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:2507.17398 · Annalen der Physik

Quantum Monte Carlo Simulation of Bipolaron Superconductivity in Extended Hubbard–Holstein models on Face‐Centered‐Cubic and Body‐Centered‐Cubic Lattices

Ganiyu D. Adebanjo, J. P. Hague, P. E. Kornilovitch

Published Dec 14, 2025• 0 citations
arXivHTMLPDF

Abstract

ABSTRACT We investigate superlight pairing of bipolarons driven by electron‐phonon interactions (EPIs) in face‐center‐cubic (FCC) and body‐center‐cubic (BCC) lattices using a continuous‐time path‐integral quantum Monte Carlo (QMC) algorithm. The EPIs are of the Holstein and extended Holstein types, and a Hubbard interaction is also included. Effects of adiabaticity are calculated. The number of phonons associated with the bipolaron, inverse mass, and radius are calculated and used to construct a phase diagram for bipolaron pairing (identifying the regions of pairing into intersite bipolarons and onsite bipolarons). From the inverse mass we determine that for the extended interaction, there is a region of light pairing associated with intersite bipolarons formed in both BCC and FCC lattices. Intersite bipolarons in the extended model at intermediate phonon frequency and large Coulomb repulsion become superlight due to first order hopping effects. We estimate the transition temperature, determining that intersite bipolarons are associated with regions of high transition temperatures.

DOI
10.1002/andp.202500343

Related papers

Bipolarons from long-range interactions: Singlet and triplet pairs in the screened Hubbard-Fröhlich model on the chain

J. P. Hague, P. E. Kornilovitch

We present details of a continuous-time quantum Monte Carlo algorithm for the screened Hubbard-Fr\"ohlich bipolaron. We simulate the bipolaron in one dimension with arbitrary interaction range in the presence of Coulomb repulsion, computing the effective mass, binding energy, total number of phonons associated with the bipolaron, mass isotope exponent, and bipolaron radius in a comprehensive survey of the parameter space. We discuss the role of the range of the electron-phonon interaction, demonstrating the evolution from Holstein to Fr\"ohlich bipolarons and we compare the properties of bipolarons with singlet and triplet pairing. Finally, we present simulations of the bipolaron dispersion. The bandwidth of the Fr\"ohlich bipolaron is found to be broad and the decrease in bandwidth as the two polarons bind into a bipolaron is found to be far less rapid than in the case of the Holstein interaction. The properties of bipolarons formed from long-range electron-phonon interactions, such as light strongly bound bipolarons and intersite pairing when Coulomb repulsion is large, are found to be robust against screening, with qualitative differences between Holstein and screened Fr\"ohlich bipolarons found even for interactions screened within a single lattice site.

arXiv:0904.3678•Physical Review B•Aug 3, 2009•21 citations

Superlight Small Bipolarons in the Presence of a Strong Coulomb Repulsion

J. P. Hague, P. E. Kornilovitch, John H. Samson +1 more

We study a lattice bipolaron on a staggered triangular ladder and triangular and hexagonal lattices with both long-range electron-phonon interaction and strong Coulomb repulsion using a novel continuous-time quantum Monte Carlo algorithm to solve the two-particle Coulomb-Fröhlich model. The algorithm is preceded by an exact integration over phonon degrees of freedom, and as such is extremely efficient. The bipolaron effective mass and radius are computed. Bipolarons on lattices constructed from triangular plaquettes have a novel crablike motion, and are small but very light over a wide range of parameters. We discuss the conditions under which such particles may form a Bose-Einstein condensate with high transition temperature, proposing a route to room temperature superconductivity.

arXiv:cond-mat/0606036•Physical Review Letters•Jan 16, 2007•93 citations

Fermion pair formation and condensation in extended Hubbard models in body-centered-cubic optical lattices

Ganiyu D. Adebanjo, P. E. Kornilovitch, J. P. Hague

We investigate the formation and condensation of fermion pairs in cold atom quantum simulators for extended Hubbard models (UV models) with body center cubic (BCC) optical lattices, predicting small and light pairs with Bose--Einstein condensation (BEC) temperatures up to the order of 100 nK. Pair mass, radius, and binding conditions are calculated, and then used to compute transition temperatures. We predict that: (a) local pairs can form in BCC optical lattices; (b) for particular cases where the onsite $U$ and intersite V are attractive with similar size, the pairs are both small and light; and (c) that transition temperatures could be as high as 100 nK (50 nK) for 6Li atoms in blue (red) BCC optical lattices. Beyond the application to pairs on BCC optical lattices, we expect our results to be relevant to strong-coupling BCC superconductors.

