arXiv subjects

Veljko Janković

Publications and source records attributed to Veljko Janković.

17 recordsLinked to original sources

arXiv2026

Applicability of the cumulant expansion method for the calculation of transport properties in electron-phonon systems

We assess the accuracy of the cumulant expansion (CE) method, combined with the independent-particle approximation (IPA), for calculating charge mobility in electron-phonon systems. As representative testbeds, we consider the Peierls and Fröhlich models, which serve as simplified frameworks where accurate or numerically exact benchmarks are available. These are used to compare the CE results with those obtained using the Boltzmann formalism, the Migdal approximation, and its self consistent extension-approaches that are presently the most commonly employed alternatives for transport calculations. Supported by analytical arguments based on spectral sum rules and by our previous results for the Holstein model, we argue that, for weak to moderate coupling strengths and not-too-low temperatures, the CE within the IPA framework yields accurate results. In the case of the Peierls model, the role of vertex corrections is also discussed.

cond-mat.str-el↗

arXiv2025

Numerically "exact" charge transport dynamics in a dissipative electron-phonon model rationalizing the success of the transient localization scenario

Optical conductivity in molecular semiconductors is suppressed in the terahertz region, featuring the displaced Drude peak that reflects carriers' transient localization (TL) by slow intermolecular vibrations. Meanwhile, recent computations in minimal models evidence optical-conductivity enhancements below the characteristic vibrational frequency, which cannot be captured by the TL phenomenology. These models assume that the carrier's hopping amplitude is modulated by a single undamped vibration. The modulation is, however, by many low-frequency modes, whose net effect can be approximated using a few effective damped oscillators. Here, we employ the dissipaton equations of motion (DEOM) method to compute the finite-temperature real-time current autocorrelation function in a one-dimensional model with Brownian-oscillator spectral density of nonlocal carrier-phonon interaction. We exploit the dissipaton algebra to handle the phonon-assisted current, reduce the method's computational requirements by working in momentum space, and confirm that numerically stable transport dynamics are virtually independent of a specific DEOM closing scheme. With increasing damping, we find that DEOM optical-conductivity profiles become increasingly qualitatively similar to TL predictions. For parameters representative of room-temperature hole transport in single-crystal rubrene, we conclude that the TL phenomenology is established already in the underdamped-oscillator regime. Reasonable variations in the damping constant weakly affect the carrier mobility, which remains within experimental bounds. Overall, our results strongly suggest that optical-conductivity enhancements at very low frequencies are artifacts of the assumed delta-like phonon spectrum and rationalize the success of the TL phenomenology in describing experimental data.

physics.chem-ph↗

arXiv2025

Charge transport limited by nonlocal electron-phonon interaction. II. Numerically exact quantum dynamics in the slow-phonon regime

Transport of charge carriers in mechanically soft semiconductors is mainly limited by their interaction with slow intermolecular phonons. Carrier motion exhibits a crossover from superdiffusive to subdiffusive, producing a distinct low-frequency peak in the dynamical-mobility profile. These features can be understood within approaches relying on the timescale separation between carrier and phonon dynamics, such as the transient localization scenario (TLS). However, recovering them from fully quantum dynamics has proved elusive. Using the hierarchical equations of motion (HEOM)-based approach exposed in a companion paper (arXiv:2501.05054), we study carrier transport in the one-dimensional Peierls model near the adiabatic limit. We find that the TLS approximates HEOM dynamics very well at higher temperatures and for stronger interactions. Then, the transport is predominantly phonon-assisted, and turns diffusive from the subdiffusive side well before one phonon period. In contrast, the band current dominates at moderate temperatures and interactions, relevant for transport in realistic materials. We then conclude that the super-to-subdiffusive crossover is transient, so that the diffusive motion sets in from the superdiffusive side on timescales comparable to the phonon period. The low-frequency dynamical mobility then additionally exhibits a dip at approximately one phonon frequency, and the zero-frequency peak. Our findings in this moderate regime show limitations of the TLS, and support the results of the most advanced quantum--classical simulations. We expect that the qualitative differences between HEOM and TLS dynamics would diminish for a more realistic phonon density of states.

