The equilibrium thermodynamics of the two-dimensional Su-Schrieffer-Heeger model is derived by means of a path integral method that accounts for the variable range of the electronic hopping processes. While the lattice degrees of freedom are classical functions of time and are integrated out exactly, the electron particle paths are treated quantum mechanically. The free energy of the system and its temperature derivatives are computed by summing at any $T$ over the ensemble of relevant particle paths which mainly contribute to the total partition function. In the low $T$ regime, the heat capacity over $T$ ratio shows an upturn peculiar of a glassy-like behavior. This feature is more sizeable in the square lattice than in the linear chain as the overall hopping potential contribution to the total action is larger in higher dimensionality.The equilibrium thermodynamics of the two-dimensional Su-Schrieffer-Heeger model is derived by means of a path integral method that accounts for the variable range of the electronic hopping processes. While the lattice degrees of freedom are classical functions of time and are integrated out exactly, the electron particle paths are treated quantum mechanically. The free energy of the system and its temperature derivatives are computed by summing at any $T$ over the ensemble of relevant particle paths which mainly contribute to the total partition function. In the low $T$ regime, the heat capacity over $T$ ratio shows an upturn peculiar of a glassy-like behavior. This feature is more sizeable in the square lattice than in the linear chain as the overall hopping potential contribution to the total action is larger in higher dimensionality.

arXiv:cond-mat/0504259Physical Review BMay 24, 200519 citations

Quantum Problem of Polaron Localization and Justification of the Su—Schrieffer—Heeger Approximation

Vladimir Nikolaevich Likhachev, George A Vinogradov

We consider a polaron localized on a trap in a one-dimensional lattice with a harmonic potential of nearest-neighbor interaction. We study the lattice oscillations in the framework of quantum mechanics and regard the polaron energy as a functional of the wave function. We take the electron—phonon interaction into account in the framework of the linear Su—Schrieffer—Heeger approximation. We show that the results do not differ from the adiabatic consideration if the lattice oscillations are described classically. For the polaron ground state, we obtain approximate analytic expressions that agree well with the results of numerical simulation.We consider a polaron localized on a trap in a one-dimensional lattice with a harmonic potential of nearest-neighbor interaction. We study the lattice oscillations in the framework of quantum mechanics and regard the polaron energy as a functional of the wave function. We take the electron—phonon interaction into account in the framework of the linear Su—Schrieffer—Heeger approximation. We show that the results do not differ from the adiabatic consideration if the lattice oscillations are described classically. For the polaron ground state, we obtain approximate analytic expressions that agree well with the results of numerical simulation.

Theoretical and Mathematical PhysicsMay 1, 20193 citations

Hamiltonian approach to Feynman's path-integral polaron treatment

J. T. Devreese, Serghei N. Klimin

Bulletin of the American Physical SocietyMar 22, 20110 citations

Sharp Transition for Single Polarons in the One-Dimensional Su-Schrieffer-Heeger Model

D. J. J. Marchand, G. De Filippis, V. Cataudella +5 more

We study a single polaron in the Su-Schrieffer-Heeger (SSH) model using four different techniques (three numerical and one analytical). Polarons show a smooth crossover from weak to strong coupling, as a function of the electron-phonon coupling strength λ, in all models where this coupling depends only on phonon momentum q. In the SSH model the coupling also depends on the electron momentum k; we find it has a sharp transition, at a critical coupling strength λ(c), between states with zero and nonzero momentum of the ground state. All other properties of the polaron are also singular at λ=λ(c). This result is representative of all polarons with coupling depending on k and q, and will have important experimental consequences (e.g., in angle-resolved photoemission spectroscopy and conductivity experiments).We study a single polaron in the Su-Schrieffer-Heeger (SSH) model using four different techniques (three numerical and one analytical). Polarons show a smooth crossover from weak to strong coupling, as a function of the electron-phonon coupling strength λ, in all models where this coupling depends only on phonon momentum q. In the SSH model the coupling also depends on the electron momentum k; we find it has a sharp transition, at a critical coupling strength λ(c), between states with zero and nonzero momentum of the ground state. All other properties of the polaron are also singular at λ=λ(c). This result is representative of all polarons with coupling depending on k and q, and will have important experimental consequences (e.g., in angle-resolved photoemission spectroscopy and conductivity experiments).

arXiv:1010.3207Physical Review LettersDec 30, 2010140 citations

Path Integrals and Continuum Fröhlich Polarons

J. T. Devreese

Springer eBooksJan 1, 19783 citations

T

over the ensemble of relevant particle paths which mainly contribute to the total partition function. In the low

T

regime, the heat capacity over

T

ratio shows an upturn peculiar of a glassy-like behavior. This feature is more sizeable in the square lattice than in the linear chain as the overall hopping potential contribution to the total action is larger in higher dimensionality.