibit unique features which make them a promising platform for exploring the ultrafast dynamics of long-range order in solids: Their free energy typically has multiple discrete minima, and electric laser fields or selectively excited phonons can exert effective forces that may be used to steer the order parameter through these free energy landscapes. Moreover, their free energy strongly depends on fluctuations, and in some cases restoring forces close to a minimum are exclusively of entropic origin (order-by-disorder mechanisms). This can open pathways to control the dynamics of the order parameter via non-thermal fluctuations. In this work, we study the laser-induced non-equilibrium dynamics in a $120^\circ$ compass model, using time-dependent Ginzburg-Landau theory. We analyze protocols to switch the order parameter between equivalent configurations, with a focus on the interplay between the external force due to the driving field, and the non-thermal entropic forces. In particular, we find that remanent non-thermal fluctuations after some excitation can stabilize the high-symmetry phase even when the homogeneous potential has retrieved its low-temperature form, which facilitates laser-induced switching.

cond-mat.str-el↗

arXiv2021

Ultrafast Mott transition driven by nonlinear electron-phonon interaction

Nonlinear phononics holds the promise for controlling properties of quantum materials on the ultrashort timescale. Using nonequilibrium dynamical mean-field theory, we solve a model for the description of organic solids, where correlated electrons couple nonlinearly to a quantum phonon mode. Unlike previous works, we exactly diagonalize the local phonon mode within the noncrossing approximation to include the full phononic fluctuations. By exciting the local phonon in a broad range of frequencies near resonance with an ultrashort pulse, we show it is possible to induce a Mott insulator-to-metal phase transition. Conventional semiclassical and mean-field calculations, where the electron-phonon interaction decouples, underestimate the onset of the quasiparticle peak. This fact, together with the nonthermal character of the photoinduced metal, suggests a leading role of the phononic fluctuations and of the dynamic nature of the state in the vibrationally induced quasiparticle coherence.

cond-mat.str-el↗

arXiv2021

A quantum Boltzmann equation for strongly correlated electrons

Collective orders and photo-induced phase transitions in quantum matter can evolve on timescales which are orders of magnitude slower than the femtosecond processes related to electronic motion in the solid. Quantum Boltzmann equations can potentially resolve this separation of timescales, but are often constructed within a perturbative framework. Here we derive a quantum Boltzmann equation which only assumes a separation of timescales (taken into account through the gradient approximation for convolutions in time), but is based on a non-perturbative scattering integral, and makes no assumption on the spectral function such as the quasiparticle approximation. In particular, a scattering integral corresponding to non-equilibrium dynamical mean-field theory is evaluated in terms of an Anderson impurity model in a non-equilibrium steady state with prescribed distribution functions. This opens the possibility to investigate dynamical processes in correlated solids with quantum impurity solvers designed for the study of non-equilibrium steady states.

cond-mat.str-el↗

arXiv2020

Simulation of time-dependent resonant inelastic X-ray scattering using non-equilibrium dynamical mean-field theory

We develop a framework to evaluate the time-dependent resonant inelastic X-ray scattering (RIXS) signal with the use of non-equilibrium dynamical mean field theory simulations. The approach is based on the solution of a time-dependent impurity model which explicitly incorporates the probe pulse. It avoids the need to compute four-point correlation functions, and can in principle be combined with different impurity solvers. This opens a path to study time-resolved RIXS processes in multi-orbital systems. The approach is exemplified with a study of the RIXS signal of a melting Mott antiferromagnet.

cond-mat.str-el↗

arXiv2020

Nonequilibrium-DMFT based RIXS investigation of the two-orbital Hubbard model

Resonant inelastic X-ray scattering (RIXS) detects various types of high- and low-energy elementary excitations in correlated solids, and this tool will play an increasingly important role in investigations of time-dependent phenomena in photo-excited systems. While theoretical frameworks for the computation of equilibrium RIXS spectra are well established, the development of appropriate methods for nonequilibrium simulations are an active research field. Here, we apply a recently developed nonequilibrium dynamical mean field theory (DMFT) based approach to compute the RIXS response of photo-excited two-orbital Mott insulators. The results demonstrate the feasibility of multi-orbital nonequilibrium RIXS calculations and the sensitivity of the quasi-elastic fluorescence-like features and d-d excitation peaks on the nonequilibrium population of the Hubbard bands.

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