Interaction-induced moiré lattices: from mosaic mobility edges to many-body localization

Abstract

We study localization driven solely by interparticle interactions in moiré lattice systems without intrinsic disorder or externally imposed quasiperiodic potentials. We consider a one-dimensional bilayer with incommensurate lattice constants, described by a spin-dependent Fermi-Hubbard-type model with short-range interlayer interactions, where quasiperiodicity emerges only through interactions. Exact diagonalization shows that quenching hopping in one layer generates an interaction-induced mosaic potential with multiple mobility edges. When both layers are dynamical, increasing interlayer interactions drives transitions among ergodic, critical, and many-body localized regimes, with energy-dependent coexistence in certain parameter ranges. An exact mapping to a noninteracting single-particle model on a higher-dimensional structured graph provides a unified interpretation of these results and suggests an experimentally accessible route to interaction-induced moiré physics and localization.

Figures (8)

• Figure 1: Schematic of the bilayer lattice model for $N_{\uparrow}=4$ on a lattice of size $L_{\uparrow}=10$ and $N_{\downarrow}=13$ on a lattice of size $L_{\downarrow}=16$. Particles hop between nearest-neighbor sites within each layer, while the two layers are coupled through short-range interlayer density-density interactions.
• Figure 2: Dependence of the dimensionless interaction strength and band-gap ratio on the lattice depth parameter $s$. The left (blue) axis shows $G_{\uparrow\downarrow}/J$ as a function of $s$, while the right (orange) axis shows the ratio of the single-particle band gap $\Delta E$ (between the first and second bands) to $G_{\uparrow\downarrow}$. The latter quantifies the separation of the lowest band from higher bands and is used to justify the single-band approximation in the parameter regime considered.
• Figure 3: The figure shows the interaction-induced effective potential $V_i^{\mathrm{eff}}$ (in unit of $J_{\uparrow}$) experienced by the upper-layer particle for regular fillings of the lower layer with $s=23$. The panels (a), (b) and (c) correspond to $\lambda=1$, $\lambda=2$ and $\lambda=3$, respectively. Insets show a magnified view of $V_i^{\mathrm{eff}}$ over lattice sites $i\in[0,100]$, highlighting the mosaic-like envelope of the quasiperiodic potential. Unit filling ($\lambda=1$) yields a dense but modulated envelope, while $\lambda\ge2$ produces a progressively diluted mosaic pattern.
• Figure 4: Phase diagrams in the quenched-layer (mosaic) limit with $N_{\uparrow}=1$ and $J_{\downarrow}=0$. The vertical axis shows the single-particle eigenenergy $E$ of the upper layer in units of $J_{\uparrow}$. In all panels, $L_{\uparrow}=900$. Panels (a), (b) and (c) correspond to regular (mosaic) fillings in the lower layer with $N_{\downarrow}/L_{\downarrow}=1$ ($\lambda=1$), $N_{\downarrow}/L_{\downarrow}=1/2$ ($\lambda=2$) and $N_{\downarrow}/L_{\downarrow}=1/3$ ($\lambda=3$), respectively. Panel (d) shows the corresponding phase diagram for an average filling of $N_{\downarrow}/L_{\downarrow}=1/3$ with random configuration in the lower layer. The color indicates the fractal dimension $\Gamma$ of the eigenstates (blue: localized, $\Gamma\!\approx\!0$; yellow: extended, $\Gamma\!\approx\!1$), revealing multiple mobility edges for the regular fillings and their disappearance for random fillings.
• Figure 5: Phase diagrams under different filling conditions. Panels (a)--(d) correspond to $N_{\uparrow}/L_{\uparrow}=2/16,\,4/16,\,15/16,\\\,14/16$ and $N_{\downarrow}/L_{\downarrow}=2/26,\,25/26,\,3/26,\,24/26$, respectively. Yellow indicates the ergodic (thermal) regime, light blue denotes an intermediate (critical) regime, and dark blue indicates the MBL regime. The colorbar shows the participation coefficient $a_1$.