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arXiv:1911.03518 · Physical review. B./Physical review. B

Interaction-driven topological phase transitions in fermionic SU(3) systems

Mohsen Hafez-Torbati, Jun-Hui Zheng, Bernhard Irsigler, Walter Hofstetter

Published Jun 25, 2020• 21 citations
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Abstract

We consider SU(3) fermions on the triangular lattice in the presence of a gauge potential which stabilizes a quantum Hall insulator (QHI) at the density of one particle per lattice site. We investigate the effect of the Hubbard interaction, favoring magnetic long-range order, and a three-sublattice potential (TSP), favoring a normal insulator (NI), on the system. For a weak TSP we find that the Hubbard interaction drives the QHI into a three-sublattice magnetic Mott insulator (MMI). For intermediate values of the TSP we identify two transition points upon increasing the Hubbard interaction. The first transition is from the NI to the QHI and the second transition is from the QHI to the MMI. For large values of the TSP a charge-ordered magnetic insulator (COMI) emerges between the NI and the QHI, leading to an interaction-driven COMI-to-QHI transition.

DOI
10.1103/physrevb.101.245159

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We consider SU(3) fermions on the triangular lattice in the presence of a gauge potential which stabilizes a quantum Hall insulator (QHI) at the density of one particle per lattice site. We investigate the effect of the Hubbard interaction, favoring magnetic long-range order, and a three-sublattice potential (TSP), favoring a normal insulator (NI), on the system. For a weak TSP we find that the Hubbard interaction drives the QHI into a three-sublattice magnetic Mott insulator (MMI). For intermediate values of the TSP we identify two transition points upon increasing the Hubbard interaction. The first transition is from the NI to the QHI and the second transition is from the QHI to the MMI. For large values of the TSP a charge-ordered magnetic insulator (COMI) emerges between the NI and the QHI, leading to an interaction-driven COMI-to-QHI transition.
Topological Criticality with Charge-3e3e3e Fluctuations in the SU(3)\mathrm{SU}(3)SU(3) Triangular-Lattice Hofstadter--Hubbard Model
A transition between an integer quantum Hall insulator and a chiral spin liquid can become critical without closing the single-electron gap, raising the question of which composite excitations govern the change in topological order. We investigate this question in the SU(3)\mathrm{SU}(3)SU(3) triangular-lattice Hofstadter--Hubbard model at one particle per site and magnetic flux π/3π/3π/3 per triangle. Using infinite density matrix renormalization group calculations, we identify a weak-coupling integer quantum Hall phase and an interaction-driven SU(3)1\mathrm{SU}(3)_1SU(3)1​ chiral spin liquid. Near the transition, both the neutral and charge-3e3e3e correlation lengths increase substantially, whereas the single-electron correlation length remains short, providing evidence for a Chern--Simons--Higgs critical theory, where a gauge-invariant monopole carries the quantum numbers of a fermionic SU(3)\mathrm{SU}(3)SU(3)-singlet trion. We discuss the implications for doping the system and recent experiments on doping ν=−2/3ν=-2/3ν=−2/3 fractional quantum anomalous Hall in tMoTe2_22​.
We consider the fermionic SU(3)\mathrm{SU}(3)SU(3) Hubbard model on the triangular lattice at 1/31/31/3 filling in the presence of a three-sublattice staggered potential which provides the possibility to investigate the competition of charge and magnetic order in three-component systems. We show that, depending on the strength of the staggered potential $\mathrm{\ensuremath{\Delta}}$, the Hubbard interaction UUU destabilizes the band insulator at small UUU into the Mott insulator at large UUU in three different ways with different intermediate phases. This leads to a rich phase diagram in the $U\text{\ensuremath{-}}\mathrm{\ensuremath{\Delta}}$ plane. Our results indicate that multicomponent systems show not only exotic states in the Mott regime as has been considered previously, but also interesting competition between charge and magnetic orders which can lead to the emergence of charge-ordered magnetic insulators and charge-ordered magnetic metals.
We study the interplay between topological and conventional long-range order of attractive fermions in a time-reversal-symmetric Hofstadter lattice using quantum Monte Carlo simulations, focusing on the case of one-third flux quantum per plaquette. At half filling, the system is unstable towards sss-wave pairing and charge-density-wave order at infinitesimally small interactions. At one-third filling, the noninteracting system is a topological insulator, and a nonzero critical interaction strength is needed to drive a transition from the quantum spin Hall insulator to a superfluid. We probe the topological signature of the phase transition by threading a magnetic flux through a cylinder and observe quantized topological charge pumping.
We study the interplay between topological and conventional long range order of attractive fermions in a time reversal symmetric Hofstadter lattice using quantum Monte Carlo simulations, focussing on the case of one-third flux quantum per plaquette. At half-filling, the system is unstable towards s-wave pairing and charge-density-wave order at infinitesimally small interactions. At one-third-filling, the noninteracting system is a topological insulator, and a nonzero critical interaction strength is needed to drive a transition from the quantum spin Hall insulator to a superfluid. We probe the topological signature of the phase transition by threading a magnetic flux through a cylinder and observe quantized topological charge pumping.
We develop a self-consistent variant of the constrained path quantum Monte Carlo approach which ensures its independence of the trial wave function, and apply the method to compute ground-state correlations in the two-dimensional SU(3) Fermi-Hubbard Hamiltonian at 13\frac{1}{3}31​ filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We provide clear evidence of a quantum critical point separating a nonmagnetic uniform metallic phase from a regime where long-range ``spin'' order is present. This discovery of multiple successive transitions to magnetic states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases, significantly extends previous work in the Heisenberg limit to itinerant fermions. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model, while preserving the square-lattice geometry. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU(N)\mathrm{SU}(N)SU(N) physics.
Motivated by recent progress in the realization of artificial gauge fields and SU(NNN) Mott insulators using alkaline-earth-like atoms in optical lattices, we develop an unbiased SU(NNN) real-space dynamical mean-field theory approach to study the effect of spin-orbit coupling and on-site Hubbard interaction UUU on SU(3) fermionic systems. We investigate the behavior of the local magnetization, double occupancies, and the triple occupancy versus the Hubbard interaction across the metal to Mott insulator transition. We map out the magnetic phase diagram in the large-UUU limit and show that the spin-orbit coupling can stabilize long-range orders such as ferromagnets, spirals, and stripes with different orientations in SU(3) Mott insulators.