Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2505.13365 · The Journal of Chemical Physics

Mixed quantum-classical methods for polaron spectral functions

Haimi Nguyen, Arkajit Mandal, Ankit Mahajan, David R. Reichman

Published Sep 15, 2025• 3 citations
arXivHTMLPDF

Abstract

In this work, using two distinct semiclassical approaches-namely, the mean-field Ehrenfest method and the mapping approach to surface hopping-we investigate the spectral function of a single charge interacting with phonons on a lattice. This quantity is relevant for the description of angle-resolved photoemission experiments. Focusing on the one-dimensional Holstein model, we compare the performance of these approaches across a range of coupling strengths and lattice sizes, exposing the relative strengths and weaknesses of each. We demonstrate that these approaches can be efficiently applied with reasonable accuracy to ab initio polaron models. Our work provides a route to the calculation of spectral properties in realistic electron-phonon-coupled systems in a computationally inexpensive manner with encouraging accuracy.

DOI
10.1063/5.0281529

Related papers

Spectral functions of the spinless Holstein model

Jan Loos, Martin Hohenadler, Holger Fehske

An analytical approach to the one-dimensional spinless Holstein model is proposed, which is valid at finite charge-carrier concentrations. Spectral functions of charge carriers are computed on the basis of self-energy calculations. A generalization of the Lang–Firsov canonical transformation method is shown to provide an interpolation scheme between the extreme weak-coupling and strong-coupling cases. The transformation depends on a variationally determined parameter that characterizes the charge distribution across the polaron volume. The relation between the spectral functions of the polaron and electron, the latter corresponding to the photoemission spectrum, is derived. Particular attention is paid to the distinction between the coherent and incoherent parts of the spectra, and their evolution as a function of band filling and model parameters. Results are discussed and compared with recent numerical calculations for the many-polaron problem.

arXiv:cond-mat/0508712•Journal of Physics Condensed Matter•Feb 10, 2006•20 citations

Phonon spectral function of the Holstein polaron

Jan Loos, Martin Hohenadler, Andreas Alvermann +1 more

The phonon spectral function of the one-dimensional Holstein model is obtained within weak and strong-coupling approximations based on analytical self-energy calculations.The characteristic excitations found in the limit of small charge-carrier density are related to the known (electronic) spectral properties of Holstein polarons such as the polaron band dispersion.Particular emphasis is laid on the different physics occurring in the adiabatic and antiadiabatic regimes, respectively.Comparison is made with a cluster approach exploiting exact numerical results on small systems to yield an approximation for the thermodynamic limit.This method, similar to cluster perturbation theory, confirms the analytical findings, and yields accurate results also in the intermediate-coupling regime.

•Jan 1, 2006•12 citations

Phonon spectral function of the Holstein polaron

J Loos, M Hohenadler, A Alvermann +1 more

The phonon spectral function of the one-dimensional Holstein model is obtained within weak and strong-coupling approximations based on analytical self-energy calculations. The characteristic excitations found in the limit of small charge-carrier density are related to the known (electronic) spectral properties of Holstein polarons such as the polaron band dispersion. Particular emphasis is laid on the different physics occurring in the adiabatic and anti-adiabatic regimes, respectively. Comparison is made with a cluster approach exploiting exact numerical results on small systems to yield an approximation for the thermodynamic limit. This method, similar to cluster perturbation theory, confirms the analytical findings, and yields accurate results also in the intermediate-coupling regime.

arXiv:cond-mat/0604040•Journal of Physics Condensed Matter•Jul 21, 2006•20 citations

Angle-resolved photoemission spectra in one-dimensional Hubbard-Holstein model

Sun Peijian, Ping Huai, Wei Zhang +2 more

In order to understand the effects of electron-phonon coupling and Coulomb interactions in angle-resolved photoemission spectroscopy (ARPES), a spin-1/2 Hubbard-Holstein model at half-filling is theoretically investigated by means of the mean field theory and classical Monte Carlo simulation method. It shows that the spectral shape of the one-dimensional system is significantly modified by the electron-phonon coupling and Coulomb interactions. The suppression of charge-density wave in one-dimensional system has been ascribed to the short-range Coulomb repulsion and thermal lattice fluctuations. The competition between these interactions can induce zero energy gaps in APPES as well as complete cancellation of charge or spin ordering.

Nuclear Science and Techniques•Jan 1, 2011•0 citations

Electron removal spectral function of a polaron coupled to dispersive optical phonons

J. Bonča, S. A. Trugman

We explore the ground state and thermodynamic properties of the polaron coupled to quantum dispersive optical phonons in one spatial dimension. Calculations are performed using the finite--temperature Lanczos method augmented by a highly efficient construction of the variational Hilbert space. We focus on the electron removal spectral function as relevant for the angle-resolved photoemission experiments. We show that photoemission spectroscopy can be used to measure the phonon dispersion relation in a dilute system of polarons. The spectral weight of observed phonon bands is proportional to the phonon contribution to the wavefunction at finite phonon momentum. In addition, we demonstrate that when removing an electron from a polaron ground state, the polaron band does not appear in the spectral function. The latter becomes observable only at elevated temperatures.

