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:1403.2920 · Progress of Theoretical and Experimental Physics

Large-radius Holstein polaron and the problem of spontaneous symmetry breaking

V. D. Lakhno

Published Jul 1, 2014• 7 citations
arXivHTMLPDF

Abstract

A translation-invariant solution is found for a large-radius Holstein polaron whose energy in the strong coupling limit is lower than that obtained by Holstein. The wave function corresponding to this solution is delocalized. A conclusion is made about the absence of a spontaneous symmetry breaking in the quantum system discussed.
DOI
10.1093/ptep/ptu075

Related papers

3 Large-radius Holstein polaron and the problem of spontaneous symmetry breaking

Victor Dmitrievich Lakhno

A translation-invariant solution is found for a large-radius Holstein polaron whose energy in the strong coupling limit is lower than that obtained by Holstein.The wave function corresponding to this solution is delocalized.A conclusion is made about the absence of a spontaneous symmetry breaking in the quantum system discussed.

De Gruyter eBooks•Jul 18, 2022•0 citations

Large-radius Holstein polaron and the problem of spontaneous symmetry breaking

Victor Dmitrievich Lakhno

A translation-invariant solution is found for a large-radius Holstein polaron whose energy in the strong coupling limit is lower than that obtained by Holstein [T. Holstein, Annals Phys., 8, 325 (1959)]. The wave function corresponding to this solution is delocalized. A conclusion is drawn about the absence of spontaneous symmetry breaking in the quantum system discussed. Subject Index I44

•Sep 22, 2016•7 citations

2 Pekar’s ansatz and the strong coupling problem in polaron theory

Victor Dmitrievich Lakhno

A detailed consideration is given to the translation-invariant theory of Tulub polaron constructed without the use of Pekar ansatz.A fundamental result of the theory is that the value of the polaron energy is lower than that obtained on the basis of Pekar ansatz which was considered as an asymptotically exact solution in the strong coupling limit.In the case of bipolarons the theory yields the best values of the coupling energy and critical parameters of their stability.Numerous physical consequences of the existence of translation-invariant polarons and bipolarons are discussed.

De Gruyter eBooks•Jul 18, 2022•0 citations

Pekar's ansatz and the strong coupling problem in polaron theory

V D Lakhno

A detailed consideration is given to the translation-invariant theory of Tulub polaron constructed without the use of Pekar ansatz. A fundamental result of the theory is that the value of the polaron energy is lower than that obtained on the basis of Pekar ansatz which was considered as an asymptotically exact solution in the strong coupling limit. In the case of bipolarons the theory yields the best values of the coupling energy and critical parameters of their stability. Numerous physical consequences of the existence of translation-invariant polarons and bipolarons are discussed.

arXiv:1505.01699•Physics-Uspekhi•Mar 8, 2015•31 citations

The virial theorem and the ground state problem in polaron theory

N. I. Kashirina, Victor Dmitrievich Lakhno, A. V. Tulub

The virial theorem for the translation-invariant theory of a polaron [3] is discussed. It is shown that, in [3], Tulub made a nonoptimal choice of variational parameters in the strong-coupling limit, which led to the violation of the virial relations. The introduction of an additional variational parameter to the test function reduces the polaron energy and makes it possible to satisfy the relations of the virial theorem for a strong-coupling polaron (the Pekar 1: 2: 3: 4 theorem).

arXiv:1310.0246•Journal of Experimental and Theoretical Physics•May 1, 2012•23 citations

Polarons by translationally invariant diagrammatic perturbation theory

O. S. Barišić, S. Barišić

The structure of the translationally-invariant diagrammatic perturbation theory for one polaron is examined on the 1D discrete lattice described by the Holstein Hamiltonian. The latter is characterized by the electron hopping t, the phonon frequency ω_0 and the electron-phonon coupling g. It is shown that the polaron localization (and translation) properties are contained in the electron propagator of one electron, intermittently added to the lattice, and/or in the phonon correlation function with one electron permanently present in the lattice. The order by order analysis in g/ω_0 shows that the expansion of the irreducible electron self-energy corresponds to the expansion of the phonon correlation function, rather than of the irreducible phonon self-energy. The range of polaronic correlations is determined in this way. For small t/ω_0 and already to the second order g/ω_0 small, the electron-lattice correlation becomes very short ranged, i.e. the polaron is already localized to one site, although the overall translational symmetry remains unbroken. For large t/ω0, the second order result is meaningful up to large g/ω_0 ≈ (t/ω_0)^\frac14, where it becomes degenerate with the results for the large adiabatic Holstein polaron. This suggests that the translationally invariant perturbation theory crosses then over smoothly, without symmetry breaking, into the adiabatic, continuous quantum limit, as rigorously demonstrated in the companion paper. Thus the quantum theory of the large adiabatic Holstein polaron provides a simple, instructive example of the quantum crossover which replaces the behavior in the quantum critical point.

FizA•Jan 1, 2005•0 citations
A detailed consideration is given to the translation-invariant theory of Tulub polaron constructed without the use of Pekar ansatz.A fundamental result of the theory is that the value of the polaron energy is lower than that obtained on the basis of Pekar ansatz which was considered as an asymptotically exact solution in the strong coupling limit.In the case of bipolarons the theory yields the best values of the coupling energy and critical parameters of their stability.Numerous physical consequences of the existence of translation-invariant polarons and bipolarons are discussed.
A detailed consideration is given to the translation-invariant theory of Tulub polaron constructed without the use of Pekar ansatz. A fundamental result of the theory is that the value of the polaron energy is lower than that obtained on the basis of Pekar ansatz which was considered as an asymptotically exact solution in the strong coupling limit. In the case of bipolarons the theory yields the best values of the coupling energy and critical parameters of their stability. Numerous physical consequences of the existence of translation-invariant polarons and bipolarons are discussed.
The structure of the translationally-invariant diagrammatic perturbation theory for one polaron is examined on the 1D discrete lattice described by the Holstein Hamiltonian. The latter is characterized by the electron hopping t, the phonon frequency ω_0 and the electron-phonon coupling g. It is shown that the polaron localization (and translation) properties are contained in the electron propagator of one electron, intermittently added to the lattice, and/or in the phonon correlation function with one electron permanently present in the lattice. The order by order analysis in g/ω_0 shows that the expansion of the irreducible electron self-energy corresponds to the expansion of the phonon correlation function, rather than of the irreducible phonon self-energy. The range of polaronic correlations is determined in this way. For small t/ω_0 and already to the second order g/ω_0 small, the electron-lattice correlation becomes very short ranged, i.e. the polaron is already localized to one site, although the overall translational symmetry remains unbroken. For large t/ω0, the second order result is meaningful up to large g/ω_0 ≈ (t/ω_0)^\frac14, where it becomes degenerate with the results for the large adiabatic Holstein polaron. This suggests that the translationally invariant perturbation theory crosses then over smoothly, without symmetry breaking, into the adiabatic, continuous quantum limit, as rigorously demonstrated in the companion paper. Thus the quantum theory of the large adiabatic Holstein polaron provides a simple, instructive example of the quantum crossover which replaces the behavior in the quantum critical point.