Partially filled stripes in the two-dimensional Hubbard model:  Statics and dynamics

Abstract

The internal structure of stripes in the two dimensional Hubbard model is studied by going beyond the Hartree-Fock approximation. Partially filled stripes, consistent with experimental observations, are stabilized by quantum fluctuations, included through the Configuration Interaction method. Hopping of short regions of the stripes in the transverse direction is comparable to the bare hopping element. The integrated value of n k compares well with experimental results.By now it is well established that charged stripes are formed in a significant doping range of cuprate oxides [1][2][3]. The existence of these stripes was predicted, on the basis of mean field calculations, in advance of its observation, both in the one [4][5][6][7] and the three bands Hubbard model [8]. This is one of the scarce theoretical results in the field of high-T c superconductivity which was confirmed after its prediction. Interest in these calculations decreased, as it was generally understood that the Hartree-Fock approximation was unable to obtain the partially filled stripes observed experimentally. Unrelated calculations found stripes with different fillings in the t-J model [9], and, using different techniques, in the Hubbard model [10], although other numerical calculations show conflicting results [11,12]. Alternatively, it has been argued that stripes in doped Mott antiferromagnets arise from a tendency towards phase separation, frustrated by electrostatic interactions [13,14]. Stripes in the Hubbard model have also been analyzed within slaveboson techniques, which use the Hartree-Fock solutions as input [15].In the present work we show that the mean field calculations, initially used to demonstrate the existence of stripes, can be systematically improved in order to study the partially filled stripes observed experimentally. In addition, they provide significant insight into the internal structure of the stripes and their fluctuations in the transverse direction. The Hartree-Fock method can be considered a quasiclassical approximation to the spin and charge degrees of freedom. Their low amplitude quantum fluctuations can be incorporated by using the Random Phase Approximation [16]. In addition, one needs to consider quantum tunneling processes between degenerate, or nearly degenerate, Hartree-Fock solutions, when there are many. This is achieved with the Configuration Interaction method (CI), widely used in quantum chemistry [17,18]. The combination of the Hartree-Fock and CI methods gives reasonable results even when applied to one dimensional systems [19]. The CI method restores the symmetries broken by the Hartree-Fock approximation, and provides information on the quantum dynamics of the static solutions obtained in mean field, which can be broadly classified into spin polarons or stripes.Previous mean field studies have focused on filled stripes [7], which tend to be the solutions with the lowest energy per hole in this approximation, especially for the values of U/t ∼ 4 used in the initial studies [4][5][6][7]. There are,...

Stripe order, depinning, and fluctuations inLa1.875Ba0.125CuO4andFujita1, Goka2, Yamada3 et al. 2004Phys. Rev. B325453581View full textAdd to dashboardCite

“…74,75,76,77,78 A first-principles calculation for 1 8 -doped LSCO using the LDA+U method yields bondcentered charge stripes 79 ; the superexchange interactions calculated within the hole-poor ladders are comparable to what we have obtained from measurements of the magnetic excitations in LBCO at higher energies. 49 Thus, there is growing theoretical support for the concept of stripe correlations as a natural consequence of doping holes into an antiferromagnetic insulator.…”

Lattice anisotropy as the microscopic origin of static stripes in cuprates

“…[62][63][64] In this approach, the ground state is constructed as a (biased) linear combination of HF solutions. This technique, which has already been applied to certain aspects of the isotropic Hubbard model, 63,51 can be shown to give a systematic description of quantum fluctuation and tunneling corrections to the HF solution, and of the quantum dynamics of the excitations.…”

“…4(b)) hole distribution within such a stripe, one may expect the latter to be favored by increasing U . Some analytical 29,51 and numerical 31 studies have addressed the issue of the additional physics which may be responsible for this result. Here we have found that hopping anisotropy represents an additional factor which may contribute to the stability of non-uniform, half-filled stripes.…”

Slave-boson based configuration-interaction approach for the Hubbard model

“…These results are now used for evaluating groundstate energy and wave-function corrections similar to the configuration-interaction approach based on unrestricted HF wave-functions. 21 We apply the method to the investigation of spin-polaron states on a square lattice, i.e., we have one hole with respect to half filling. Minimization of the KR ͑or GA͒ energy functional leads to the localization of this hole at a given site R ␣ ͑cf.…”

“…Now we have to deal again with the problem that the z-factors as defined in Eqs. (17) do not yield the uncorrelated limit, i.e. z αβ i,σ = z αβ i,σ → 1 for U → 0.…”