Physical review. B./Physical review. B•Nov 17, 2022•10 citations

A DQMC study of the spectral and conductive properties of the two-dimensional Holstein model

J. Neuhaus, Benjamin Cohen-Stead, N. Mannella +1 more

We study the dynamical properties of the two-dimensional square lattice Holstein Hamiltonian using numerically exact determinant quantum Monte Carlo simulations. In particular, we report systematic calculations of the model's single-particle spectral function and optical conductivity over a range of phonon energies, electron-phonon coupling strengths, carrier concentrations, and temperatures. In doing so, we map the evolution of the system from a dressed metallic phase to a (bi)polaron liquid/insulator to a charge-density-wave insulator as the carrier concentration is tuned from dilute values to half-filling. We corroborate these results using several equal-time correlation measurements and related proxy quantities reconstructed from time-displaced correlation measurements. This paper is also accompanied by an extensive open data set, covering over 16,640 unique parameter values.

arXiv:2608.23379•Aug 24, 2026•0 citations
In this work, using two distinct semiclassical approaches-namely, the mean-field Ehrenfest method and the mapping approach to surface hopping-we investigate the spectral function of a single charge interacting with phonons on a lattice. This quantity is relevant for the description of angle-resolved photoemission experiments. Focusing on the one-dimensional Holstein model, we compare the performance of these approaches across a range of coupling strengths and lattice sizes, exposing the relative strengths and weaknesses of each. We demonstrate that these approaches can be efficiently applied with reasonable accuracy to ab initio polaron models. Our work provides a route to the calculation of spectral properties in realistic electron-phonon-coupled systems in a computationally inexpensive manner with encouraging accuracy.
An analytical approach to the one-dimensional spinless Holstein model is proposed, which is valid at finite charge-carrier concentrations. Spectral functions of charge carriers are computed on the basis of self-energy calculations. A generalization of the Lang–Firsov canonical transformation method is shown to provide an interpolation scheme between the extreme weak-coupling and strong-coupling cases. The transformation depends on a variationally determined parameter that characterizes the charge distribution across the polaron volume. The relation between the spectral functions of the polaron and electron, the latter corresponding to the photoemission spectrum, is derived. Particular attention is paid to the distinction between the coherent and incoherent parts of the spectra, and their evolution as a function of band filling and model parameters. Results are discussed and compared with recent numerical calculations for the many-polaron problem.
The phonon spectral function of the one-dimensional Holstein model is obtained within weak and strong-coupling approximations based on analytical self-energy calculations.The characteristic excitations found in the limit of small charge-carrier density are related to the known (electronic) spectral properties of Holstein polarons such as the polaron band dispersion.Particular emphasis is laid on the different physics occurring in the adiabatic and antiadiabatic regimes, respectively.Comparison is made with a cluster approach exploiting exact numerical results on small systems to yield an approximation for the thermodynamic limit.This method, similar to cluster perturbation theory, confirms the analytical findings, and yields accurate results also in the intermediate-coupling regime.
The phonon spectral function of the one-dimensional Holstein model is obtained within weak and strong-coupling approximations based on analytical self-energy calculations. The characteristic excitations found in the limit of small charge-carrier density are related to the known (electronic) spectral properties of Holstein polarons such as the polaron band dispersion. Particular emphasis is laid on the different physics occurring in the adiabatic and anti-adiabatic regimes, respectively. Comparison is made with a cluster approach exploiting exact numerical results on small systems to yield an approximation for the thermodynamic limit. This method, similar to cluster perturbation theory, confirms the analytical findings, and yields accurate results also in the intermediate-coupling regime.
In order to understand the effects of electron-phonon coupling and Coulomb interactions in angle-resolved photoemission spectroscopy (ARPES), a spin-1/2 Hubbard-Holstein model at half-filling is theoretically investigated by means of the mean field theory and classical Monte Carlo simulation method. It shows that the spectral shape of the one-dimensional system is significantly modified by the electron-phonon coupling and Coulomb interactions. The suppression of charge-density wave in one-dimensional system has been ascribed to the short-range Coulomb repulsion and thermal lattice fluctuations. The competition between these interactions can induce zero energy gaps in APPES as well as complete cancellation of charge or spin ordering.
We explore the ground state and thermodynamic properties of the polaron coupled to quantum dispersive optical phonons in one spatial dimension. Calculations are performed using the finite--temperature Lanczos method augmented by a highly efficient construction of the variational Hilbert space. We focus on the electron removal spectral function as relevant for the angle-resolved photoemission experiments. We show that photoemission spectroscopy can be used to measure the phonon dispersion relation in a dilute system of polarons. The spectral weight of observed phonon bands is proportional to the phonon contribution to the wavefunction at finite phonon momentum. In addition, we demonstrate that when removing an electron from a polaron ground state, the polaron band does not appear in the spectral function. The latter becomes observable only at elevated temperatures.
We study the dynamical properties of the two-dimensional square lattice Holstein Hamiltonian using numerically exact determinant quantum Monte Carlo simulations. In particular, we report systematic calculations of the model's single-particle spectral function and optical conductivity over a range of phonon energies, electron-phonon coupling strengths, carrier concentrations, and temperatures. In doing so, we map the evolution of the system from a dressed metallic phase to a (bi)polaron liquid/insulator to a charge-density-wave insulator as the carrier concentration is tuned from dilute values to half-filling. We corroborate these results using several equal-time correlation measurements and related proxy quantities reconstructed from time-displaced correlation measurements. This paper is also accompanied by an extensive open data set, covering over 16,640 unique parameter values.