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.
| Which topic best fits your talk? | Condensed Matter Physics and Nanomaterials |
|---|---|
| Affiliations | CF-UM-UP |