We present a vibrational dynamical mean-field theory (VDMFT) of the dynamics of atoms in solids with anharmonic interactions. Like other flavors of DMFT, VDMFT maps the dynamics of a periodic anharmonic lattice of atoms onto those of a self-consistently defined impurity problem with local anharmonicity and coupling to a bath of harmonic oscillators. VDMFT is exact in the harmonic and molecular limits, nonperturbative systematically improvable through its cluster extensions, usable with classical or quantum impurity solvers (depending on the importance of nuclear quantum effects) and can be combined with existing low-level diagrammatic theories of anharmonicity. When tested on models of anharmonic optical and acoustic phonons; we find that classical VDMFT gives good agreement with classical molecular dynamics, including the temperature dependence of phonon frequencies and lifetimes. Using a quantum impurity solver, signatures of nuclear quantum effects are observed at low temperatures. We test the description of nonlocal anharmonicity via cellular VDMFT and the combination with self-consistent phonon (SCPH) theory, yielding the powerful SCPH $+$ VDMFT approach.We present a vibrational dynamical mean-field theory (VDMFT) of the dynamics of atoms in solids with anharmonic interactions. Like other flavors of DMFT, VDMFT maps the dynamics of a periodic anharmonic lattice of atoms onto those of a self-consistently defined impurity problem with local anharmonicity and coupling to a bath of harmonic oscillators. VDMFT is exact in the harmonic and molecular limits, nonperturbative systematically improvable through its cluster extensions, usable with classical or quantum impurity solvers (depending on the importance of nuclear quantum effects) and can be combined with existing low-level diagrammatic theories of anharmonicity. When tested on models of anharmonic optical and acoustic phonons; we find that classical VDMFT gives good agreement with classical molecular dynamics, including the temperature dependence of phonon frequencies and lifetimes. Using a quantum impurity solver, signatures of nuclear quantum effects are observed at low temperatures. We test the description of nonlocal anharmonicity via cellular VDMFT and the combination with self-consistent phonon (SCPH) theory, yielding the powerful SCPH $+$ VDMFT approach.

arXiv:2109.00028Physical review. B./Physical review. BOct 13, 20226 citations

Phonons from a many-body viewpoint

R. D. Mattuck

Annals of PhysicsApr 1, 196414 citations

Phonons from a many-body viewpoint

R. D. Mattuck

Annals of PhysicsFeb 1, 19640 citations

Electron-phonon coupling in the self-consistent Born approximation of the t−J model

O. Gunnarsson, O. Rösch

We study an undoped $t\text{\ensuremath{-}}J$ model with electron-phonon interaction using the self-consistent Born approximation (SCBA). By neglecting vertex corrections, the SCBA solves a boson-holon model, where a holon couples to phonons and magnons. Comparison with exact diagonalization results for the $t\text{\ensuremath{-}}J$ model suggests that the SCBA describes the electron-phonon interaction fairly accurately over a substantial range of $J∕t$ values. Exact diagonalization of the boson-holon model shows that the deviations are mainly due to the neglect of vertex corrections for small $J∕t$ and due to the replacement of the $t\text{\ensuremath{-}}J$ model by the boson-holon model for large $J∕t$ . For typical values of $J∕t$ , the electron-phonon part ${\ensuremath{\Sigma}}_{\mathrm{ep}}$ of the electron self-energy has comparable contributions from the second-order diagram in the electron-phonon interaction and a phonon-induced change of magnon diagrams. A very simple approximation to ${\ensuremath{\Sigma}}_{\mathrm{ep}}$ gives a rather accurate effective mass. Using this approximation, we study the factors influencing the electron-phonon interaction. Typically, we find that the magnons nominally have a stronger coupling to the holon than the phonons. The phonons, nevertheless, drive the formation of small polarons (self-localization) due to important differences between the character of the phonon and magnon couplings.We study an undoped $t\text{\ensuremath{-}}J$ model with electron-phonon interaction using the self-consistent Born approximation (SCBA). By neglecting vertex corrections, the SCBA solves a boson-holon model, where a holon couples to phonons and magnons. Comparison with exact diagonalization results for the $t\text{\ensuremath{-}}J$ model suggests that the SCBA describes the electron-phonon interaction fairly accurately over a substantial range of $J∕t$ values. Exact diagonalization of the boson-holon model shows that the deviations are mainly due to the neglect of vertex corrections for small $J∕t$ and due to the replacement of the $t\text{\ensuremath{-}}J$ model by the boson-holon model for large $J∕t$. For typical values of $J∕t$, the electron-phonon part ${\ensuremath{\Sigma}}_{\mathrm{ep}}$ of the electron self-energy has comparable contributions from the second-order diagram in the electron-phonon interaction and a phonon-induced change of magnon diagrams. A very simple approximation to ${\ensuremath{\Sigma}}_{\mathrm{ep}}$ gives a rather accurate effective mass. Using this approximation, we study the factors influencing the electron-phonon interaction. Typically, we find that the magnons nominally have a stronger coupling to the holon than the phonons. The phonons, nevertheless, drive the formation of small polarons (self-localization) due to important differences between the character of the phonon and magnon couplings.

arXiv:cond-mat/0602327Physical Review BMay 23, 200624 citations

+

VDMFT approach.

J∕t

values. Exact diagonalization of the boson-holon model shows that the deviations are mainly due to the neglect of vertex corrections for small

J∕t

and due to the replacement of the $t\text{\ensuremath{-}}J$ model by the boson-holon model for large

J∕t

. For typical values of

J∕t

, the electron-phonon part ${\ensuremath{\Sigma}}_{\mathrm{ep}}$ of the electron self-energy has comparable contributions from the second-order diagram in the electron-phonon interaction and a phonon-induced change of magnon diagrams. A very simple approximation to ${\ensuremath{\Sigma}}_{\mathrm{ep}}$ gives a rather accurate effective mass. Using this approximation, we study the factors influencing the electron-phonon interaction. Typically, we find that the magnons nominally have a stronger coupling to the holon than the phonons. The phonons, nevertheless, drive the formation of small polarons (self-localization) due to important differences between the character of the phonon and magnon couplings.