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arXiv:cond-mat/0006439 · Journal of the Physical Society of Japan

Doped Two Orbital Chains with Strong Hund's Rule Couplings - Ferromagnetism, Spin Gap, Singlet and Triplet Pairings

Beat Ammon, Masatoshi Imada

Published Feb 15, 2001• 10 citations
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Abstract

Different models for doping of two-orbital chains with mobile $S=1/2$ fermions and strong, ferromagnetic (FM) Hund's rule couplings stabilizing the S=1 spins are investigated by density matrix renormalization group (DMRG) methods. The competition between antiferromagnetic (AF) and FM order leads to a rich phase diagram with a narrow FM region for weak AF couplings and strongly enhanced triplet pairing correlations. Without a level difference between the orbitals, the spin gap persists upon doping, whereas gapless spin excitations are generated by interactions among itinerant polarons in the presence of a level difference. In the charge sector we find dominant singlet pairing correlations without a level difference, whereas upon the inclusion of a Coulomb repulsion between the orbitals or with a level difference, charge density wave (CDW) correlations decay slowest. The string correlation functions remain finite upon doping for all models.

DOI
10.1143/jpsj.70.547

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Different models for doping of two-orbital chains with mobile S=1/2S=1/2S=1/2 fermions and strong, ferromagnetic (FM) Hund's rule couplings stabilizing the S=1 spins are investigated by density matrix renormalization group (DMRG) methods. The competition between antiferromagnetic (AF) and FM order leads to a rich phase diagram with a narrow FM region for weak AF couplings and strongly enhanced triplet pairing correlations. Without a level difference between the orbitals, the spin gap persists upon doping, whereas gapless spin excitations are generated by interactions among itinerant polarons in the presence of a level difference. In the charge sector we find dominant singlet pairing correlations without a level difference, whereas upon the inclusion of a Coulomb repulsion between the orbitals or with a level difference, charge density wave (CDW) correlations decay slowest. The string correlation functions remain finite upon doping for all models.
Doping of a two-orbital chain with mobile S=1/2 Fermions and strong Hund's rule couplings stabilizing the S=1 spins strongly depends on the presence of a level difference among these orbitals. By DMRG methods we find a finite spin gap upon doping and dominant pairing correlations without level-difference, whereas the presence of a level difference leads to dominant charge density wave (CDW) correlations with gapless spin-excitations. The string correlation function also shows qualitative differences between the two models.
We investigate the doping of a two-orbital chain with mobile S=1/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2S=1/2 fermions as a valid model for ${\mathrm{Y}}_{2\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{BaNiO}}_{5}$. The S=1S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1S=1 spins are stabilized by strong, ferromagnetic Hund's rule couplings. We calculate correlation functions and thermodynamic quantities by density matrix renormalization group methods and find a new hierarchy of energy scales in the spin sector upon doping. Gapless spin excitations are generated at a lower energy scale by interactions among itinerant polarons created by each hole and coexist with the larger scale of the gapful spin-liquid background of the S=1S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1S=1 chain accompanied by a finite string order parameter.
We study itinerant hole doping of the spin-111 Haldane symmetry-protected topological (SPT) phase in two ttt--JJJ chains coupled by ferromagnetic (FM) Hund exchange. Density-matrix renormalization group calculations show that string order, a finite spin gap, and the Haldane entanglement structure coexist over a broad doping range. Combined with entanglement-entropy scaling consistent with a single gapless charge mode, these results support a metallic doped Haldane SPT with a C1S0C1S0C1S0 low-energy description. At low doping, short-range charge correlations reduce the density of spin-1/21/21/2 defect rungs, whereas at larger doping their positions become nearly uncorrelated while their spins are collectively incorporated into the correlated spin sector. The doped Haldane SPT terminates in a fully spin-polarized FM phase, which forms a reentrant pocket at high doping in the global phase diagram. Dilute-limit analyses trace the two FM boundaries to spin--charge factorization at weak Hund coupling and to rung-triplet binding with reduced pair mobility at strong Hund coupling. Our results show how mobile carriers reorganize the Haldane spin structure while preserving its characteristic signatures.
We investigate the pairing tendencies in the hole-doped Haldane spin-1 chain. To allow for doping, we extend the original spin chain Hamiltonian into a fermionic model involving a two-orbital Hubbard chain at intermediate or strong repulsive interaction strengths UUU and for degenerate orbitals. At half filling and large UUU, the ferromagnetic Hund's coupling, JH{J}_{\mathrm{H}}JH​, generates effective spin-1 moments, with antiferromagnetic correlations between sites. Using large-scale density matrix renormalization group calculations, we accurately study the system's behavior under light hole-doping. For U=1.6U=1.6U=1.6 in units of the noninteracting bandwidth and for ${J}_{\mathrm{H}}/U\ensuremath{\gtrsim}0.275$, we find that singlet pairing dominates the long-distance physics, establishing this system as a promising platform for repulsively mediated superconductivity. We provide concrete examples of materials that could realize the physics described here. We also provide evidence that the system approaches a Luther-Emery liquid state at large system sizes, reminiscent of the behavior of doped one-orbital two-leg ladders at weak coupling, which also have superconducting tendencies. The numerically calculated central charge approaches one in the thermodynamic limit, indicating a single gapless mode as is expected for the Luther-Emery state. Exponents characterizing the power-law decays of singlet pair-pair and charge density-density correlations are determined, and found to approximately satisfy the Luther-Emery identity.
We study the ground-state properties of the double-chain Hubbard model coupled with ferromagnetic exchange interaction by using the weak-coupling theory, density-matrix renormalization-group technique, and Lanczos exact-diagonalization method. We determine the ground-state phase diagram in the parameter space of the ferromagnetic exchange interaction and band filling. We find that, in high electron-density regime, the spin gap opens and the spin-singlet dxy{d}_{xy}dxy​-wave-like pairing correlation is most dominant, whereas in low electron-density regime, the fully-polarized ferromagnetic state is stabilized where the spin-triplet py{p}_{y}py​-wave-like pairing correlation is most dominant.
A broad class of correlated quantum materials features strong Hund’s coupling, yet cold-atom quantum simulators have so far focused primarily on single-orbital Fermi-Hubbard systems near a Mott insulator. Here, we show that repulsively interacting fermions loaded into the p bands of a hexagonal lattice offer a unique platform to study the interplay of “Hundness” and “Mottness.” Our theory predicts that the orbital degrees of freedom, despite geometric frustration, produce a rich phase diagram featuring a competing itinerant ferromagnetic (FM) metal and a spin-1 antiferromagnetic (AFM) insulator. While FM order is known to emerge at low fillings near the flat-band limit, we show that this itinerant ferromagnetism is remarkably robust, persisting to stronger interactions and higher fillings well beyond the flat-band regime. More importantly, we identify that near half filling, FM is stabilized by a different mechanism: the double exchange with spins aligning to avoid Hund-rule penalties at the expense of the kinetic energy of Dirac fermions. The competition between the kinetic and double-exchange energies leads to, within our approximations, a first-order transition between FM and AFM orders in the chemical potential-interaction strength plane. Our analysis suggests that p -orbital Fermi gases—as multiorbital systems with coexisting localized and itinerant spins—reveal a rich competition between correlated “Hund metals” and other unconventional states driven by quantum fluctuations.