Hartree-Fock study of the magnetism in the single-band Hubbard model

Inui, M.; Littlewood, P. B.

doi:10.1103/physrevb.44.4415

Cited by 105 publications

(83 citation statements)

References 35 publications

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“…8 Such a behavior of ǫ indicates a fixed hole density of one hole per Ni ion in a DW, and is consistent with the HF predictions both in the single and in multiband models. 19,20,21,22,23,60,61,62 Finally, a fixed hole density along the DWs results in the pinning of the chemical potential µ for x ≤ 1/3, whereas a large (≃ 1 eV/hole) downward shift appears in the higher doping regime. 46 It is interesting to establish whether the above results concerning the stripe phases in the ground state and their variation under increasing doping appear solely in the realistic e g model, or they are generic and remain also a common feature of the DDH model with only diagonal hopping elements given by Eq.…”

Section: Ground State Energiesmentioning

confidence: 99%

“…Panels (a) and (b) in Figs. 11 and 12 show the DOS N α (ω) (23), projected on the orbital |x and |z , respectively. Here, one finds that the mid-gap bands have mainly |x character close to the gap between themthe |x orbitals optimize the kinetic energy of holes doped into them, whereas the vast majority of the more localized |z states of DW atoms belongs to the energy regimes within the LHB and close to the UHB.…”

Section: Densities Of Statesmentioning

confidence: 99%

“…In contrast, the HF approximation used here allows one to describe charge and spin modulation with larger unit cells and hence it should provide an answer to the important question whether the description of NiO 2 planes by the simplified effective e g model described below yields results consistent with the predictions of the CT model. 60,61,62 An important aspect of these studies, qualitatively different from the pioneering work on the cuprates where the relevant models yield DWs with nonmagnetic Cu 3+ ions, 19,20,21,22,23 is that DWs in the nickelates are formed of Ni 3+ ions carrying a finite spin S = 1/2 leading to a FM polarization around them.…”

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confidence: 99%

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Microscopic origin of diagonal stripe phases in doped nickelates

2006

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We investigate the electron density distribution and the stability of stripe phases in the realistic two-band model with hopping elements between eg orbitals at Ni sites on the square lattice, and compare these results with those obtained for the doubly degenerate Hubbard model with two equivalent orbitals and diagonal hopping. For both models we determine the stability regions of filled and half-filled stripe phases for increasing hole doping x = 2 − n in the range of x < 0.4, using Hartree-Fock approximation for large clusters. In the parameter range relevant to the nickelates, we obtain the most stable diagonal stripe structures with filling of nearly one hole per atom, as observed experimentally. In contrast, for the doubly degenerate Hubbard model the most stable stripes are somewhat reminiscent of the cuprates, with half-filled atoms at the domain wall sites. This difference elucidates the crucial role of the off-diagonal eg hopping terms for the stripe formation in La2−xSrxNiO4. The influence of crystal field is discussed as well. I. STRIPE PHASES IN NICKELATESStripe phases are one of the most exciting phenomena of modern condensed matter physics. They have been observed in a variety of systems, including nickelates, 1,2,3,4,5,6,7,8 cuprates, 9,10,11,12,13,14,15 and manganites. 16,17,18 Among them, layered La 2−x Sr x CuO 4 (LSCO), La 2−x−y Nd y Sr x CuO 4 (Nd-LSCO), La 2−x Sr x NiO 4 (LSNO), and La 2 NiO 4+δ (LNO) compounds play plausibly the most prominent role. However the similarity between them is superficial only, and the stripes in the cuprates differ from the stripes in the nickelates in many respects. For instance, they are dynamical in the former, and static in the latter. In addition, in Nd-LSCO 9,10,11,12,13,14 and LSCO, 15 one finds the so-called half-filled stripes, with the density of one doped hole per two atoms along the domain wall (DW). In contrast, it is clear from a variety of experiments that magnetic states within doped NiO 2 planes of the nickelates are filled stripes with density of one doped hole per one atom in a DW. 1,2,3,4,5,6,7,8 The question of filling is not the only difference between the nickelate and cuprate stripes, however. Neutron diffraction measurements performed on Nd-LSCO revealed that magnetic peaks are displaced from the antiferromagnetic (AF) maximum at Q AF = π(1, 1) to the points Q s = π(1 ± 2ǫ, 1) and Q s = π(1, 1 ± 2ǫ) and the shift ǫ depends linearly on hole doping x for x < 1/8, while it is almost constant at higher doping. These values correspond to a superposition of vertical (01) and horizontal (10) DWs. The essentially identical modulation and doping dependence of ǫ was observed in superconducting crystals of LSCO with x > 0.05. Conversely, experiments on LSNO established that spin order is characterized by the wave vectors Q s = π(1 ± ǫ, 1 ± ǫ) with ǫ ≃ x for x < 1/3, corresponding to a constant charge of one hole/Ni ion along a diagonal DW, in agreement with the predictions made in the pioneering works by Zaanen and Gunnarsson 19 and others, 20,21,...

