From the Hubbard to a Plaquette Boson-Fermion Model for Cuprates

Zhe Chang

Sebastian Will

Ehud Altman, Assa Auerbach

The strongly interacting Hubbard model on the square lattice is reduced to the low energy plaquette boson fermion model (PBFM). The four bosons (an antiferromagnon triplet and a d-wave hole pair), and the fermions are defined by the lowest plaquette eigenstates. We apply the contractor renormalization method of Morningstar and Weinstein to compute the boson effective interactions. The range-3 truncation error is found to be very small, signaling short hole-pair and magnon coherence lengths. The pair-hopping and magnon interactions are comparable, which explains the rapid destruction of antiferromagnetic order with emergence of superconductivity, and validates a key assumption of the projected SO(5) theory. A vacuum crossing at larger doping marks a transition into the overdoped regime. With hole fermions occupying small Fermi pockets and Andreev coupled to hole pair bosons, the PBFM yields several testable predictions for photoemission, tunneling asymmetry, and entropy measurements.

Michael Danilov, Erik G. C. P. van Loon, Sergey Brener +3 more

Abstract We study the physics of high-temperature cuprate superconductors starting from the highly degenerate four-site plaquette of the $$t-t^{\prime} -U$$ t − t ′ − U Hubbard model as a reference system. The degeneracy causes strong fluctuations when a lattice of plaquettes is constructed. We show that there is a large binding energy between holes when a set of four plaquettes is considered. The next-nearest-neighbour hopping $$t^{\prime}$$ t ′ plays a crucial role in the formation of these strongly bound electronic bipolarons whose coherence at lower temperature could be the explanation for superconductivity. A complementary approach is cluster dual fermion starting from a single degenerate plaquette, which contains the relevant short-ranged fluctuations from the beginning. It gives d-wave superconductivity as the leading instability under a reasonably broad range of parameters. The origin of the pseudogap is also discussed in terms of the coupling of degenerate plaquettes. Thus, some of the essential elements of cuprate superconductivity appear from the local plaquette physics.

Silvia B. Bacci, Eduardo R. Gagliano, Richard M. Martin

Chia-Min Chung, Mingpu Qin, Shiwei Zhang +2 more

The Hubbard model and its extensions are important microscopic models for understanding high-${T}_{c}$ superconductivity in cuprates. In the model with next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ (the ${t}^{\ensuremath{'}}$-Hubbard model), pairing is strongly influenced by ${t}^{\ensuremath{'}}$. In particular, a recent study on a width-4 cylinder observed quasi-long-range superconducting order, associated with a negative ${t}^{\ensuremath{'}}$, which was taken to imply superconductivity in the two-dimensional (2D) limit. In this work we study more carefully pairing in the width-$4\phantom{\rule{4pt}{0ex}}{t}^{\ensuremath{'}}$-Hubbard model. We show that in this specific system, the pairing symmetry with ${t}^{\ensuremath{'}}<0$ is not the ordinary $d$-wave one would expect in the 2D limit. Instead we observe a so-called plaquette $d$-wave pairing. We show that the plaquette $d$-wave or its extension is difficult to generalize in other geometries, for example a 4-leg ladder with open boundaries or a width-6 cylinder. We find that a negative ${t}^{\ensuremath{'}}$ suppresses the conventional $d$-wave, leading to plaquette pairing. In contrast, a different ${t}^{\ensuremath{'}\ensuremath{'}}$ coupling acting diagonally on the plaquettes suppresses plaquette pairing, leading to conventional $d$-wave pairing.