Hidden Mott transition and large- U superconductivity in the two-dimensional Hubbard model

Abstract

We consider the one-band Hubbard model on the square lattice by using variational and Green's function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction U , we can identify a hidden critical point UMott, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Slater insulator (at small values of U ), where magnetism induces a potential energy gain, and a Mott insulator (at large values of U ), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of UMott has crucial consequences when doping the system: We observe a tendency to phase separation into a hole-rich and a hole-poor region only when doping the Slater insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above UMott, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above UMott shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.

Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard-Holstein model

“…In addition, we studied the effect of hole doping for both regimes where the half-filled ground state has either CDW or superconducting order. In the former case, a substantial phase separation is present at small dopings, resembling the case of a doped repulsive-U Hubbard [56][57][58][59][60][61][62]. In the latter case, instead, the ground state remains uniform with superconducting order.…”

“…When doping an antiferromagnet, phase separation could appear for small hole concentrations, as found in the repulsive-U Hubbard model, whenever the loss in the magnetic contribution to the total energy is larger than the gain due to the kinetic part. The presence of phase separation in the repulsive-U Hubbard model has been confirmed by different methods, even if its extension as a function of U is still controversial [56][57][58][59][60][61][62]. In order to highlight the possible presence of phase separation in the Hubbard-Holstein model, it is very useful to consider the so-called energy per hole [63]:…”

Signatures of the Mott transition in the antiferromagnetic state of the two-dimensional Hubbard model

“…An even more remarkable finding is apparent from Fig.1e, where ∆E pot is color coded for the AF region: the change of sign in ∆E pot (see sharp white region) that signals the crossover from weak to strong interactions occurs at the normal state Mott transition for T < T MIT , and continues for T > T MIT in a nontrivial crossover connecting the Mott endpoint to approximately T 45 find that ∆E pot crosses zero between U = 6 and U = 7 (see magenta circle at T = 0 in Fig. 1e).…”

“…Cluster extensions of DMFT are a way to include some of this momentum dependence. These methods and others have been used to study the AF phase [35][36][37][38][39][40][41][42][43][44] , but the influence of the normal-state Mott transition, if any, on the AF phase has been less investigated 45 and remains a challenge. Here, we contribute to decipher the interplay between Mott transition and AF by studying the finite temperature aspects of both normal and AF states of the half-filled 2D Hubbard model using a cluster extension of DMFT 32,40,46 .…”

Period 4 stripe in the extended two-dimensional Hubbard model

“…Meanwhile, the two-dimensional (2D) Hubbard model [33] -which has been suggested as the most elementary microscopic model that may reproduce the essential features of the cuprates' phase diagram -has been a prominent subject of intense theoretical and numerical investigations. Much attention has been given especially on the underdoped region in the strongly correlated regime, where several low-energy states are very closely competing, including a uniform d-wave superconducting (SC) state [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] and various stripe states [20][21][22][23][52][53][54][55][56][57][58][59][60][61] with or without coexisting superconducting order. A similar competition can also be found for the t − J model -the effective model in the strong coupling limit [62][63][64][65][66][67][68][69][70][71].…”