Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

Competition between Vertical and Diagonal Stripes in the Hartree-Fock Approximation

Marcin Raczkowski

Published Jan 1, 2003• 1 citation
Publisher

Abstract

Using the Hartree‐Fock approximation we analyze the properties and stability of the filled (one doped hole per stripe site) vertical stripes (VS) and diagonal stripes (DS), found in the two‐dimensional Hubbard model at two representative doping levels x = 1/8 and x = 1/6, by varying the ratio of the on‐site Coulomb repulsion U to the hopping element t. In the weak coupling regime of U ∼ 3.5t the stability of VS is best explained by the solitonic mechanism which leads to the kinetic energy gain due to the hopping perpendicular to the stripes, while DS have a lower potential energy which explains their stability in the regime of large U. The results obtained beyond the Hubbard model are shortly reviewed as well.

DOI
10.1063/1.1612397

Related papers

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

Enrique Louis, F. Guinea, María P. López-Sancho +1 more

The internal structure of stripes in the two-dimensional Hubbard model is studied by going beyond the Hartree-Fock approximation. Partially filled stripes with inhomogeneous magnetization and charge along the stripe core, consistent with experimental observations, are stabilized by quantum fluctuations, included through the configuration interaction method. Similar configurations result to be stable for filled stripes, and have a lower energy than the standard paramagnetic core solution. Away from half-filling, solitonlike solutions show up within the Hartree-Fock approximation. The hopping of short regions of the stripes in the transverse direction is comparable to the bare hopping element. The hole-hole correlation shows maxima along the stripe direction, while the integrated value of ${n}_{\stackrel{\ensuremath{\rightarrow}}{k}}$ compares satisfactorily with experimental results.

arXiv:cond-mat/0007319•Physical review. B, Condensed matter•Nov 6, 2001•4 citations

Stability of metallic stripes in the one-band extended Hubbard model

G. Seibold, J. Lorenzana

Based on an unrestricted Gutzwiller approximation (GA) we investigate static stripe configurations with regard to the orientation and periodicity in an extended one-band Hubbard model. A negative ratio between next-nearest-neighbor and nearest-neighbor hoppings, ${t}^{\ensuremath{'}}/t,$ as appropriate for cuprates, favors partially filled (metallic) stripes for both vertical and diagonal configurations. At around optimal doping diagonal stripes and site centered (SC) and bond centered (BC) vertical stripes become degenerate suggesting strong lateral and orientational fluctuations. We find that within the GA the resulting phase diagram is in agreement with experiment whereas it is not in the Hartree-Fock approximation due to a strong overestimation of the stripe filling. Results are in agreement with previous calculations within the three-band Hubbard model but with the role of SC and BC stripes interchanged.

arXiv:cond-mat/0307636•Physical Review B•Apr 21, 2004•43 citations

Diagonal Stripe States in the Light-doping Region in the Two-dimensional Hubbard Model

Mitake Miyazaki, Takashi Yanagisawa, Yamaji K.

We studied the ground state of the two-dimensional Hubbard model near half filling on the square lattice. Using Variational Monte Carlo method, we show that the diagonal stripe state of bond-centered type, in which the domain wall is located between two sites, becomes more stable than the vertical stripe state when the doping hole density x is as low as x ≃0.06. The inverse of stripe periodicity δ and the hole density x are observed to have the relationship δ∼ x (δ< x ) for the bond-centered diagonal stripe state (the vertical stripe state) in the light-doping region. These results are in good agreement with elastic neutron scattering experiments in La 2- x Sr x CuO 4 .

Journal of the Physical Society of Japan•Jul 15, 2004•34 citations

Holes and Magnetic Textures in the Two-Dimensional Hubbard Model

A. R. Bishop, F. Guinea, Peter S. Lomdahl +2 more

The Hubbard model in a two-dimensional square lattice is studied within the unrestricted Hartree-Fock approximation. A wide variety of solutions are found, as a function of filling and value of the Coulomb repulsion. Their properties range from those of magnetic polarons to a behavior similar to electrons in an external magnetic field (flux phases). The main features of the vortex solution are studied. It is shown that its energy increases logarithmically with system size, and that it becomes more stable for high values of the Coulomb repulsion and doping levels. Also, multivortex configurations are shown to exist. The implications of our results in the qualitative behavior of the Hubbard model as function of doping and strength of the interaction are discussed.

Europhysics Letters (EPL)•Jan 15, 1991•39 citations

Stripe Orders in the Extended Hubbard Model

Taira Kato, Masaru Kato

We study stripe orders of charge and spin density waves in the extended Hubbard model with the nearest-neighbor Coulomb repulsion V within the mean field approximation. We obtain V vs. T(temperature) phase diagram for the on-site Coulomb interaction U/t=8.0 and the filling n=0.8, here t is a nearest-neighbor transfer energy. Our result shows that the diagonal stripe spin density wave state (SDW) is stable for small V, but for large V the most stable state changes to a charge density wave-antiferromagnetic (CDW-AF) state. Especially we find at low temperature and for a certain range of value of V, a vertical stripe CDW-AF state becomes stable.

arXiv:cond-mat/0003347•Journal of the Physical Society of Japan•Dec 15, 2000•8 citations

Ground-state properties of the Hubbard model by Lanczos diagonalizations

Federico Becca, Alberto Parola, Sandro Sorella

We investigate the Hubbard model on a two-dimensional cluster of 18 sites using Lanczos algorithm for different strengths of Coulomb repulsion in the low doping region. Energies and correlation functions are given for half-filling and two holes. In the strong coupling regime we compare our results with the $t\ensuremath{-}J$ model. We confirm the tendency of holes to repel, although a significant value of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductive order parameter is measured. These data represent a benchmark for future quantum simulations.

