Comment on “Absence of a Slater Transition in the Two-Dimensional Hubbard Model”

Kyung, Bumsoo; Landry, Jean‐Sébastien; Poulin, David; Tremblay, A.–M. S.

doi:10.1103/physrevlett.90.099702

Cited by 46 publications

(49 citation statements)

References 3 publications

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“…On the contrary, for large U/t, magnetism is favored by the super-exchange coupling J = 4t 2 /U and consequently drives a kinetic energy gain, leading to the so-called Mott magnetism. The crossover between these two regimes has been investigated by many authors in the past: Even if it has been proposed that the Slater mechanism is absent in the Hubbard model 56 , successive works show a general consensus on the existence of a sharp crossover between the two regimes, with the precise location of it depending on the method of investigation [57][58][59][60][61][62] .…”

Section: A the Half-filled Casementioning

confidence: 99%

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

2016

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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.

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Section: A the Half-filled Casementioning

confidence: 99%

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

2016

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“…It yields [11] a splitting into two bands and may lead to an energy gap in the charge excitations spectrum. Another mechanism for a charge gap formation has been proposed [18,19] recently in the 2D Hubbard model with t ′ = 0 at weak coupling. The band splitting phase is developed in the region of electron concentration around half-filling, and is one of the strongest in that region.…”

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confidence: 99%

Pomeranchuk and other instabilities in thet−t′Hubbard model at the Van Hove filling

2002

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We present a stability analysis of the two-dimensional t − t ′ Hubbard model for various values of the next-nearest-neighbor hopping t ′ , and electron concentrations close to the Van Hove filling by means of the flow equation method. For t ′ ≥ −t/3 a d x 2 −y 2 -wave Pomeranchuk instability dominates (apart from antiferromagnetism at small t ′ ). At t ′ < −t/3 the leading instabilities are a g-wave Pomeranchuk instability and p-wave particle-hole instability in the triplet channel at temperatures T < 0.15t, and an s * -magnetic phase for T > 0.15t; upon increasing the electron concentration the triplet analog of the flux phase occurs at low temperatures. Other weaker instabilities are found also.PACS numbers: 71.10. Fd, 71.27.+a, 74.20.Rp, 75.10.Lp In recent years the two-dimensional (2D) Hubbard model has been used [1,2] as the simplest model which maps the electron correlations in the copper-oxide planes of high-temperature superconductors since experimental data suggest that superconductivity in cuprates basically originates from the CuO 2 layers [3]. Although in the high-temperature cuprate superconductors electron-electron interactions are strong some important features of these systems (in particular, antiferromagnetic and d-wave superconducting instabilities) are captured already by the 2D Hubbard model at weak to moderate Coulomb coupling.Apart from the antiferromagnetism and d x 2 −y 2 -wave superconductivity mentioned above (for review see [1, 2, 4] and references therein), a few other instabilities related to symmetry-broken states [5,6,7,8,9,10,11] in the 2D t − t ′ Hubbard model with next-nearest-neighbor hopping t ′ have been reported recently. Specially, much interest of researchers has been attracted by the case when the Fermi surface passes through the saddle points of the single particle dispersion (Van Hove filling). One of the instabilities found in such a case is a d-wave Pomeranchuk instability breaking the tetragonal symmetry of the Fermi surface, i.e. a spontaneous deformation of the Fermi surface reducing its symmetry to orthorhombic. It has been recently observed for small values of t ′ from renormalization group calculations by Halboth and Metzner [5]. They argued that the Pomeranchuk instability occurs more easily if the Fermi surface is close to the saddle points with a sizable t ′ (reducing nesting which leads to antiferromagnetism). However, within their technique it is difficult to compare the strength of the Fermi surface deformation with other instabilities and to conclude which one dominates. The authors of Ref.[10] have investigated the interplay of d-density wave [12,13] and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism by means of a similar temperature-flow renormalization group approach. They have found that the d-wave Pomeranchuk instability never dominates in the 2D t − t ′ Hubbard model (even under the conditions mentioned above). On the other hand, Vollhardt et al. [14] showed that the t ′ -hopping term destroys the an...

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“…Indeed if one forces the symmetry and follow the paramagnetic CDMFT solution inside the AF region a pseudo-gap opens because of the Slater mechanism. Some previous work have focused on increasing the cluster size [8,9]. The Néel temperature then decreases to 0, but the T = 0 AF order can still induce long range fluctuations at finite temperature and open a pseudo-gap.…”

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“…Let us first focus on the unfrustrated case (t ′ = 0) at half-filling (See also [8,9,10,11]). We computed the Néel temperature, corresponding to the continuous onset of an antiferromagnetic solution, as a function of U .…”

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Cluster Dynamical Mean Field Analysis of the Mott Transition

2004

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We investigate the Mott transition using a cluster extension of dynamical mean field theory (DMFT). In the absence of frustration we find no evidence for a finite temperature Mott transition. Instead, in a frustrated model, we observe signatures of a finite temperature Mott critical point in agreement with experimental studies of κ−organics and with single site DMFT. As the Mott transition is approached, a clear momentum dependence of the electron lifetime develops on the Fermi surface with the formation of cold regions along the diagonal direction of the Brillouin zone. Furthermore the variation of the effective mass is no longer equal to the inverse of the quasi particle residue, as in DMFT, and is reduced approaching the Mott transition.

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Comment on “Absence of a Slater Transition in the Two-Dimensional Hubbard Model”

Cited by 46 publications

References 3 publications

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

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

Pomeranchuk and other instabilities in thet−t′Hubbard model at the Van Hove filling

Cluster Dynamical Mean Field Analysis of the Mott Transition

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