cond-mat.str-el↗

arXiv2025

Charge transport limited by nonlocal electron-phonon interaction. I. Hierarchical equations of motion approach

Studying charge transport in models with nonlocal carrier--phonon interaction is difficult because it requires finite-temperature real-time correlation functions of mixed carrier--phonon operators. Focusing on models with discrete undamped phonon modes, we show that such correlation functions can be retrieved from the hierarchical equations of motion (HEOM), although phonons have been integrated out. Our procedure relies on the general explicit expression of HEOM auxiliaries in terms of phonon creation and annihilation operators. It reveals that the auxiliaries describe multiphonon-assisted carrier transitions induced by genuine many-phonon correlations, from which lower-order correlations are subtracted according to the finite-temperature Wick's theorem. Applying the procedure to our recently developed momentum-space HEOM method featuring appropriate hierarchy closing, we compute the numerically exact dynamical mobility of a carrier within the one-dimensional Peierls model. The carrier mobility at moderate temperatures decreases with increasing interaction, whereas high temperatures see the opposite trend, reflecting the prevalence of the phonon-assisted current over the purely electronic band current. The pronounced finite-size effects and HEOM instabilities delimit the range of applicability of our approach to moderate interactions, moderate to high temperatures, and not too fast phonons. Importantly, this range comprises the values relevant for charge transport in crystalline organic semiconductors, and we present and discuss the corresponding numerically exact results in a companion paper (arXiv:2501.05055).

cond-mat.str-el↗

arXiv2024

Self-consistent approach to the dynamics of excitation energy transfer in multichromophoric systems

Computationally tractable and reliable, albeit approximate, methods for studying exciton transport in molecular aggregates immersed in structured bosonic environments have been actively developed. Going beyond the lowest-order (Born) approximation for the memory kernel of the quantum master equation typically results in complicated and possibly divergent expressions. Starting from the memory kernel in the Born approximation, and recognizing the quantum master equation as the Dyson equation of Green's functions theory, we formulate the self-consistent Born approximation to resum the memory-kernel perturbation series in powers of the exciton--environment interaction. Our formulation is in the Liouville space and frequency domain and handles arbitrary exciton--environment spectral densities. In a molecular dimer coupled to an overdamped oscillator environment, we conclude that the self-consistent cycle significantly improves the Born-approximation energy-transfer dynamics. The dynamics in the self-consistent Born approximation agree well with the solutions of hierarchical equations of motion over a wide range of parameters, including the most challenging regimes of strong exciton--environment interactions, slow environments, and low temperatures. This is rationalized by the analytical considerations of coherence-dephasing dynamics in the pure-dephasing model. We find that the self-consistent Born approximation is good (poor) at describing energy transfer modulated by an underdamped vibration resonant (off-resonant) with the exciton energy gap. Nevertheless, it reasonably describes exciton dynamics in the seven-site model of the Fenna--Matthews--Olson complex in a realistic environment comprising both an overdamped continuum and underdamped vibrations.

physics.chem-ph↗

arXiv2024

Vertex corrections to conductivity in the Holstein model: A numerical-analytical study

The optical-conductivity profile carries information on electronic dynamics in interacting quantum many-body systems. Its computation is a formidable task that is usually approached by invoking the single-particle (bubble) approximation and neglecting the vertex corrections, the importance of which remains elusive even in model Hamiltonian calculations. Here, we combine analytical arguments with our recent breakthroughs in numerically exact and approximate calculations of finite-temperature real-time correlation functions to thoroughly assess the importance of vertex corrections in the one-dimensional Holstein polaron model. We find, both analytically and numerically, vanishing vertex corrections to optical conductivity in the limits of zero electron--phonon interaction, zero electronic bandwidth, and infinite temperature. Furthermore, our numerical results show that vertex corrections to the electron mobility also vanish in many parameter regimes between these limits. In some of these cases, the vertex corrections still introduce important qualitative changes to the optical-conductivity profile in comparison to the bubble approximation even though the self-energy remains approximately local. We trace these changes back to the bubble approximation not fully capturing a time-limited slow-down of the electron on intermediate time scales between ballistic and diffusive transport. We find that the vertex corrections are overall most pronounced for intermediate electron--phonon interaction and may increase or decrease the bubble-approximation mobility depending on the values of model parameters.

