Stabilizing Fractional Chern States in Twisted MoTe2: Multi-band Correlations via Non-perturbative Renormalization Group

TL;DR

This work tackles the challenge of multi-band correlations in twisted MoTe$_2$ by applying a non-perturbative driven similarity renormalization group (DSRG) with a multi-Slater reference to downfold interband dynamics into an effective single-band Hamiltonian. The method non-perturbatively captures dynamic correlations via generalized normal ordering and a BCH-based renormalization that retains up to two-body terms, enabling scalable treatment beyond exact diagonalization. For fillings $\nu={1/3,2/3}$ across twist angles, the authors find that interband dynamics reduce FCI gaps at $\nu=1/3$ relative to one-band projections, while at $\nu=2/3$ these correlations stabilize FCI phases at larger twist angles, in line with experiments. The stabilization is attributed to dynamic interband correlations rather than single-particle quantum geometry, and the framework preserves topology by operating in momentum space and connects to broader lattice-topology models, offering a versatile route to study correlated topological phases in moiré materials. The approach thus provides a robust, scalable tool to incorporate multi-band effects in FCIs and related phases, with potential implications for correlated superconductivity and topological lattice models.

Abstract

The observation of fraction quantum Hall states in twisted MoTe2 has sparked a lof of interest in this phenomenon. Most theoretical works to date rely on the brute-force exact diagonalization which is limited to the one partially occupied band. In this work, we present strong evidence that the effect of higher lying bands cannot be ignored due to strong interband interactions. To tackle these effects, we introduce a non-perturbative driven similarity renormalization group (DSRG) method, originally developed for problems in quantum chemistry. We apply this methodology to twisted MoTe2 at fractional hole fillings of ν = 1/3 and 2/3 across a spectrum of twist angles. Our results show that at ν = 1/3, the many-body excitation energy gaps are substantially reduced compared to the one-band treatment. For ν = 2/3, we find that the dynamic correlations stemming from interband interactions stabilize fractional Chern insulating phases at larger twist angles, consistent with the experimental findings. By examining the correlated orbitals and their single-particle topological features, we demonstrate that this stabilization at higher twist angles arises predominantly from the dynamic correlations, rather than conditions on the single-particle quantum geometric tensor.

Figures (6)

• Figure 1: The minimum energy difference between CDW and FCI states, $E_{CDW} - E_{FCI}$, as a function of gate distance $d_g$ and twist angle $\theta$. Panels (a) and (b) show one-band ED results at fillings $\nu = 1/3$ and $2/3$, respectively. Panels (c) and (d) display the corresponding DSRG(2) results at these fillings.
• Figure 2: Band occupation analysis for ground state $e^{A} \vert \Phi'\rangle$, as a function of gate distance $d_g$ and twist angle $\theta$. Panels (a) and (b) show first-band occupation percentages at fillings $\nu = 1/3$ and $2/3$, respectively. Panels (c) and (d) display the corresponding second-band results at these fillings.
• Figure 3: Excitation energies $E-E_g$ and structure factors $S(\bm{q})$ in $\Gamma-K$ line at fillings $\nu = 1/3$ and $\nu = 2/3$, when $\theta = 4.5\degree$ and $d_g = 10~\text{nm}$. The moiré $K$ point corresponds to $q_y = 3$ in the structure factor plots.
• Figure 4: (a) the trace condition violation $T$ and (b) the Berry curvature standard deviation $\sigma_{BC}$ as a function of twist angle $\theta$ with fixed interlayer spacing $d_g = 10~\mathrm{nm}$.
• Figure 5: Numerical results of two-band DSRG(2) vs. one-band and two-band ED at twist angle $\theta = 3.5\degree$, filling fraction $n=1/3$, and gate distance $d_g = 20 ~\text{nm}$ in a $2\times 6$ cluster. (a) The first energy eigenvalues of each momentum. The DSRG(2) method captures the energies from interband interactions. (b) The particle-entanglement spectrum $\xi$ of three calculations. The counting of states below the dashed line is 42, which is consistent with the expectation from the generalized Pauli principle for the FCI state Regnault2011.