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:2104.13344 · Physical review. B./Physical review. B

Diagrammatic quantum Monte Carlo study of an acoustic lattice polaron

Thomas Hahn, Naoto Nagaosa, Cesare Franchini, Andrei S. Mishchenko

Published Oct 15, 2021• 11 citations
arXivHTMLPDF

Abstract

We present a diagrammatic Monte Carlo study of a lattice polaron interacting with an acoustic phonon branch through the deformation potential. Weak and strong coupling regimes are separated by a self-trapping region where quantum resonance between various possible lattice deformations is seen in the ground-state properties, spectral function, and optical conductivity. This study shows that the acoustic lattice polaron represents a distinct quantum object with unique features, markedly different from any previously considered polaron model. In particular, the acoustic lattice polaron exhibits an interplay between long- and short wavelength acoustic vibrations, resulting in a composite phonon cloud which leads to the formation of multiple competing polaron states with a complex spectral response.

DOI
10.1103/physrevb.104.l161111

Related papers

Ground State Properties of Three-Dimensional Acoustic Polarons

Xiaoqun Wang

The ground state properties of a three-dimensional acoustic polaron are studied using the path integral Monte Carlo technique. In the strong coupling regime, there exists a self-trapped state, which originates from a short ranged electron–phonon interaction, and is of delocalized nature.

Modern Physics Letters B•Aug 20, 1998•6 citations

Polaron physics beyond the Holstein model

D. J. J. Marchand

Many condensed matter problems involve a particle coupled to its environment. The polaron, originally introduced to describe electrons in a polarizable medium, describes a particle coupled to a bosonic field. The Holstein polaron model, although simple, including only optical Einstein phonons and an interaction that couples them to the electron density, captures almost all of the standard polaronic properties. We herein investigate polarons that differ significantly from this behaviour. We study a model with phonon-modulated hopping, and find a radically different behaviour at strong couplings. We report a sharp transition, not a crossover, with a diverging effective mass at the critical coupling. We also look at a model with acoustic phonons, away from the perturbative limit, and again discover unusual polaron properties. Our work relies on the Bold Diagrammatic Monte Carlo (BDMC) method, which samples Feynman diagrammatic expansions efficiently, even those with weak sign problems. Proposed by Prokof'ev and Svistunov, it is extended to lattice polarons for the first time here. We also use the Momentum Average (MA) approximation, an analytical method proposed by Berciu, and find an excellent agreement with the BDMC results. A novel MA approximation able to treat dispersive phonons is also presented, along with a new exact solution for finite systems, inspired by the same formalism.

•Jan 1, 2011•1 citation

Diagrammatic quantum Monte Carlo study of the Fröhlich polaron

Andrei S. Mishchenko, Nikolay V. Prokof'ev, Akira Sakamoto +1 more

A detailed study of the Fr\"ohlich polaron model is performed on the basis of diagrammatic quantum Monte Carlo method [N. V. Prokof'ev and B. V. Svistunov, Phys. Rev. Lett. $81,$ 2514 (1998)]. The method is further developed both quantitatively (performance) and qualitatively (new estimators), and is enhanced by spectral analysis of the polaron Green's function, within an approach developed in the present paper. We present up to date results for the binding energy, and make available precise data for the effective mass, including the region of intermediate and strong couplings. We look at the structure of the polaron cloud and answer such questions as the average number of phonons in the cloud and their number/momentum distribution. The spectral analysis reveals nontrivial structure of the spectral density at intermediate and large coupling: the spectral continuum features pronounced peaks that we attribute to unstable excited states of the polaron.

Physical review. B, Condensed matter•Sep 1, 2000•375 citations

Optical conductivity of polarons: Double phonon cloudconcept verified by diagrammatic Monte Carlo simulations

G. De Filippis, V. Cataudella, Andrei S. Mishchenko +1 more

We study theoretically a fundamental issue in solids: the evolution of the optical spectra of polaron as the electron-phonon coupling increases. By comparing the exact results obtained by the diagrammatic Monte Carlo method and the data obtained through exact diagonalization within an appropriate subspace of the phononic wavefunctions, the physical nature of the crossover from weak to strong coupling is revealed. The optical spectra are well understood by the quantum mechanical superposition of states with light and heavy phonon clouds corresponding to large and small polarons, respectively. It is also found that the strong coupling Franck-Condon regime is not accessible at realistic values of the coupling constant.

arXiv:1111.5253•Physical Review B•Mar 9, 2012•27 citations

Diagrammatic Monte Carlo study of the acoustic and the Bose–Einstein condensate polaron

Jonas Vlietinck, Wim Casteels, Kris Van Houcke +3 more

We consider two large polaron systems that are described by a Fröhlich type of Hamiltonian, namely the Bose–Einstein condensate (BEC) polaron in the continuum and the acoustic polaron in a solid. We present ground-state energies of these two systems calculated with the Diagrammatic Monte Carlo (DiagMC) method and with a Feynman all-coupling approach. The DiagMC method evaluates up to very high order a diagrammatic series for the polaron's self-energy. The Feynman all-coupling approach is a variational method that has been used for a wide range of polaronic problems. For the acoustic and BEC polaron both methods provide remarkably similar non-renormalized ground-state energies that are obtained after introducing a finite momentum cutoff. For the renormalized ground-state energies of the BEC polaron, there are relatively large discrepancies between the DiagMC and the Feynman predictions. These differences can be attributed to the renormalization procedure for the contact interaction.