Physical review. B, Condensed matter•Jun 15, 2000•27 citations
Using the Hartree‐Fock approximation we analyze the properties and stability of the filled (one doped hole per stripe site) vertical stripes (VS) and diagonal stripes (DS), found in the two‐dimensional Hubbard model at two representative doping levels x = 1/8 and x = 1/6, by varying the ratio of the on‐site Coulomb repulsion U to the hopping element t. In the weak coupling regime of U ∼ 3.5t the stability of VS is best explained by the solitonic mechanism which leads to the kinetic energy gain due to the hopping perpendicular to the stripes, while DS have a lower potential energy which explains their stability in the regime of large U. The results obtained beyond the Hubbard model are shortly reviewed as well.
The internal structure of stripes in the two-dimensional Hubbard model is studied by going beyond the Hartree-Fock approximation. Partially filled stripes with inhomogeneous magnetization and charge along the stripe core, consistent with experimental observations, are stabilized by quantum fluctuations, included through the configuration interaction method. Similar configurations result to be stable for filled stripes, and have a lower energy than the standard paramagnetic core solution. Away from half-filling, solitonlike solutions show up within the Hartree-Fock approximation. The hopping of short regions of the stripes in the transverse direction is comparable to the bare hopping element. The hole-hole correlation shows maxima along the stripe direction, while the integrated value of ${n}_{\stackrel{\ensuremath{\rightarrow}}{k}}$ compares satisfactorily with experimental results.
Based on an unrestricted Gutzwiller approximation (GA) we investigate static stripe configurations with regard to the orientation and periodicity in an extended one-band Hubbard model. A negative ratio between next-nearest-neighbor and nearest-neighbor hoppings, ${t}^{\ensuremath{'}}/t,$ as appropriate for cuprates, favors partially filled (metallic) stripes for both vertical and diagonal configurations. At around optimal doping diagonal stripes and site centered (SC) and bond centered (BC) vertical stripes become degenerate suggesting strong lateral and orientational fluctuations. We find that within the GA the resulting phase diagram is in agreement with experiment whereas it is not in the Hartree-Fock approximation due to a strong overestimation of the stripe filling. Results are in agreement with previous calculations within the three-band Hubbard model but with the role of SC and BC stripes interchanged.
We studied the ground state of the two-dimensional Hubbard model near half filling on the square lattice. Using Variational Monte Carlo method, we show that the diagonal stripe state of bond-centered type, in which the domain wall is located between two sites, becomes more stable than the vertical stripe state when the doping hole density x is as low as x ≃0.06. The inverse of stripe periodicity δ and the hole density x are observed to have the relationship δ∼ x (δ< x ) for the bond-centered diagonal stripe state (the vertical stripe state) in the light-doping region. These results are in good agreement with elastic neutron scattering experiments in La 2- x Sr x CuO 4 .
The Hubbard model in a two-dimensional square lattice is studied within the unrestricted Hartree-Fock approximation. A wide variety of solutions are found, as a function of filling and value of the Coulomb repulsion. Their properties range from those of magnetic polarons to a behavior similar to electrons in an external magnetic field (flux phases). The main features of the vortex solution are studied. It is shown that its energy increases logarithmically with system size, and that it becomes more stable for high values of the Coulomb repulsion and doping levels. Also, multivortex configurations are shown to exist. The implications of our results in the qualitative behavior of the Hubbard model as function of doping and strength of the interaction are discussed.
We study stripe orders of charge and spin density waves in the extended Hubbard model with the nearest-neighbor Coulomb repulsion V within the mean field approximation. We obtain V vs. T(temperature) phase diagram for the on-site Coulomb interaction U/t=8.0 and the filling n=0.8, here t is a nearest-neighbor transfer energy. Our result shows that the diagonal stripe spin density wave state (SDW) is stable for small V, but for large V the most stable state changes to a charge density wave-antiferromagnetic (CDW-AF) state. Especially we find at low temperature and for a certain range of value of V, a vertical stripe CDW-AF state becomes stable.
We investigate the Hubbard model on a two-dimensional cluster of 18 sites using Lanczos algorithm for different strengths of Coulomb repulsion in the low doping region. Energies and correlation functions are given for half-filling and two holes. In the strong coupling regime we compare our results with the $t\ensuremath{-}J$ model. We confirm the tendency of holes to repel, although a significant value of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductive order parameter is measured. These data represent a benchmark for future quantum simulations.