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Quantum spin structures and phase separation in the Hubbard model

Zahid Asghar

Published Jul 1, 2001• 0 citations
OpenAlex

Abstract

In this thesis we focus on a systematic study of the ground state of the one-dimensional one-band Hubbard model in the Hartree-Fock approximation. Phases with non-uniform charge density and states with coexisting phases separated by a domain wall are included in the study. We calculate the full Hartree-Fock phase diagram for uniform and non-uniform phases, and we show that at particular electron densities the uniform phase is unstable to phase separation. Supercell calculations are carried out, and we use the computational minimisation procedure to calculate the Hartree-Fock energies for the self-consistent spin configurations. (author)

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In this thesis we focus on a systematic study of the ground state of the one-dimensional one-band Hubbard model in the Hartree-Fock approximation. Phases with non-uniform charge density and states with coexisting phases separated by a domain wall are included in the study. We calculate the full Hartree-Fock phase diagram for uniform and non-uniform phases, and we show that at particular electron densities the uniform phase is unstable to phase separation. Supercell calculations are carried out, and we use the computational minimisation procedure to calculate the Hartree-Fock energies for the self-consistent spin configurations. (author)
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 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.
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 authors use an unrestricted self-consistent mean-field approach to the one-dimensional periodic Hubbard model to study its ground-state phase diagram. Their approach allows one to incorporate spin and electron correlations as well as spin and charge fluctuations. The authors find that a homogeneous antiferromagnetic state exists only at half-filling, where the state is also insulating. Off half-filling, it was found that the ground state of the Hubbard model consists of clusters with different magnetic and charge properties. For certain values of the parameters of the system the cluster formation develops to a full phase separation. The effects of the intersite repulsive or attractive interaction on the ground-state properties were also examined. Implications of the authors results for the existence of a superconducting ground state as well as comparison with other studies will be briefly discussed.