Speaker
Description
The emergence of correlated phases, such as unconventional superconductivity, in two-dimensional moiré materials is one of the most fascinating developments in condensed matter physics. However, the interplay between the large-scale moiré patterns, the formation of flat bands, and the subsequent interaction-induced phases poses a significant challenge for numerical simulations. In realistic settings, twist-angle disorder or substrate interactions are sufficient to break translation symmetry or create super-moiré effects precluding the use of standard continuum models.
To overcome this, we propose a mean-field approach enhanced by quantics tensor networks. By utilizing a tensor-train representation of the mean-field Hamiltonian and the reduced density matrix, this method achieves logarithmic scaling with the system size. This scaling is a crucial advantage, enabling the simulation of exponentially large systems and capturing super-moiré physics. By comparison, exact diagonalization or even linear scaling methods such as the Fermi Operator Expansion become prohibitive at this length scales.
In this work, we study a two-dimensional model hosting both flat bands and incommensurability-induced critical states. We introduce a zero-temperature purification scheme of the reduced density matrix that takes the tensor-network representation of the mean-field Hamiltonian and iteratively applies a low-order polynomial, converging to the density matrix.
We analyze the real-space distribution of the charge density as well as its Fourier transform, to detect the presence of quasi-fractal order. Finally, we will discuss the physical implications of this quasi-fractal order for the broader understanding of strongly correlated phases in super-moiré systems.