High correlation regime of the Hubbard model

Jakob Bernasconi

I. V. Sankar, Ashok Chatterjee

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.

Jakob Bernasconi

J. Vučičević, J. Kokalj, Rok Žitko +3 more

Calculating transport properties presents a great challenge in the study of strongly correlated electrons, particularly in two dimensions where the non-local processes and the vertex corrections are important, but remain poorly understood. We study the Hubbard model on the square lattice in the strongly correlated regime. We use several complementary state-of-the-art numerical methods to disentangle the different effects and resolve the problem conclusively at high temperatures. In this regime, non-local correlations and long-distance quantum fluctuations have little impact, yet the vertex corrections survive and substantially suppress resistivity. Our study becomes particularly relevant in the light of recent experiments on optical lattices that provide realizations of the two-dimensional Hubbard model in a similar parameter regime.

MANFRED L. RISTIG

Alexander Wietek, Jie Wang, Jiawei Zang +3 more

The moir\'e Hubbard model describes correlations in certain homobilayer twisted transition metal dichalcogenides. Using exact diagonalization and density matrix renormalization group methods, we find magnetic Mott insulating and metallic phases which, upon doping, exhibit intertwined charge and spin ordering and, in some regimes, pair binding of holes. The phases are highly tunable via an interlayer potential difference. Remarkably, the hole-binding energy is found to be highly tunable, revealing an experimentally accessible regime where holes become attractive. In this attractive regime, we study the superconducting correlation function and point out the possibility of weak superconductivity.