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

TL;DR

This study investigates magnetic excitations and phase stability in the extended triangular-lattice Hubbard model, revealing how quantum fluctuations influence magnetic order and mapping the phase diagram consistent with recent numerical findings.

Contribution

It extends the order-by-disorder mechanism to Hubbard systems and provides a detailed phase diagram including magnetic excitations and degeneracy lifting.

Findings

Quantum fluctuations stabilize stripe order.

Accidental zero modes relate to classical degeneracy.

Phase diagram aligns with recent numerical results.

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.