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Spin density wave selection in the one-dimensional Hubbard model

Samson, J.H.

Published Jan 1, 1995• 2 citations
OpenAlex

Abstract

The Hartree-Fock ground state phase diagram of the one-dimensional Hubbard model is calculated, constrained to uniform phases, which have no charge density modulation. The allowed solutions are saturated ferromagnetism (FM), a spiral spin density wave (SSDW) and a double spin density wave} (DSDW). The DSDW phase comprises two canted interpenetrating antiferromagnetic sublattices. FM occurs for small filling, SSDW in most of the remainder of the phase diagram, and DSDW in a narrow tongue near quarter (and three-quarter) filling. Itinerant electrons lift the degeneracy with respect to canting angle in the DSDW. The Hartree-Fock states are metallic except at multiples of a quarter filling. Near half filling the uniform SSDW phase is unstable against phase separation into a half-filled antiferromagnetic phase and a hole-rich SSDW phase. The dependence of the ground state wave number on chemical potential is conjectured to be a staircase. Comparison is made with higher dimensional Hubbard models and the $J_{1}-J_{2}$ Heisenberg model.

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Spin density wave selection in the one-dimensional Hubbard model

J H Samson

The Hartree - Fock ground-state phase diagram of the one-dimensional Hubbard model is calculated, constrained to uniform phases, which have no charge density modulation. The allowed solutions are saturated ferromagnetism (FM), a spiral spin density wave (SSDW) and a double spin density wave (DSDW). The DSDW phase comprises two canted interpenetrating antiferromagnetic sublattices. FM occurs for small filling, SSDW in most of the remainder of the phase diagram, and DSDW in a narrow tongue near quarter (and three-quarter) filling. Itinerant electrons lift the degeneracy with respect to canting angle in the DSDW. The Hartree - Fock states are metallic except at multiples of a quarter filling. Near half filling the uniform SSDW phase is unstable against phase separation into a half-filled antiferromagnetic phase and a hole-rich SSDW phase. The dependence of the ground-state wave number on chemical potential is conjectured to be a staircase. Comparison is made with higher-dimensional Hubbard models and the Heisenberg model.

arXiv:cond-mat/9511116•Journal of Physics Condensed Matter•Jan 29, 1996•1 citation

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Fengming Hu, Sanjoy Kumar Sarker, Ciriyam Jayaprakash

We study, within the Hartree-Fock approximation, the relative stability of different classes of states for the single-band Hubbard model on a square lattice in the presence of a nearest-neighbor Coulomb repulsion V and away from half-filling. We consider (i) homogeneous metallic states (including spiral phases), (ii) states that exhibit phase separation into hole-rich and antiferromagnetic regions, and (iii) insulating (longitudinally polarized) spin-density-wave states with domain walls that trap holes. For V=0, the spiral states have the lowest energy for hole concentration \ensuremath{\delta}>${\mathrm{\ensuremath{\delta}}}_{\mathit{s}}$. At ${\mathrm{\ensuremath{\delta}}}_{\mathit{s}}$\ensuremath{\sim}0.25--0.3, there is a transition to domain walls for small to intermediate U/t. At larger U/t the transition is to a phase-separated state, with ${\mathrm{\ensuremath{\delta}}}_{\mathit{s}}$ decreasing slowly with increasing U/t. We find that even a small V destabilizes the domain walls relative to the spiral states; e.g., for V/t\ensuremath{\sim}0.2, the domain-wall states are unstable for all U/t and all \ensuremath{\delta}\ensuremath{\ge}0.05. The effect of V on the phase-separated state is much less drastic; its region of stability relative to the spiral states also shrinks to smaller \ensuremath{\delta}, but rather slowly. The last results are in agreement with the findings from a Schwinger-boson treatment of the t-J model.

