Static and Dynamic Effective Mass of the Polaron

A concise approach for static polarons is extended to study the dynamic polaron system having nonspherical symmetry. The general properties of moving polarons, such as the ground-state energy, the phonon number, the effective mass, and the density distribution of phonon momentum---studied as functions of the total polaron momentum and electron-phonon coupling strength---are calculated numerically in a wide range of intermediate coupling strengths. In particular, a modified Fr\"ohlich Hamiltonian is derived for the problem of polaron momentum Q\ensuremath{\geqslant}1. \textcopyright{} 1996 The American Physical Society.A concise approach for static polarons is extended to study the dynamic polaron system having nonspherical symmetry. The general properties of moving polarons, such as the ground-state energy, the phonon number, the effective mass, and the density distribution of phonon momentum---studied as functions of the total polaron momentum and electron-phonon coupling strength---are calculated numerically in a wide range of intermediate coupling strengths. In particular, a modified Fr\"ohlich Hamiltonian is derived for the problem of polaron momentum Q\ensuremath{\geqslant}1. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterNov 1, 199611 citations

The effective mass of a quantum polaron

Alexander O. Gogolin, Alexei S. Ioselevich

Sep 1, 19911 citation

Effective mass of the polaron: A functional integral approach

Herbert E. Spohn

Annals of PhysicsMay 1, 198789 citations

Lattice polaron formation: Effects of nonscreened electron-phonon interaction

Holger Fehske, Jan Loos, Gerhard Wellein

We explore the quasiparticle properties of lattice polarons on the basis of a quite general electron-phonon Hamiltonian with a long-range displacement-type interaction. To treat the dynamical quantum phonons without significant loss of accuracy we adapt an exact Lanczos diagonalization method and compute various static and dynamical quantities, such as the electron-lattice correlation function, the polaron band dispersion, the effective polaron mass, the kinetic energy, the single-particle spectral function, and the optical conductivity, on finite one-dimensional lattices for a wide range of model parameters. We compare the results with those obtained for the standard Holstein model with short-range electron-phonon interaction only.We explore the quasiparticle properties of lattice polarons on the basis of a quite general electron-phonon Hamiltonian with a long-range displacement-type interaction. To treat the dynamical quantum phonons without significant loss of accuracy we adapt an exact Lanczos diagonalization method and compute various static and dynamical quantities, such as the electron-lattice correlation function, the polaron band dispersion, the effective polaron mass, the kinetic energy, the single-particle spectral function, and the optical conductivity, on finite one-dimensional lattices for a wide range of model parameters. We compare the results with those obtained for the standard Holstein model with short-range electron-phonon interaction only.

arXiv:cond-mat/9911218Physical review. B, Condensed matterMar 15, 200096 citations

Finite-temperature mass gap and quench dynamics of mobile impurities in a Fermi gas

Baihua Gong

Recently, a mass-gap description of mobile impurities in a Fermi gas was introduced, which connects Anderson's orthogonality catastrophe for static impurities to the quasiparticle picture of Fermi polarons through a recoil-induced energy gap in the fermionic dispersion. That description, however, was restricted to zero temperature and did not address dynamics. Here we generalize the mass-gap model to finite temperature by combining the Lee--Low--Pines transformation with a self-consistent Hartree--Fock decoupling of the recoil-induced interaction, and we study the quench dynamics within this framework using the functional-determinant approach. At finite temperature the effective mass gap obeys the self-consistency equation $Δ(T)=2U_F\tanh[Δ(T)/4k_B T]$ , with $U_F=k_F^2/2M$ and $M$ the impurity mass. This equation admits a nonzero solution below the characteristic temperature $T^*=U_F/(2k_B)$ and closes as $(T^*-T)^{1/2}$ . We identify this closing as the mean-field signature of the thermal melting of the polaron and molecule quasiparticles. Computing the Ramsey response $S(t)$ after a sudden quench of the impurity--fermion interaction, we find that its long-time oscillations---quantum beats between the bound and in-gap states---disappear precisely above $T^*$ . Our work ties the thermodynamic and dynamical fingerprints of polaron formation to a single temperature-dependent mean-field parameter.Recently, a mass-gap description of mobile impurities in a Fermi gas was introduced, which connects Anderson's orthogonality catastrophe for static impurities to the quasiparticle picture of Fermi polarons through a recoil-induced energy gap in the fermionic dispersion. That description, however, was restricted to zero temperature and did not address dynamics. Here we generalize the mass-gap model to finite temperature by combining the Lee--Low--Pines transformation with a self-consistent Hartree--Fock decoupling of the recoil-induced interaction, and we study the quench dynamics within this framework using the functional-determinant approach. At finite temperature the effective mass gap obeys the self-consistency equation $Δ(T)=2U_F\tanh[Δ(T)/4k_B T]$, with $U_F=k_F^2/2M$ and $M$ the impurity mass. This equation admits a nonzero solution below the characteristic temperature $T^*=U_F/(2k_B)$ and closes as $(T^*-T)^{1/2}$. We identify this closing as the mean-field signature of the thermal melting of the polaron and molecule quasiparticles. Computing the Ramsey response $S(t)$ after a sudden quench of the impurity--fermion interaction, we find that its long-time oscillations---quantum beats between the bound and in-gap states---disappear precisely above $T^*$. Our work ties the thermodynamic and dynamical fingerprints of polaron formation to a single temperature-dependent mean-field parameter.

arXiv:2609.03656Sep 3, 20260 citations

The Self-Energy and Effective Mass of the Polaron.

John T. Marshall

Jan 1, 19621 citation

Δ(T)=2U_F\tanh[Δ(T)/4k_B T]

, with

U_F=k_F^2/2M

and

M

the impurity mass. This equation admits a nonzero solution below the characteristic temperature

T^*=U_F/(2k_B)

and closes as

(T^*-T)^{1/2}

. We identify this closing as the mean-field signature of the thermal melting of the polaron and molecule quasiparticles. Computing the Ramsey response

S(t)

after a sudden quench of the impurity--fermion interaction, we find that its long-time oscillations---quantum beats between the bound and in-gap states---disappear precisely above

T^*

. Our work ties the thermodynamic and dynamical fingerprints of polaron formation to a single temperature-dependent mean-field parameter.