•Feb 15, 2021•0 citations

Light and stable triplet bipolarons on square and triangular lattices

J. P. Hague, P. E. Kornilovitch

We compute the properties of singlet and triplet bipolarons on two-dimensional lattices using the continuous-time quantum Monte Carlo algorithm. Properties of the bipolaron including the total energy, inverse mass, bipolaron radius, and number of phonons associated with the bipolaron demonstrate the qualitative difference between models of electron-phonon interaction with long-range interaction (screened Fr\"ohlich) and those with purely local (Holstein) interaction. A major result of our survey of the parameter space is the existence of extra-light hybrid singlet bipolarons consisting of an on-site and an off-site component on both square and triangular lattices. We also compute triplet properties of the bipolarons and the pair dispersion. For pair momenta on the edge of the Brillouin zone of the triangular lattice, we find that triplet states are more stable than singlets.

arXiv:0910.1215•Physical Review B•Sep 1, 2010•18 citations

Long-range electron-phonon interactions lead to superlight small bipolarons

J. P. Hague, P. E. Kornilovitch, John H. Samson +1 more

A finite-range Fröhlich electron-phonon interaction (EPI) with c-axis polarized optical phonons has been identified in cuprate superconductors by photoemission spectroscopy, in agreement with an earlier proposal by Alexandrov and Kornilovitch [1]. In this article, we discuss the consequences of long-range interactions on phonon-mediated local pairing. First, we examine the effects of modifying interaction range and lattice geometries with regard to analytical strong-coupling/non-adiabatic results for ladder systems. To test the applicability of the analytic results to experimentally achievable couplings and phonon frequencies, we apply a continuous time quantum Monte-Carlo algorithm (CTQMC) to the computation of the effective mass and pairing radius of lattice bipolarons. We demonstrate that bipolarons can be simultaneously small and light due to a novel crab-like motion. Such light, small bipolarons are a necessary precursor to high-temperature Bose-Einstein condensation in solids.

Journal of Physics Conference Series•Dec 1, 2007•4 citations

Temperature and quantum phonon effects on Holstein-Hubbard bipolarons

Martin Hohenadler, Wolfgang von der Linden

The one-dimensional Holstein-Hubbard model with two electrons of opposite spin is studied using an extension of a recently developed quantum Monte Carlo method and a very simple yet rewarding variational approach, both based on a canonically transformed Hamiltonian. The quantum Monte Carlo method yields very accurate results in the regime of small but finite phonon frequencies, characteristic of many strongly correlated materials, e.g., the cuprates and the manganites. The influence of electron-electron repulsion, phonon frequency, and temperature on the bipolaron state is investigated. Thermal dissociation of the intersite bipolaron is observed at high temperatures, and its relation to an existing theory of the manganites is discussed.

