Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Tensor-network methodology for super-moiré excitons beyond one billion sites

Anouar Moustaj, Yitao Sun, Tiago V. C. Antão, Lumen Eek, Jose L. Lado

Abstract

Computing excitonic spectra in quasicrystal and super-moiré systems constitutes a formidable challenge due to the exceptional size of the excitonic Hilbert space. Here, we demonstrate a tensor-network method for the real-space Bethe-Salpeter Hamiltonian, allowing us to access the spectra of an excitonic $10^{18}$-dimensional Hamiltonian, and enabling the direct computation of bound-exciton spectral functions for systems exceeding one billion lattice sites, several orders of magnitude beyond the capabilities of conventional approaches. Our method combines a tensor-network encoding of the real-space Bethe-Salpeter Hamiltonian with a Chebyshev tensor network algorithm. This strategy bypasses explicit storage of the Hamiltonian while preserving full real-space resolution across widely different length scales. We demonstrate our methodology for one- and two-dimensional super-moiré systems, achieving the simultaneous resolution of atomistic and mesoscopic structures in the excitonic spectra in billion-size systems, showing exciton miniband formation and moiré-induced spatial confinement. Our results establish a real-space methodology enabling the simulation of excitonic physics in large-scale quasicrystal and super-moiré quantum matter.

Tensor-network methodology for super-moiré excitons beyond one billion sites

Abstract

Computing excitonic spectra in quasicrystal and super-moiré systems constitutes a formidable challenge due to the exceptional size of the excitonic Hilbert space. Here, we demonstrate a tensor-network method for the real-space Bethe-Salpeter Hamiltonian, allowing us to access the spectra of an excitonic -dimensional Hamiltonian, and enabling the direct computation of bound-exciton spectral functions for systems exceeding one billion lattice sites, several orders of magnitude beyond the capabilities of conventional approaches. Our method combines a tensor-network encoding of the real-space Bethe-Salpeter Hamiltonian with a Chebyshev tensor network algorithm. This strategy bypasses explicit storage of the Hamiltonian while preserving full real-space resolution across widely different length scales. We demonstrate our methodology for one- and two-dimensional super-moiré systems, achieving the simultaneous resolution of atomistic and mesoscopic structures in the excitonic spectra in billion-size systems, showing exciton miniband formation and moiré-induced spatial confinement. Our results establish a real-space methodology enabling the simulation of excitonic physics in large-scale quasicrystal and super-moiré quantum matter.
Paper Structure (6 sections, 6 equations, 3 figures)

This paper contains 6 sections, 6 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Tensor Network Methodology
  3. 1D incommensurate super-moiré potential
  4. 2D quasiperiodic incommensurate super-moiré potential
  5. Discussion
  6. Conclusion

Figures (3)

  • Figure 1: (a) Schematic of the exciton Hamiltonian, with purple corresponding to the conduction band and light brown to the valence band, together with their corresponding single-particle basis. (b) The encoding of the two-particle $2^{2L}\times2^{2L}$ Hamiltonian matrix into a $2L$ pseudo-spin MPO. (c) The combination of the single-particle Hamiltonians and the interaction kernel using interleaved ordering.
  • Figure 2: (a) Spectral band in real space of the bound super-moiré excitons, together with a zoom of the central region of linear extent $\ell = 64$. (b) Super-moiré on-site potential modulation, with a corresponding zoom of the central region of length $\ell = 64$. The outlined region is not shown to scale with respect to the full domain and serves only as a visual guide.
  • Figure 3: (a) 2D exciton LDOS $\rho(x,y,E=E_X)$ evaluated at the bound-exciton energy $E=E_X$, together with a zoom of the central region of area $A=128\times128$. (b) Corresponding on-site potential, with an analogous zoom of the central region of area $A=128\times128$. The square outline is not drawn to scale relative to the full domain and is included as a visual guide.