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arXiv:1607.05227 · Physical Review A

Stabilization of the chiral phase of the SU(6m) Heisenberg model on the honeycomb lattice with m particles per site for m larger than 1

Jérôme Dufour, Frédéric Mila

Published Sep 15, 2016• 5 citations
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Abstract

We show that, when $N$ is a multiple of 6 ($N=6m$, where $m$ is an integer), the $\mathrm{SU}\phantom{\rule{0.16em}{0ex}}{\left(N\right)}_{}$ Heisenberg model on the honeycomb lattice with $m$ particles per site has a clear tendency toward chiral order as soon as $m\ensuremath{\ge}2$. This conclusion has been reached by a systematic variational Monte Carlo investigation of Gutzwiller projected wave functions as a function of $m$ between the case of one particle per site ($m=1$), for which the ground state has recently been shown to be in a plaquette singlet state, and the $m\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, where a mean-field approach has established that the ground state has chiral order. This demonstrates that the chiral phase can indeed be stabilized for not too large values of $m$, opening the way to its experimental realizations in other lattices.

DOI
10.1103/physreva.94.033617

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We show that, when NNN is a multiple of 6 (N=6mN=6mN=6m, where mmm is an integer), the SU(N)\mathrm{SU}\phantom{\rule{0.16em}{0ex}}{\left(N\right)}_{}SU(N)​ Heisenberg model on the honeycomb lattice with mmm particles per site has a clear tendency toward chiral order as soon as m\ensuremath≥2m\ensuremath{\ge}2m\ensuremath≥2. This conclusion has been reached by a systematic variational Monte Carlo investigation of Gutzwiller projected wave functions as a function of mmm between the case of one particle per site (m=1m=1m=1), for which the ground state has recently been shown to be in a plaquette singlet state, and the m\ensuremath→\ensuremath∞m\ensuremath{\rightarrow}\ensuremath{\infty}m\ensuremath→\ensuremath∞ limit, where a mean-field approach has established that the ground state has chiral order. This demonstrates that the chiral phase can indeed be stabilized for not too large values of mmm, opening the way to its experimental realizations in other lattices.
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Conflicting predictions have been made for the ground state of the SU(3) Heisenberg model on the honeycomb lattice: Tensor network simulations found a plaquette order [Zhao et al., Phys. Rev. B 85, 134416 (2012)], where singlets are formed on hexagons, while linear flavor-wave theory suggested a dimerized, color-ordered state [Lee and Yang, Phys. Rev. B 85, 100402 (2012)]. In this work we show that the former state is the true ground state by a systematic study with infinite projected-entangled pair states (iPEPS), for which the accuracy can be systematically controlled by the so-called bond dimension DDD. Both competing states can be reproduced with iPEPS by using different unit cell sizes. For small DDD the dimer state has a lower variational energy than the plaquette state; however, for large DDD it is the latter which becomes energetically favorable. The plaquette formation is also confirmed by exact diagonalizations and variational Monte Carlo studies, according to which both the dimerized and plaquette states are nonchiral flux states.
The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the eg{e}_{g}eg​ Mott insulator Ba3CuSb2O9{\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}Ba3​CuSb2​O9​ and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantum spin-orbital liquid over a wide parameter regime around the SU(4)-symmetric point. For large Hund's coupling, a ferromagnetic antiferro-orbital ordered state appears, while a valence-bond crystal combined with a vortex orbital state is stabilized by dominant orbital-dependent exchange interactions.
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