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arXiv:cond-mat/9801157 · Europhysics Letters (EPL)

Hole pairs in the two-dimensional Hubbard model

Enrique Louis, F. Guinea, María P. López-Sancho, José Antonio Vergés

Published Oct 15, 1998• 9 citations
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Abstract

The interactions between holes in the Hubbard model, in the low-density, inter mediate-to-strong coupling limit, are investigated. Dressed spin polarons in neighboring sites have an increased kinetic energy and an enhanced hopping rate. Both effects are of the order of the hopping integral and lead to an effective attraction at intermediate couplings. Our results are derived by systematically improving mean-field calculations. The method can also be used to derive known properties of isolated spin polarons.

DOI
10.1209/epl/i1998-00461-5

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The interactions between holes in the Hubbard model, in the low-density, inter mediate-to-strong coupling limit, are investigated. Dressed spin polarons in neighboring sites have an increased kinetic energy and an enhanced hopping rate. Both effects are of the order of the hopping integral and lead to an effective attraction at intermediate couplings. Our results are derived by systematically improving mean-field calculations. The method can also be used to derive known properties of isolated spin polarons.
The interactions between holes in the Hubbard model, in the low density, intermediate- to strong-coupling limit, are investigated by systematically improving mean field calculations. The configuration-interaction basis set is constructed by applying to local unrestricted Hartree-Fock configurations all lattice translations and rotations. It is shown that this technique reproduces, correctly, the properties of the Heisenberg model, in the limit of large U. Upon doping, dressed spin polarons in neighboring sites have an increased kinetic energy and an enhanced hopping rate. Both effects are of the order of the hopping integral and lead to an effective attraction at intermediate couplings. The numerical results also show that when more than two holes are added to the system, they do not tend to cluster, but rather hole pairs remain far apart. Hole-hole correlations are also calculated and shown to be in qualitative agreement with exact calculations for $4\ifmmode\times\else\texttimes\fi{}4$ clusters. In particular our results indicate that for intermediate coupling the hole-hole correlation attains a maximum when the holes are in the same sublattice at a distance of 2\sqrt{2}2​ times the lattice spacing, in agreement with exact results and the $t\ensuremath{-}J$ model. The method is also used to derive known properties of the quasiparticle band structure of isolated spin polarons.
The Holstein-Hubbard model is studied in two dimensions to explore the nature of polarons as a function of hole concentration in the strong correlation regime. A series of canonical transformations is performed to obtain an effective extended Hubbard model which, in the strong on-site electron-electron correlation regime, transforms into a t-J model and is solved using the mean-field Hartree-Fock approximation (HFA). It is shown that the hopping parameter which is related to the bandwidth of the polaron is very small for low (x ≈ 0) and high (x ≈ 1) hole concentrations whereas the hopping parameter is much larger for the intermediate hole concentrations.
A two-dimensional (2D) spin-up ideal Fermi gas interacting attractively with a spin-down impurity in the continuum undergoes, at zero temperature, a first-order phase transition from a polaron to a dimeron state. Here, we study a similar system on a square lattice, by considering the attractive 2D Fermi-Hubbard model with a single spin-down and a finite filling fraction of spin-up fermions. We study polaron and dimeron quasiparticle properties via variational ansatz up to one particle-hole excitation. Moreover, we develop a determinant diagrammatic Monte Carlo algorithm for this problem based on expansion in bare on-site coupling U . This algorithm turns out to be sign-problem-free at any filling of spin-up fermions, allowing one to sample very high diagram order (larger than 200 in our study) and to do simulations for large U / t (we go up to U / t = − 20 with t the hopping strength). Both methods give qualitatively consistent results. With variational ansatz we go to even larger on-site attraction. At very low spin-up filling fraction, we observe the polaron-to-dimeron transition, in agreement with the continuum case. Upon increasing the filling fraction, however, the transition shifts to higher values of | U | / t and the transition disappears beyond a filling fraction of about 20 % . In this region, the polaron state always gives a lower energy and has a finite quasiparticle residue. Our findings are directly relevant to cold atom experiments with 2D optical lattices: A small and finite density of spin-down impurities in the ground state will form a superfluid at strong coupling at low spin-up filling fraction. Above some critical spin-up filling fraction, the system is expected to remain a normal Fermi liquid, even in the strong-coupling limit.
We have used exact diagonalization and quantum Monte Carlo methods to study the one-dimensional t-J model including the three-site hopping term derived from the strong-coupling limit of the Hubbard model. The three-site term may be important to superconducting correlations since it allows direct hopping of local singlet electron pairs. The phase diagram is determined for several values of the strength of the three-site term and compared with that of the t-J and Hubbard models. Phase separation, which exists in the t-J model, is suppressed. In the low electron density region the formation of local singlet electron pairs is enhanced, leading to stronger superconducting correlations even for values J/t2. A large spin gap region extends from low electron densities up to high densities. In the low hole density region the superconducting correlations are suppressed at J/t>2.8 in spite of enhanced pair formation. This is because the three-site term, while enhancing the formation of electron pairs, leads to a repulsion between holes.
Intertwining of spin, charge, and pairing correlations in the repulsive two-dimensional Hubbard model is shown through unrestricted variational calculations, with projected wave functions free of symmetry breaking. A crossover from incommensurate antiferromagnetism to stripe order naturally emerges in the hole-doped region when increasing the on-site coupling. Although effective attractive pairing interactions are identified, they are strongly fragmented in several modes including ddd-wave pairing and more exotic channels related to an underlying stripe. We demonstrate that the entanglement of a mean-field wave function by symmetry restoration can largely account for interaction effects, and that our approach is exact for a two-site cluster.