arXiv:cond-mat/0409573•Physical Review B•May 31, 2005•28 citations
ABSTRACT We investigate superlight pairing of bipolarons driven by electron‐phonon interactions (EPIs) in face‐center‐cubic (FCC) and body‐center‐cubic (BCC) lattices using a continuous‐time path‐integral quantum Monte Carlo (QMC) algorithm. The EPIs are of the Holstein and extended Holstein types, and a Hubbard interaction is also included. Effects of adiabaticity are calculated. The number of phonons associated with the bipolaron, inverse mass, and radius are calculated and used to construct a phase diagram for bipolaron pairing (identifying the regions of pairing into intersite bipolarons and onsite bipolarons). From the inverse mass we determine that for the extended interaction, there is a region of light pairing associated with intersite bipolarons formed in both BCC and FCC lattices. Intersite bipolarons in the extended model at intermediate phonon frequency and large Coulomb repulsion become superlight due to first order hopping effects. We estimate the transition temperature, determining that intersite bipolarons are associated with regions of high transition temperatures.
We present details of a continuous-time quantum Monte Carlo algorithm for the screened Hubbard-Fr\"ohlich bipolaron. We simulate the bipolaron in one dimension with arbitrary interaction range in the presence of Coulomb repulsion, computing the effective mass, binding energy, total number of phonons associated with the bipolaron, mass isotope exponent, and bipolaron radius in a comprehensive survey of the parameter space. We discuss the role of the range of the electron-phonon interaction, demonstrating the evolution from Holstein to Fr\"ohlich bipolarons and we compare the properties of bipolarons with singlet and triplet pairing. Finally, we present simulations of the bipolaron dispersion. The bandwidth of the Fr\"ohlich bipolaron is found to be broad and the decrease in bandwidth as the two polarons bind into a bipolaron is found to be far less rapid than in the case of the Holstein interaction. The properties of bipolarons formed from long-range electron-phonon interactions, such as light strongly bound bipolarons and intersite pairing when Coulomb repulsion is large, are found to be robust against screening, with qualitative differences between Holstein and screened Fr\"ohlich bipolarons found even for interactions screened within a single lattice site.
We study a lattice bipolaron on a staggered triangular ladder and triangular and hexagonal lattices with both long-range electron-phonon interaction and strong Coulomb repulsion using a novel continuous-time quantum Monte Carlo algorithm to solve the two-particle Coulomb-Fröhlich model. The algorithm is preceded by an exact integration over phonon degrees of freedom, and as such is extremely efficient. The bipolaron effective mass and radius are computed. Bipolarons on lattices constructed from triangular plaquettes have a novel crablike motion, and are small but very light over a wide range of parameters. We discuss the conditions under which such particles may form a Bose-Einstein condensate with high transition temperature, proposing a route to room temperature superconductivity.
We investigate the formation and condensation of fermion pairs in cold atom quantum simulators for extended Hubbard models (UV models) with body center cubic (BCC) optical lattices, predicting small and light pairs with Bose--Einstein condensation (BEC) temperatures up to the order of 100 nK. Pair mass, radius, and binding conditions are calculated, and then used to compute transition temperatures. We predict that: (a) local pairs can form in BCC optical lattices; (b) for particular cases where the onsite UUU and intersite V are attractive with similar size, the pairs are both small and light; and (c) that transition temperatures could be as high as 100 nK (50 nK) for 6Li atoms in blue (red) BCC optical lattices. Beyond the application to pairs on BCC optical lattices, we expect our results to be relevant to strong-coupling BCC superconductors.
We compute the properties of singlet and triplet bipolarons on two-dimensional lattices using the continuous-time quantum Monte Carlo algorithm. Properties of the bipolaron including the total energy, inverse mass, bipolaron radius, and number of phonons associated with the bipolaron demonstrate the qualitative difference between models of electron-phonon interaction with long-range interaction (screened Fr\"ohlich) and those with purely local (Holstein) interaction. A major result of our survey of the parameter space is the existence of extra-light hybrid singlet bipolarons consisting of an on-site and an off-site component on both square and triangular lattices. We also compute triplet properties of the bipolarons and the pair dispersion. For pair momenta on the edge of the Brillouin zone of the triangular lattice, we find that triplet states are more stable than singlets.
A finite-range Fröhlich electron-phonon interaction (EPI) with c-axis polarized optical phonons has been identified in cuprate superconductors by photoemission spectroscopy, in agreement with an earlier proposal by Alexandrov and Kornilovitch [1]. In this article, we discuss the consequences of long-range interactions on phonon-mediated local pairing. First, we examine the effects of modifying interaction range and lattice geometries with regard to analytical strong-coupling/non-adiabatic results for ladder systems. To test the applicability of the analytic results to experimentally achievable couplings and phonon frequencies, we apply a continuous time quantum Monte-Carlo algorithm (CTQMC) to the computation of the effective mass and pairing radius of lattice bipolarons. We demonstrate that bipolarons can be simultaneously small and light due to a novel crab-like motion. Such light, small bipolarons are a necessary precursor to high-temperature Bose-Einstein condensation in solids.
The one-dimensional Holstein-Hubbard model with two electrons of opposite spin is studied using an extension of a recently developed quantum Monte Carlo method and a very simple yet rewarding variational approach, both based on a canonically transformed Hamiltonian. The quantum Monte Carlo method yields very accurate results in the regime of small but finite phonon frequencies, characteristic of many strongly correlated materials, e.g., the cuprates and the manganites. The influence of electron-electron repulsion, phonon frequency, and temperature on the bipolaron state is investigated. Thermal dissociation of the intersite bipolaron is observed at high temperatures, and its relation to an existing theory of the manganites is discussed.