Phase diagram of the anisotropic triangular lattice Hubbard model

Abstract

In a recent study [Phys. Rev. X 10, 021042 (2020)], we showed using large-scale density matrix renormalization group (DMRG) simulations on infinite cylinders that the triangular lattice Hubbard model has a chiral spin liquid phase. In this work, we introduce hopping anisotropy in the model, making one of the three distinct bonds on the lattice stronger or weaker compared with the other two. We implement the anisotropy in two inequivalent ways, one which respects the mirror symmetry of the cylinder and one which breaks this symmetry. In the full range of anisotropy, from the square lattice to weakly coupled one-dimensional chains, we find a variety of phases. Near the isotropic limit we find the three phases identified in our previous work: metal, chiral spin liquid, and 120${}^{\circ }$ spiral order; we note that a recent paper suggests the apparently metallic phase may actually be a Luther-Emery liquid, which would also be in agreement with our results. When one bond is weakened by a relatively small amount, the ground state quickly becomes the square lattice Néel order. When one bond is strengthened, the story is much less clear, with the phases that we find depending on the orientation of the anisotropy and on the cylinder circumference. While our work is to our knowledge the first DMRG study of the anisotropic triangular lattice Hubbard model, the overall phase diagram we find is broadly consistent with that found previously using other methods, such as variational Monte Carlo and dynamical mean field theory.

arXiv commentv3: Added data regarding incommensurate spiral order using flux insertion, 20 pages, 6 figures, plus 23 pages (35 figures) Supplemental Material; v2: Slightly increased parameter space resolution for largest cylinder; v1: 19 pages, 6 figures, plus 22 pages (34 figures) Supplemental Material

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• Ground-state and thermodynamic properties of the spin-$\frac{1}{2}$ Heisenberg model on the anisotropic triangular lattice
• Magnetic excitations, phase diagram and order-by-disorder in the extended triangular-lattice Hubbard model
• Chiral spin liquid and quantum phase diagram of spin-$1/2$ $J_1$-$J_2$-$J_{\chi }$ model on the square lattice
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• How quantum phases on cylinders approach the 2d limit
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