Three-body problem in a multiband Hubbard model

Abstract

We first apply functional-integral approach to a multiband Hubbard model near the critical pairing temperature, and derive a generic effective action that is quartic in the fluctuations of the pairing order parameter. Then we consider time-reversal-symmetric systems with uniform (i.e., at both low-momentum and low-frequency) pairing fluctuations in a unit cell, and derive the corresponding time-dependent Ginzburg-Landau (TDGL) equation. In addition to the conventional intraband contribution that depends on the derivatives of the Bloch bands, we show that the kinetic coefficients of the TDGL equation have a geometric contribution that is controlled by both the quantum-metric tensor of the underlying Bloch states and their band-resolved quantum-metric tensors. Furthermore we show that thermodynamic properties such as London penetration depth, GL coherence length, GL parameter and upper critical magnetic field have an explicit dependence on quantum geometry.

Dimers, trimers, tetramers, and other multimers in a multiband Bose-Hubbard model

“…However, since Eq. ( 8) is formally identical to that of the two-fermion case, we skip their detailed analysis here and refer the reader to the recent literature [2,3]. Just like the fermion problem, it can be shown that, by representing Eq.…”

“…The three-body bound states can be determined by the integral Eq. ( 9) through an iterative procedure [3]. Instead, in order to reveal the full three-body spectrum, where we recast Eq.…”

“…However, since almost all of the studies in the literature are about single-band lattices, the effects of multiple bands have entirely been overlooked. For instance while dimers have long been known to be the only possible bound state between identical (i.e., equal-mass) fermions in a single-band lattice [1], the energetic stability of trimers, tetramers and some other multimers have recently been shown in the presence of multiple Bloch bands [2][3][4]. It is conceivable that there may not even be an upper bound on the size of the possible multimers when they are formed in a flat band, albeit with smaller and smaller binding energies [4].…”

Effect of a flat band on a multiband two-dimensional Lieb lattice with intra- and interband interactions

“…The Hubbard model provides a theoretical framework to study multiband systems, and serves as a protoypical model for studying electron-electron interactions and electron itinerancy [16][17][18]. The Hubbard model incorporates a tight-binding term to describe electron hopping between lattice sites and a local Coulomb interaction term to account for electron-electron interactions.…”