cond-mat.str-el↗

arXiv2023

Holstein polaron transport from numerically "exact" real-time quantum dynamics simulations

Numerically "exact" methods addressing the dynamics of coupled electron--phonon systems have been intensively developed. Nevertheless, the corresponding results for the electron mobility $μ_\mathrm{dc}$ are scarce, even for the one-dimensional (1d) Holstein model. Building on our recent progress on single-particle properties, here, we develop the momentum-space hierarchical equations of motion (HEOM) method to evaluate real-time two-particle correlation functions of the 1d Holstein model at finite temperature. We compute numerically "exact" dynamics of the current--current correlation function up to real times sufficiently long to capture the electron's diffusive motion and provide reliable results for $μ_\mathrm{dc}$ in a wide range of model parameters. In contrast to the smooth ballistic-to-diffusive crossover in the weak-coupling regime, we observe a temporally limited slow-down of the electron on intermediate time scales already in the intermediate-coupling regime, which translates to a finite-frequency peak in the optical response. Our momentum-space formulation lowers the numerical effort with respect to existing HEOM-method implementations, while we remove the numerical instabilities inherent to the undamped-mode HEOM by devising an appropriate hierarchy closing scheme. Still, our HEOM remains unstable at too low temperatures, for too strong electron--phonon coupling, and for too fast phonons.

cond-mat.str-el↗

arXiv2023

Cumulant expansion in the Holstein model: Spectral functions and mobility

We examine the range of validity of the second-order cumulant expansion (CE) for the calculation of spectral functions, quasiparticle properties, and mobility of the Holstein polaron. We devise an efficient numerical implementation that allows us to make comparisons in a broad interval of temperature, electron-phonon coupling, and phonon frequency. For a benchmark, we use the dynamical mean-field theory (DMFT) which gives, as we have recently shown, rather accurate spectral functions in the whole parameter space, even in low dimensions. We find that in one dimension, the CE resolves well both the quasiparticle and the first satellite peak in a regime of intermediate coupling. At high temperatures, the charge mobility assumes a power law $μ\propto T^{-2}$ in the limit of weak coupling and $μ\propto T^{-3/2}$ for stronger coupling. We find that, for stronger coupling, the CE gives slightly better results than the self-consistent Migdal approximation (SCMA), while the one-shot Migdal approximation is appropriate only for a very weak electron-phonon interaction. We also analyze the atomic limit and the spectral sum rules. We derive an analytical expression for the moments in CE and find that they are exact up to the fourth order, as opposed to the SCMA where they are exact to the third order. Finally, we analyze the results in higher dimensions.

cond-mat.str-el↗

arXiv2023

Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice

Ultracold-atom simulations of the Hubbard model provide insights into the character of charge and spin correlations in and out of equilibrium. The corresponding numerical simulations, on the other hand, remain a significant challenge. We build on recent progress in the quantum Monte Carlo (QMC) simulation of electrons in continuous space, and apply similar ideas to the square-lattice Hubbard model. We devise and benchmark two discrete-time QMC methods, namely the fermionic-propagator QMC (FPQMC) and the alternating-basis QMC (ABQMC). In FPQMC, the time evolution is represented by snapshots in real space, whereas the snapshots in ABQMC alternate between real and reciprocal space. The methods may be applied to study equilibrium properties within grand-canonical or canonical ensemble, external field quenches, and even the evolution of pure states. Various real-space/reciprocal-space correlation functions are also within their reach. Both methods deal with matrices of size equal to the number of particles (thus independent of the number of orbitals or time slices), which allows for cheap updates. We benchmark the methods in relevant setups. In equilibrium, the FPQMC method is found to have excellent average sign and, in some cases, yields correct results even with poor imaginary-time discretization. ABQMC has significantly worse average sign, but also produces good results. Out of equilibrium, FPQMC suffers from a strong dynamical sign problem. On the contrary, in ABQMC, the sign problem is not time dependent. Using ABQMC, we compute survival probabilities for several experimentally relevant pure states.