arXiv:1406.6506•New Journal of Physics•Mar 12, 2015•87 citations

Analytic method for quadratic polarons in nonparabolic bands

Serghei N. Klimin, Jacques Tempere, Matthew Houtput +4 more

Including the effect of lattice anharmonicity on electron-phonon interactions has recently garnered attention due to its role as a necessary and significant component in explaining various phenomena, including superconductivity, optical response, and temperature dependence of mobility. This study focuses on analytically treating the effects of anharmonic electron-phonon coupling on the polaron self-energy, combined with numerical Diagrammatic Monte Carlo (DiagMC) data. Specifically, we incorporate a quadratic interaction into the method of squeezed phonon states, which has proven effective for analytically calculating the polaron parameters. Additionally, we extend this method to nonparabolic finite-width conduction bands while maintaining the periodic translation symmetry of the system. Our results are compared with those obtained from Diagrammatic Monte Carlo, partially reported in a recent study [S. Ragni et al., Phys. Rev. B 107, L121109 (2023)], covering a wide range of coupling strengths for the nonlinear interaction. Remarkably, our analytic method predicts the same features as the Diagrammatic Monte Carlo simulation.

arXiv:2403.18019•Physical review. B./Physical review. B•Aug 5, 2024•5 citations
We present a diagrammatic Monte Carlo study of a lattice polaron interacting with an acoustic phonon branch through the deformation potential. Weak and strong coupling regimes are separated by a self-trapping region where quantum resonance between various possible lattice deformations is seen in the ground-state properties, spectral function, and optical conductivity. This study shows that the acoustic lattice polaron represents a distinct quantum object with unique features, markedly different from any previously considered polaron model. In particular, the acoustic lattice polaron exhibits an interplay between long- and short wavelength acoustic vibrations, resulting in a composite phonon cloud which leads to the formation of multiple competing polaron states with a complex spectral response.
Many condensed matter problems involve a particle coupled to its environment. The polaron, originally introduced to describe electrons in a polarizable medium, describes a particle coupled to a bosonic field. The Holstein polaron model, although simple, including only optical Einstein phonons and an interaction that couples them to the electron density, captures almost all of the standard polaronic properties. We herein investigate polarons that differ significantly from this behaviour. We study a model with phonon-modulated hopping, and find a radically different behaviour at strong couplings. We report a sharp transition, not a crossover, with a diverging effective mass at the critical coupling. We also look at a model with acoustic phonons, away from the perturbative limit, and again discover unusual polaron properties. Our work relies on the Bold Diagrammatic Monte Carlo (BDMC) method, which samples Feynman diagrammatic expansions efficiently, even those with weak sign problems. Proposed by Prokof'ev and Svistunov, it is extended to lattice polarons for the first time here. We also use the Momentum Average (MA) approximation, an analytical method proposed by Berciu, and find an excellent agreement with the BDMC results. A novel MA approximation able to treat dispersive phonons is also presented, along with a new exact solution for finite systems, inspired by the same formalism.
A detailed study of the Fr\"ohlich polaron model is performed on the basis of diagrammatic quantum Monte Carlo method [N. V. Prokof'ev and B. V. Svistunov, Phys. Rev. Lett. 81,81,81, 2514 (1998)]. The method is further developed both quantitatively (performance) and qualitatively (new estimators), and is enhanced by spectral analysis of the polaron Green's function, within an approach developed in the present paper. We present up to date results for the binding energy, and make available precise data for the effective mass, including the region of intermediate and strong couplings. We look at the structure of the polaron cloud and answer such questions as the average number of phonons in the cloud and their number/momentum distribution. The spectral analysis reveals nontrivial structure of the spectral density at intermediate and large coupling: the spectral continuum features pronounced peaks that we attribute to unstable excited states of the polaron.
We study theoretically a fundamental issue in solids: the evolution of the optical spectra of polaron as the electron-phonon coupling increases. By comparing the exact results obtained by the diagrammatic Monte Carlo method and the data obtained through exact diagonalization within an appropriate subspace of the phononic wavefunctions, the physical nature of the crossover from weak to strong coupling is revealed. The optical spectra are well understood by the quantum mechanical superposition of states with light and heavy phonon clouds corresponding to large and small polarons, respectively. It is also found that the strong coupling Franck-Condon regime is not accessible at realistic values of the coupling constant.
We consider two large polaron systems that are described by a Fröhlich type of Hamiltonian, namely the Bose–Einstein condensate (BEC) polaron in the continuum and the acoustic polaron in a solid. We present ground-state energies of these two systems calculated with the Diagrammatic Monte Carlo (DiagMC) method and with a Feynman all-coupling approach. The DiagMC method evaluates up to very high order a diagrammatic series for the polaron's self-energy. The Feynman all-coupling approach is a variational method that has been used for a wide range of polaronic problems. For the acoustic and BEC polaron both methods provide remarkably similar non-renormalized ground-state energies that are obtained after introducing a finite momentum cutoff. For the renormalized ground-state energies of the BEC polaron, there are relatively large discrepancies between the DiagMC and the Feynman predictions. These differences can be attributed to the renormalization procedure for the contact interaction.
Including the effect of lattice anharmonicity on electron-phonon interactions has recently garnered attention due to its role as a necessary and significant component in explaining various phenomena, including superconductivity, optical response, and temperature dependence of mobility. This study focuses on analytically treating the effects of anharmonic electron-phonon coupling on the polaron self-energy, combined with numerical Diagrammatic Monte Carlo (DiagMC) data. Specifically, we incorporate a quadratic interaction into the method of squeezed phonon states, which has proven effective for analytically calculating the polaron parameters. Additionally, we extend this method to nonparabolic finite-width conduction bands while maintaining the periodic translation symmetry of the system. Our results are compared with those obtained from Diagrammatic Monte Carlo, partially reported in a recent study [S. Ragni et al., Phys. Rev. B 107, L121109 (2023)], covering a wide range of coupling strengths for the nonlinear interaction. Remarkably, our analytic method predicts the same features as the Diagrammatic Monte Carlo simulation.