Polarons originating from phonon displacement modulated hopping have relatively light masses and thus are of significant current interest as candidates for the bipolaron mechanism of high-temperature superconductivity [Sous et al., Phys. Rev. Lett. 121, 247001 (2018)]. We observe that the bond model, when the dominant coupling comes from atomic vibrations on lattice bonds, can be solved by efficient sign-free Monte Carlo methods based on the path-integral formulation of the particle sector in combination with either the (real-space) diagrammatic or Fock-path-integral representation of the phonon sector. We introduce the corresponding algorithms and provide illustrative results for singlet bipolarons in two dimensions. The data suggest that the route towards high-temperature superconductivity (if any) in the multiparametric space of the model lies between the Scylla of large size of moderately light bipolarons and the Charybdis of large mass of compact bipolarons. As a result, on-site repulsion is helping
s-wave superconductivity in sharp contrast with existing expectations.
It is remarkable how the Froehlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of ion displacements, has resisted full analytical or numerical solution at all coupling since 1950, when its Hamiltonian was first written. The field has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalisation (ED), and quantum Monte Carlo (QMC) techniques. This article reviews recent developments in the field of continuum and discrete (lattice) Froehlich (bi)polarons starting with the basics and covering a number of active directions of research.
We employ the diagrammatic Monte Carlo method with a lattice path-integral formulation for both electron and phonon degrees of freedom to investigate the formation and properties of bond polarons and bipolarons on a two-dimensional triangular lattice. In the deep adiabatic regime ($\ensuremath{\omega}/t<1.0$), single polarons remain light with a small effective mass, while bipolarons remain compact and lightweight, resulting in a high superfluid transition temperature
Tc. We systematically study the dependence of
Tc on electron-phonon coupling strength and on-site interaction in the bond bipolaron model. Our results show that a moderate on-site repulsion enhances
Tc by stabilizing compact yet lightweight bipolarons, leading to high-
Tc superconductivity in the dilute limit. Notably, the triangular lattice sustains relatively high
Tc across a wide range of phonon frequencies, outperforming square lattice geometry. This enhancement arises from the higher coordination number and the bond-centered nature of the electron-phonon coupling. These findings suggest that triangular lattice geometry offers a promising platform for realizing high-
Tc bipolaronic superconductivity.