Fractionalization from Kinetic Frustration in Doped Two-Dimensional SU(4) Quantum Magnets

Abstract

Separating electrons into emergent fractional quasiparticles is a hallmark of exotic quantum phases of matter with strong interactions. Understanding under which circumstances fractionalized excitations appear is a major conceptual challenge and can help realize long sought-after states, such as quantum spin liquids. Here, we identify a distinct mechanism for fractionalization. Starting from the plaquette-ordered ground state of an SU(4) symmetric t-J model at quarter filling on frustrated triangular lattices, we reveal a compelling interplay between order and fractionalization as a function of doping. For hole doping, we find that the kinetic frustration can be relieved by fractionalizing the holes into fermionic spinons and bosonic holons: the holons minimize their kinetic energy when the spinons form a spinon Fermi surface. We support this mechanism analytically in the large-N limit as well as numerically by simulating the SU(4) case with matrix product states on cylinder geometries and with variational Monte Carlo methods on system sizes up to 40x40. Conversely, electron doping drives the system into a ferromagnetic phase, akin to Nagaoka's theorem. We discuss possible experimental realizations in moiré heterostructures as well as ultracold atoms, and propose dynamical probes to search for key characteristics of the fractionalized quasiparticles.

Figures (9)

• Figure 1: Kinetic frustration in the SU(4)-symmetric $t$-$J$ model.a) In a Mott insulator with one electron per site, the SU(4)-symmetric model Eq. \ref{['eq::Heisenberg_SU4']} on a triangular lattice breaks translational invariance. Hole doping this state in the limit of infinite interactions leads to a state where bosonic holons (red) move freely in an SU(4) symmetric background of fermionic spinons (four flavors represented by different shades of blue). b) SU(4) spin correlations on nearest-neighbor bonds of the doped state are antiferromagnetic. Bond colors are proportional to $\langle \mathcal{S}_{i} \cdot \mathcal{S}_{j} \rangle$. c) The electronic momentum distribution $n_e(\mathbf{k})$ shows a large Fermi surface on top of a constant background for small hole doping $\delta = 1/21$. Presented data are obtained with SU(4)-symmetric matrix product states with a U(1)-equivalent bond dimension of $D=36000$ on infinite 5-leg cylinders (green dashed line in b).
• Figure 2: Spinon Fermi surface.a) Single-particle dispersion $\varepsilon(\mathbf{k})$ and Fermi surfaces for several fillings $\nu=1/N$. On a triangular lattice, they are approximately circular for sufficiently large $N$. b) A parton mean-field approach predicts that the electronic momentum distribution $n_e(\mathbf{k})$ is given by a convolution of the spinon Fermi surface and the holon distribution, see Eq. \ref{['eq::convolution']}. We show mean-field values of the cylinder geometry studied numerically in Fig. \ref{['fig::kinetic_magnetism']} to facilitate their comparison. c) The SU(4) structure factor $\mathcal{S}(\mathbf{k})$ for the same geometry along distinct momentum cuts for a parton mean field (green), variational Monte Carlo (red), and MPS with several bond dimensions up to 36000 (blue).
• Figure 3: Central charge of quasi-1D matrix product states. We fit the central charge from the slope of Eq. \ref{['eq::central_charge']} for infinite MPS simulations of several bond dimensions up to $D=36000$ for different simulated cylinder geometries with spiral boundary conditions SC5 (dark blue) and SC3 (light blue). The insets show the allowed momenta in the hexagonal Brillouin zone (solid lines). The MPS transfer matrix yields the largest correlation lengths in the charge-neutral sector, indicated by the index $\xi_0$. Consistent with a spinon Fermi surface (SFS; green dashed lines), each cut through the Fermi surface contributes an SU(4) fermionic mode with $c=3$ to the total central charge. Contrary, a paramagnetic Fermi liquid (FL) at dopings $\delta =1/21$ ($1/25$) would yield a central charge $c=4$ for both cylinder geometries due to the small Fermi surface (red dashed lines). For better visualization, we added a constant to $S$ for the SC3 cylinder.
• Figure 4: Stability of the spinon Fermi surface state at finite $t/J$. From variational Monte Carlo sampling (VMC), we estimate the critical hopping strengths $t_c/J$ by analyzing the competition between kinetic energy, favoring the spinon Fermi surface, and interaction energy, favoring SU(4) plaquettes, for several dopings and system sizes (green color intensity). We estimate the phase diagram in the regime of low dopings and strong interactions. The dashed line represents a fit $t_c/J = \mathrm{const.}/\delta$ to the VMC data. For interactions $t/J\lesssim 1$ (not shown), a full Hubbard description is necessary instead of the $t$-$J$ model to capture other metallic phases.
• Figure 5: Experimental realization and signatures.a) A trilayer heterostructure of TMDs to realize an approximately SU(4)-symmetric Hubbard model. Lattice mismatches between the top and bottom layers with the middle layer generate moiré potentials, leading to strong interactions on a triangular lattice with electrons having spin and layer quantum numbers. b) By tuning the filling around $n=1$, we predict a spinon Fermi surface on the hole-doped site, and a Nagaoka ferromagnet for the electron-doped side. The hole spectral function $A(\mathbf{k}, \omega)$ distinguishes these two scenarios. The fractionalization in the spinon Fermi surface leads to a convolution of the spinon dispersion $\varepsilon_\mathrm{sp}(\mathbf{k})$ and the holon dispersion $\varepsilon_h(\mathbf{k})$. The corresponding lines along energy minima are sketched in green and blue, respectively. In the ferromagnet, the spectrum consists of a free dispersion and a contribution from the small Fermi surfaces around the $\Gamma$ point. c) Sketch of quantum oscillations to distinguish between a small Fermi surface of a paramagnetic Fermi liquid with low doping $\delta =1/20$ (red) and a fractionalized state with large Fermi surface (blue).