Singlet and triplet bipolarons on the triangular lattice

TL;DR

This paper investigates the properties of singlet and triplet bipolarons on a triangular lattice, revealing differences in their band structure and mass, and explores how electron-phonon coupling and retardation effects influence these states.

Contribution

It introduces a simplified model of crab bipolarons with angular momentum and compares singlet and triplet states using quantum Monte Carlo simulations.

Findings

Triplet states have flat bands and are significantly heavier than singlet states.

Quantum interference effects contribute to the increased mass of triplet bipolarons.

Retardation effects diminish differences between singlet and triplet states by affecting effective mass.

Abstract

We study the Coulomb-Fr\"ohlich model on a triangular lattice, looking in particular at states with angular momentum. We examine a simplified model of crab bipolarons with angular momentum by projecting onto the low energy subspace of the Coulomb-Fr\"ohlich model with large phonon frequency. Such a projection is consistent with large long-range electron-phonon coupling and large repulsive Hubbard $U$. Significant differences are found between the band structure of singlet and triplet states: The triplet state (which has a flat band) is found to be significantly heavier than the singlet state (which has mass similar to the polaron). We test whether the heavier triplet states persist to lower electron-phonon coupling using continuous time quantum Monte Carlo (QMC) simulation. The triplet state is both heavier and larger, demonstrating that the heavier mass is due to quantum interference effects on the motion. We also find that retardation effects reduce the differences between singlet and triplet states, since they reintroduce second order terms in the hopping into the inverse effective mass.