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arXiv:2007.11963 · Physical review. B./Physical review. B

Doped Mott insulators in the triangular-lattice Hubbard model

Zheng Zhu, D. N. Sheng, Ashvin Vishwanath

Published May 10, 2022• 57 citations
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Abstract

We investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping $\ensuremath{\delta}$ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping $\ensuremath{\delta}\ensuremath{\lesssim}10%$, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well-defined Fermi surface. On further doping, $\ensuremath{\delta}\ensuremath{\approx}10%\ensuremath{\sim}20%$ SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping $\ensuremath{\delta}\ensuremath{\gtrsim}20%$, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.

DOI
10.1103/physrevb.105.205110

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We investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping \ensuremathδ\ensuremath{\delta}\ensuremathδ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping \ensuremathδ\ensuremath≲10\ensuremath{\delta}\ensuremath{\lesssim}10%\ensuremathδ\ensuremath≲10, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well-defined Fermi surface. On further doping, \ensuremathδ\ensuremath≈10\ensuremath{\delta}\ensuremath{\approx}10%\ensuremath{\sim}20%\ensuremathδ\ensuremath≈10 SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping \ensuremathδ\ensuremath≳20\ensuremath{\delta}\ensuremath{\gtrsim}20%\ensuremathδ\ensuremath≳20, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.
We use unrestricted Hartree-Fock, density matrix renormalization group, and variational projected entangled-pair state calculations to investigate the ground-state phase diagram of the triangular-lattice Hubbard model at “half doping” relative to single occupancy, i.e., at fillings of ( 1 ± 1 2 ) electrons per site. The electron-doped case has a nested Fermi surface in the noninteracting limit, and hence a weak-coupling instability toward density-wave orders whose wave vectors are determined by Fermi-surface nesting conditions. We find that at moderate-to-strong interaction strengths, other spatially modulated orders arise, with wave vectors distinct from the nesting vectors. In particular, we identify a series of closely competing, itinerant long-wavelength magnetically ordered states, yielding to uniform ferromagnetic order at the largest interaction strengths. For half-hole doping and a similar range of interaction strengths, our data indicate that magnetic orders are most likely absent.
Understanding ferromagnetism mechanism in doped Mott insulators on frustrated lattices remains challenging at intermediate coupling and finite doping. Here, we study the itinerant ferromagnetism and propose its mechanism in doped Mott insulators on a geometrically frustrated triangular lattice. Using large-scale density matrix renormalization group (DMRG) and unrestricted Hartree–Fock mean-field methods, we reveal that itinerant ferromagnetism appears at intermediate coupling (10 ≲ U ≪ ∞) near 50% electron doping in the triangular-lattice Hubbard model. By analyzing all microscopic hopping processes, we find that doublon-singlon exchange alone drives the fully polarized ferromagnetism and uncovers the particle-hole asymmetry. We also establish the magnetic phase diagram and compare local spin correlations with recent experiments. Random phase approximation and DMRG calculations consistently confirm that the ferromagnetism persists when SU(2) symmetry is explicitly broken by magnetic anisotropy. These results clarify a microscopic route to itinerant ferromagnetism at intermediate coupling and finite doping in doped Mott insulators. Understanding the mechanism of ferromagnetism in strongly correlated systems is an ongoing theoretical challenge and the Hubbard model is typically adopted to investigate such systems. Here, the authors numerically investigate the doped triangular Fermi-Hubbard model and show ferromagnetism at intermediate coupling and finite doping, which results from the interplay of kinetic doublon-singlon exchange and lattice geometry.
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Two-dimensional density-matrix renormalization group method is employed to examine the ground-state phase diagram of the Hubbard model on the triangular lattice at half-filling. The calculation reveals two discontinuities in the double occupancy with increasing the repulsive Hubbard interaction UUU at ${U}_{\mathrm{c}1}\ensuremath{\sim}7.8t$ and ${U}_{\mathrm{c}2}\ensuremath{\sim}9.9t$ (ttt being the hopping integral), indicating that there are three phases separated by first-order transitions. The absence of any singularity in physical quantities for $0\ensuremath{\le}U<{U}_{\mathrm{c}1}$ implies a metallic phase in this regime. For U>Uc2U>{U}_{\mathrm{c}2}U>Uc2​, the local spin density induced by an applied pinning magnetic field exhibits a three sublattice feature, which is compatible with the ${120}^{\ensuremath{\circ}}$ N\'eel-ordered state realized in the limit of $U\ensuremath{\rightarrow}\ensuremath{\infty}$. For Uc1<U<Uc2{U}_{\mathrm{c}1}<U<{U}_{\mathrm{c}2}Uc1​<U<Uc2​, a response to the applied pinning magnetic field is comparable to that in the metallic phase with a relatively large spin correlation length, but showing neither valence bond nor chiral magnetic order, which therefore resembles gapless spin liquid. However, the spin structure factor for the intermediate phase exhibits the maximum at the K\mathrm{K}K and ${\mathrm{K}}^{\ensuremath{'}}$ points in the momentum space, which is not compatible to spin liquid with a large spinon Fermi surface. The calculation also finds that the pairing correlation function monotonically decreases with increasing UUU and thus the superconductivity is unlikely in the intermediate phase.