paper: https://journals.aps.org/prx/abstract/10.1103/y5kd-7prs
We warmly welcome you to use and further develop the density matrix framework to explore rich localization problems!
- Ziyue Qi (IOP, UCAS)
- Yi Zhang (SHU)
- Mingpu Qin (SJTU)
- Hongming Weng (IOP, UCAS)
- Kun Jiang (IOP, UCAS)
We provide a new framework to study Anderson localization via the density matrix. From it, we directly extract the localization length, which measures how far electrons spread in a system. Combined with finite-size scaling, this approach distinguishes metallic and insulating behavior across different dimensions naturally extends to interacting systems by using many-body ground-state wave functions.
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For non-interacting systems, we define modular density matrix (MDM). The localization lengths extracted from it are benchmarked with standard transfer matrix method (TMM) and typical medium dynamical cluster approximation (TMDCA).
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For interacting systems, we define the subtraction density matrix (SDM) and calculate it using DMRG. We used this method to show (1) attractive interactions promote metallic behavior in disordered one-dimensional systems, (2) a metallic tendency in disordered two-dimensional Hubbard models.
This repository provides the source code and raw data supporting the results in arXiv:2509.26206, including the figures in the paper and the corresponding processed datasets used in the plots.
The project is organized into two parts:
- Non-interacting: Localization length, including finite-size scaling and data collapse analysis, from the MDM and benchmarks with the TMM for
- the 3D Anderson model,
- the 2D Anderson model with SOC
- a two-orbital model,
- Interacting: Localization length from the SDM for
- a 1D spinless interacting model
- the 2D Anderson-Hubbard model. Many-body ground-state wave functions are computed from DMRG. Data processing scripts and benchmark results are also provided.