[qmc] zhong-guo-ren-neng-fei: total positivity for sign-free determinants

[LiuZY613]

Team

Team name	zhong-guo-ren-neng-fei
Members	Zong-yue Liu

Challenge

Row
Challenge	Test total nonnegativity and ordered one-dimensional fermion propagation as a determinant-QMC sign-free principle beyond fixed split-metric, Kramers, and Majorana constructions.
Catalog issue	Addresses #121 — “Sign-problem free hunter,” released by Lei Wang, Institute of Physics, Chinese Academy of Sciences.
Track	tracks/qmc/ — selected from the issue’s Method: Quantum Monte Carlo field.

Current result

• Proves that arbitrary products of exponentials of real tridiagonal Metzler generators are totally nonnegative, hence det(I + P) >= 1.
• Maps the class to an open, off-half-filled interacting spinless-fermion auxiliary-field formulation.
• Includes reduction checks, 8,000 randomized products, Fock-space cross-checks, and an exact directed-cycle counterexample.
• Interprets total positivity through Vandermonde Slater states and one-dimensional noncrossing imaginary-time propagation.

Validation

python tracks/qmc/solutions/zhong-guo-ren-neng-fei/verify.py

[wangleiphy]

One-dimensional models models with short-range hopping are know to be sign-problem free in path-integral Monte Carlo.

What can you say about fermions in higher dimensional space ?