Magnetic excitations, phase diagram and order-by-disorder in the extended triangular-lattice Hubbard model

Abstract

The dynamical structure factor is an important observable of quantum magnets but due to numerical and theoretical limitations, it remains a challenge to make predictions for Hubbard-like models beyond one dimension. In this work, we study the magnetic excitations of the triangular lattice Hubbard model including next-nearest neighbor hopping. Starting from the 120${}^{\circ }$ and stripe magnetic orders we compute the magnon spectra within a self-consistent random phase approximation. In the stripe phase, we generically find accidental zero modes related to a classical degeneracy known from the corresponding $J_1$-$J_2$ Heisenberg model. We extend the order-by-disorder mechanism to Hubbard systems and show how quantum fluctuations stabilize the stripe order. In addition, the frustration-induced condensation of magnon modes allows us to map out the entire phase diagram which is in remarkable agreement with recent numerical works. We discuss connections to experiments on triangular lattice compounds and the relation of our results to the proposed chiral spin liquid phase.

arXiv comment10 pages, 6 figures

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• Dynamical Signatures of Symmetry Broken and Liquid Phases in an $S=1/2$ Heisenberg Antiferromagnet on the Triangular Lattice
• Probing magnetism in moiré heterostructures with quantum twisting microscopes
• Extended Hubbard model describing small multi-dot arrays in bilayer graphene
• Dynamical response theory of interacting Majorana fermions and its application to generic Kitaev quantum spin liquids in a field
• Electric field control of a quantum spin liquid in weak Mott insulators
• Kinetic Ferromagnetism and Topological Magnons of the Hole-Doped Kitaev Spin Liquid
• Magnetism and superconductivity in doped triangular-lattice Mott insulators