Physical review. B, Condensed matter•Dec 15, 1994•11 citations
The Hartree-Fock ground state phase diagram of the one-dimensional Hubbard model is calculated, constrained to uniform phases, which have no charge density modulation. The allowed solutions are saturated ferromagnetism (FM), a spiral spin density wave (SSDW) and a double spin density wave} (DSDW). The DSDW phase comprises two canted interpenetrating antiferromagnetic sublattices. FM occurs for small filling, SSDW in most of the remainder of the phase diagram, and DSDW in a narrow tongue near quarter (and three-quarter) filling. Itinerant electrons lift the degeneracy with respect to canting angle in the DSDW. The Hartree-Fock states are metallic except at multiples of a quarter filling. Near half filling the uniform SSDW phase is unstable against phase separation into a half-filled antiferromagnetic phase and a hole-rich SSDW phase. The dependence of the ground state wave number on chemical potential is conjectured to be a staircase. Comparison is made with higher dimensional Hubbard models and the J1−J2J_{1}-J_{2}J1​−J2​ Heisenberg model.
The Hartree - Fock ground-state phase diagram of the one-dimensional Hubbard model is calculated, constrained to uniform phases, which have no charge density modulation. The allowed solutions are saturated ferromagnetism (FM), a spiral spin density wave (SSDW) and a double spin density wave (DSDW). The DSDW phase comprises two canted interpenetrating antiferromagnetic sublattices. FM occurs for small filling, SSDW in most of the remainder of the phase diagram, and DSDW in a narrow tongue near quarter (and three-quarter) filling. Itinerant electrons lift the degeneracy with respect to canting angle in the DSDW. The Hartree - Fock states are metallic except at multiples of a quarter filling. Near half filling the uniform SSDW phase is unstable against phase separation into a half-filled antiferromagnetic phase and a hole-rich SSDW phase. The dependence of the ground-state wave number on chemical potential is conjectured to be a staircase. Comparison is made with higher-dimensional Hubbard models and the Heisenberg model.
The Hartree-Fock ground-state phase diagram of the one-dimensional Hubbard model is calculated in the μ−Uμ-Uμ−U plane, restricted to phases with no charge density modulation, extending the results presented in cond-mat/9511116. This allows antiferromagnetism, saturated ferromagnetism, spiral spin density waves and a collinear structure with unit cell ↑↑↓↓\uparrow \uparrow \downarrow \downarrow↑↑↓↓. The spiral phase is unstable against phase separation near quarter-, half- and three-quarter-filling. For large UUU this occurs at hole (or electron) doping of (3t/π2U)1/3(3t/π^{2}U)^{1/3}(3t/π2U)1/3 from half filling.
Tle Hartree-Fock ground-state phase diagram of the one-dimensional Hubbard model is calculated in the μ-U plane, restricted to phases with no charge density modulation.This allows antiferromagnetism, saturated ferromagnetism, spiral spin density waves and a collinear structure with unit cell H e i s e n b e r g s .T h e s p i r a l p h a s e i s u n s t a b l e a g a i n s t p h a s e s e p a r a t i o n n e a r quarter-, half-and three-quarter-flling.For large U this occurs at hole (or electron) doping of (3t/π2U)1/3 from half-filling.
We studied ferromagnetism in the one-dimensional Hubbard model with doubly degenerate atomic orbitals by means of the density-matrix renormalization-group method and obtained the ground-state phase diagrams. It was found that ferromagnetism is stable from low to high (0<n<1.75)(0<n<1.75)(0<n<1.75) electron density when the interactions are sufficiently strong. The quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the interorbital interaction ${U}^{\ensuremath{'}}\ensuremath{-}J$ is attractive. At quarter-filling (n=1),(n=1),(n=1), the insulating ferromagnetic state appears, accompanying orbital quasi-long-range order. For low densities (n<1),(n<1),(n<1), ferromagnetism occurs owing to the ferromagnetic exchange interaction caused by virtual hoppings of electrons, the same as in the quarter-filled system. This comes from separation of the charge and spin-orbital degrees of freedom in the strong-coupling limit. This ferromagnetism is fragile against variation of band structure. For high densities (n>1),(n>1),(n>1), the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative for stabilizing the ferromagnetic order and this long-range order is robust against variation of the band dispersion. A partially polarized state appears in the density region $1.68\ensuremath{\lesssim}n\ensuremath{\lesssim}1.75$ and phase separation occurs for n just below the half-filling (n=2).(n=2).(n=2).
We study, within the Hartree-Fock approximation, the relative stability of different classes of states for the single-band Hubbard model on a square lattice in the presence of a nearest-neighbor Coulomb repulsion V and away from half-filling. We consider (i) homogeneous metallic states (including spiral phases), (ii) states that exhibit phase separation into hole-rich and antiferromagnetic regions, and (iii) insulating (longitudinally polarized) spin-density-wave states with domain walls that trap holes. For V=0, the spiral states have the lowest energy for hole concentration \ensuremath{\delta}>${\mathrm{\ensuremath{\delta}}}_{\mathit{s}}$. At ${\mathrm{\ensuremath{\delta}}}_{\mathit{s}}$\ensuremath{\sim}0.25--0.3, there is a transition to domain walls for small to intermediate U/t. At larger U/t the transition is to a phase-separated state, with ${\mathrm{\ensuremath{\delta}}}_{\mathit{s}}$ decreasing slowly with increasing U/t. We find that even a small V destabilizes the domain walls relative to the spiral states; e.g., for V/t\ensuremath{\sim}0.2, the domain-wall states are unstable for all U/t and all \ensuremath{\delta}\ensuremath{\ge}0.05. The effect of V on the phase-separated state is much less drastic; its region of stability relative to the spiral states also shrinks to smaller \ensuremath{\delta}, but rather slowly. The last results are in agreement with the findings from a Schwinger-boson treatment of the t-J model.