I’m investigating the spin-spin correlation behavior of the repulsive 2D Hubbard model at half-filling under a narrow cylinder geometry (periodic boundary in circumferential direction, open in axial direction). Theoretical studies (e.g.cond-mat/0103159) suggest a striking even-odd width dependence:
- Even widths (4-leg, 6-leg): Exponential decay of spin correlation while the correlation length is expected to diverge as width increases. (I guess this can be a spin-1 chain analogy as the spin-1/2 fermion paired into integer spin along the circumferential direction and there is Haldane gap?).
- Odd widths: Algebraic decay from gapless spinon modes (I guess this is a half-integer spin chain analogy?).
Key questions:
- Validation: Have DMRG studies explicitly observed this?
- Haldane connection: Do numerical results support the interpretation via Haldane’s conjecture? (e.g., extracted spin gaps vs. width parity)
- Width scaling: For wider cylinders (e.g., 6-leg+), does the correlation length diverge (algebraic recovery) as 2D fluctuations dominate?
My results:
cylinder geometry, strong U=10t, Lx=48:
- Width=4 (even): Clear exponential decay.
- Width=3 (odd):
- Ambiguous Power-law: Attempted r^{-\alpha} fits fail at long distances (e.g., beyond r>15).
- Technical details: Bond dimension=20000, cutoff=1e-9, reference points averaged over ix=Nx/4-2:Nx/4+2 and circumferential positions (y). I think the result is free from bond dimension and boundary effect.