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Section: Ground State Energiesmentioning

confidence: 99%

Section: Densities Of Statesmentioning

confidence: 99%

mentioning

confidence: 99%

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Microscopic origin of diagonal stripe phases in doped nickelates

2006

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“…As U increases, ξ 0 decreases, approaching a lattice spacing at larger values of U/t. Eventually, when U exceeds twice the bandwidth, the mean-field stripes disappear [7]. Note, however, that the Hartree-Fock treatments do not include pairing and that their energy per hole is of order 1t too high.…”

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confidence: 99%

Stripes on a 6-Leg Hubbard Ladder

2003

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While DMRG calculations find stripes on doped n-leg t-J ladders, little is known about the possible formation of stripes on n-leg Hubbard ladders. Here we report results for a 7×6 Hubbard model with 4 holes. We find that a stripe forms for values of U/t ranging from 6 to 20. For U/t ∼ 3 − 4, the system exhibits the domain wall feature of a stripe, but the hole density is very broadened. PACS numbers: PACSThe nature of the ground state of the two dimensional t-J model continues to be controversial, even if one restricts one's attention to numerical simulations. Density matrix renormalization group (DMRG) calculations [1] for n-leg t-J ladders (with n ranging from 2 to 8) with J/t in the physical region of interest for the cuprates, find that stripes are formed when the ladders are doped with holes [2]. In contrast, the Green's function Monte Carlo (GFMC) results of Sorella, et al., on square, periodic t-J lattices find a d x 2 −y 2 -wave superconducting ground state [3]. The aspect ratio of an n-leg lattice and the open boundary conditions used in the DMRG calculations may be sufficient to favor a striped state. Alternatively, the choice of the guiding trial wave function for the GFMC may bias the system towards a superconducting state [4]. It is clear that the t-J model is a delicately balanced system. Thus it is interesting to go back one step and study the underlying Hubbard model in which the onsite Coulomb interaction U is a parameter.Much less is known about the nature of the ground state of the 2D Hubbard model, which is computationally more demanding. Previous DMRG calculations[5] on 3-leg Hubbard ladders found that diagonal three-hole stripes with a linear filling density of unity formed when U/t was greater than 5. Early mean-field Hartree-Fock calculations for the 2D Hubbard model found that vertical stripes were favored for U/t less than of order 4 and diagonal stripes formed at larger values of U/t [6]. These Hartree-Fock stripes have a linear filling density of one and their width is set by a coherence length ξ 0 ∼ t/∆ 0 with ∆ 0 the gap of the half-filled system. As U increases, ξ 0 decreases, approaching a lattice spacing at larger values of U/t. Eventually, when U exceeds twice the bandwidth, the mean-field stripes disappear [7]. Note, however, that the Hartree-Fock treatments do not include pairing and that their energy per hole is of order 1t too high. Here, we extend the DMRG study of stripe formation in the Hubbard model and in particular examine the question of whether stripes form on a 6-leg Hubbard ladder and how their structure depends upon U/t. Our results represent the first reliable ground state results for a Hubbard cluster large enough to exhibit an unambiguous stripe. From this single cluster we are not able to make conclusions about the infinite 2D lattice; on the other hand, our results strongly suggest that stripes are low-lying states in the Hubbard model, as they are in the t-J model.The cluster geometry was chosen with some care. Stripe-like behavior involving only two holes c...

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“…One of the most important class of such competing orders are generalized "charge density" waves [5]. We use the phrase " charge density" in a very general sense, to imply any order parameter that is scalar under spin rotation and even under time reversal, and hence includes, e.g., stripes [6,7,8,9,10] and valence bond solids [11,12,13,14]. Non-magnetic impurities couple efficiently to these fluctuation since they break translational symmetry and like the "charge density" waves do not carry any spin.…”

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confidence: 99%

Imaging Bond Order near Nonmagnetic Impurities in Square-Lattice Antiferromagnets

et al. 2008

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We study the textures of generalized "charge densities" (scalar objects invariant under time reversal), in the vicinity of non-magnetic impurities in square-lattice quantum anti-ferromagnets, by order parameter field theories. Our central finding is the structure of the "vortex" in the generalized density wave order parameter centered at the non-magnetic impurity. Using exact numerical data from quantum Monte Carlo simulations on an antiferromagnetic spin model, we are able to verify the results of our field theoretic study. We extend our phenomenological approach to the period-4 bond-centered density wave found in the underdoped cuprates Introduction: The response of quantum many-body systems to impurities is a rich subject with important experimental consequences. At vanishingly small concentrations, the impurities behave independently and hence experimental measurements directly probe the physics of a single isolated impurity. The response of an otherwise translationally invariant quantum system to the introduction of a single quantum impurity can teach us fundamentally new things about many-body quantum physics; perhaps the most famous example is the introduction of magnetic impurities in non-magnetic metals, the so-called Kondo problem [1]. Although the role of single non-magnetic impurities is innocuous in conventional metals, it has been recognized that they can have profound consequences on strongly correlated quantum magnets, because the removal of a moment from the lattice results in an uncompensated Berry phase Even small amounts of frustration are known to lead to enhanced fluctuations of competing order parameters in quantum magnets. One of the most important class of such competing orders are generalized "charge density" waves [5]. We use the phrase " charge density" in a very general sense, to imply any order parameter that is scalar under spin rotation and even under time reversal, and hence includes, e.g., stripes [6,7,8,9,10] and valence bond solids [11,12,13,14]. Non-magnetic impurities couple efficiently to these fluctuation since they break translational symmetry and like the "charge density" waves do not carry any spin. Hence the response of a magnet to non-magnetic impurities contains important information about competing orders and their quantum fluctuations.In this paper we address the pattern of "charge density" modulations in real space around a non-magnetic impurity in square lattice anti-ferromagnets through order parameter field theories as well as exact quantum Monte Carlo (QMC) simulations. One of our central results, that we verify explicitly by QMC, is the de-

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Hartree-Fock study of the magnetism in the single-band Hubbard model

Cited by 105 publications

References 35 publications

Microscopic origin of diagonal stripe phases in doped nickelates

Microscopic origin of diagonal stripe phases in doped nickelates

Stripes on a 6-Leg Hubbard Ladder

Imaging Bond Order near Nonmagnetic Impurities in Square-Lattice Antiferromagnets

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