cond-mat.str-el↗

arXiv2022

Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions

It is generally accepted that the dynamical mean field theory gives a good solution of the Holstein model, but only in dimensions greater than two. Here, we show that this theory, which becomes exact in the weak coupling and in the atomic limit, provides an excellent, numerically cheap, approximate solution for the spectral function of the Holstein model in the whole range of parameters, even in one dimension. To establish this, we make a detailed comparison with the spectral functions that we obtain using the newly developed momentum-space numerically exact hierarchical equations of motion method, which yields electronic correlation functions directly in real time. We crosscheck these conclusions with our path integral quantum Monte Carlo and exact diagonalization results, as well as with the available numerically exact results from the literature.

cond-mat.str-el↗

arXiv2022

Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach

We develop a hierarchical equations of motion (HEOM) approach to compute real-time single-particle correlation functions and thermodynamic properties of the Holstein model at finite temperature. We exploit the conservation of the total momentum of the system to formulate the momentum-space HEOM whose dynamical variables explicitly keep track of momentum exchanges between the electron and phonons. Our symmetry-adapted HEOM enable us to overcome the numerical instabilities inherent to the commonly used real-space HEOM. The HEOM method is then used to study the spectral function and thermodynamic quantities of chains containing up to ten sites. The HEOM results compare favorably to existing literature. To provide an independent assessment of the HEOM approach and to gain insight into the importance of finite-size effects, we devise a quantum Monte Carlo (QMC) procedure to evaluate finite-temperature single-particle correlation functions in imaginary time and apply it to chains containing up to twenty sites. QMC results reveal that finite-size effects are quite weak, so that the results on 5 to 10-site chains, depending on the parameter regime, are representative of larger systems. A detailed comparison between the HEOM and QMC data place our HEOM method among reliable methods to compute real-time finite-temperature correlation functions in parameter regimes ranging from low- to high-temperature, and weak- to strong-coupling regime.

cond-mat.str-el↗

arXiv2020

Exact description of excitonic dynamics in molecular aggregates weakly driven by light

We present a rigorous theoretical description of excitonic dynamics in molecular light-harvesting aggregates photoexcited by weak-intensity radiation of arbitrary properties. While the interaction with light is included up to the second order, the treatment of the excitation-environment coupling is exact and results in an exact expression for the reduced excitonic density matrix that is manifestly related to the spectroscopic picture of the photoexcitation process. This expression takes fully into account the environmental reorganization processes triggered by the two interactions with light. This is particularly important for slow environments and/or strong excitation-environment coupling. Within the exponential decomposition scheme, we demonstrate how our result can be recast as the hierarchy of equations of motion (HEOM) that explicitly and consistently includes the photoexcitation step. We analytically describe the environmental reorganization dynamics triggered by a delta-like excitation of a single chromophore, and demonstrate how our HEOM, in appropriate limits, reduces to the Redfield equations comprising a pulsed photoexcitation and the nonequilibrium Foerster theory. We also discuss the relation of our formalism to the combined Born-Markov-HEOM approaches in the case of excitation by thermal light.

physics.chem-ph↗

arXiv2020

Nonequilibrium steady-state picture of incoherent light-induced excitation harvesting

We formulate a comprehensive theoretical description of excitation harvesting in molecular aggregates photoexcited by weak incoherent radiation. An efficient numerical scheme that respects the continuity equation for excitation fluxes is developed to compute the nonequilibrium steady state (NESS) arising from the interplay between excitation generation, excitation relaxation, dephasing, trapping at the load, and recombination. The NESS is most conveniently described in the so-called preferred basis in which the steady-state excitonic density matrix is diagonal. The NESS properties are examined by relating the preferred-basis description to the descriptions in the site or excitonic bases. Focusing on a model photosynthetic dimer, we find that the NESS in the limit of long trapping time is quite similar to the excited-state equilibrium in which the stationary coherences originate from the excitation-environment entanglement. For shorter trapping times, we demonstrate how the properties of the NESS can be extracted from the time-dependent description of an incoherently driven but unloaded dimer. This relation between stationary and time-dependent pictures is valid, provided that the trapping time is longer than the decay time of dynamic coherences accessible in femtosecond spectroscopy experiments.

physics.chem-ph↗

arXiv2017

Identification of Ultrafast Photophysical Pathways in Photoexcited Organic Heterojunctions

The exciton dissociation and charge separation occurring on subpicosecond time scales following the photoexcitation are studied in a model donor/acceptor heterojunction using a fully quantum approach. Higher-than-LUMO acceptor orbitals which are energetically aligned with the donor LUMO orbital participate in the ultrafast interfacial dynamics by creating photon-absorbing charge-bridging states in which charges are spatially separated and which can be directly photoexcited. Along with the states brought about by single-particle resonances, the two-particle (exciton) mixing gives rise to bridge states in which charges are delocalized. Bridge states open up a number of photophysical pathways that indirectly connect the initial donor states with states of spatially separated charges and compete with the efficient progressive deexcitation within the manifold of donor states. The diversity and efficiency of these photophysical pathways depend on a number of factors, such as the precise energy alignment of exciton states, the central frequency of the excitation, and the strength of carrier-phonon interaction.

physics.chem-ph↗

arXiv2017

Origin of space-separated charges in photoexcited organic heterojunctions on ultrafast time scales

We present a detailed investigation of ultrafast (subpicosecond) exciton dynamics in the lattice model of a donor/acceptor heterojunction. Exciton generation by means of a photoexcitation, exciton dissociation, and further charge separation are treated on equal footing. The experimentally observed presence of space-separated charges at $\lesssim 100$ fs after the photoexcitation is usually attributed to ultrafast transitions from excitons in the donor to charge transfer and charge separated states. Here, we show, however, that the space-separated charges appearing on $\lesssim 100$-fs time scales are predominantly directly optically generated. Our theoretical insights into the ultrafast pump-probe spectroscopy challenge usual interpretations of pump-probe spectra in terms of ultrafast population transfer from donor excitons to space-separated charges.

cond-mat.mes-hall↗

arXiv2015

Dynamics of exciton formation and relaxation in photoexcited semiconductors

We investigate the dynamics of the exciton formation and relaxation on a picosecond time scale following a pulsed photoexcitation of a semiconductor. The study is conducted in the framework of the density matrix theory complemented with the dynamics controlled truncation scheme. We truncate the phonon branch of the resulting hierarchy of equations and propose the form of coupling among single-phonon-assisted and higher-order phonon-assisted density matrices so as to ensure the energy and particle-number conservation in a closed system. Time scales relevant for the exciton formation and relaxation processes are determined from numerical investigations performed on a one-dimensional model for the values of model parameters representative of a typical organic and inorganic semiconductor. The exciton dynamics is examined for different values of central frequency of the exciting field, temperature, and microscopic model parameters, such as the strengths of carrier-carrier and carrier-phonon couplings. We find that for typical organic semiconductor parameters, formation of bound excitons occurs on a several-hundred-femtosecond time scale, while their subsequent relaxation and equilibration takes at least several picoseconds. These time scales are consistent with recent experimental studies of the exciton formation and relaxation in conjugated polymer-based materials.

cond-mat.mes-hall↗

arXiv2014

Non-equilibrium Optical Conductivity in Materials with Localized Electronic States

A wide range of disordered materials contain electronic states that are spatially well localized. In this work, we investigated the electrical response of such systems in non-equilibrium conditions to external electromagnetic field. We obtained the expression for optical conductivity valid for any non-equilibrium state of electronic subsystem. In the case of incoherent non-equilibrium state, this expression contains only the positions of localized electronic states, Fermi's golden rule transition probabilities between the states and the populations of electronic states. The same form of expression is valid both in the case of weak electron-phonon interaction and weak electron-impurity interaction that act as perturbations of electronic Hamiltonian. The derivation was performed by expanding the general expression for AC conductivity in powers of small electron-phonon interaction or electron-impurity interaction parameter. Applications of the expression to two model systems, a simple one- dimensional Gaussian disorder model and the model of a realistic three-dimensional organic polymer material, were presented, as well.

cond-mat.dis-nn↗