[peps] ybli: criticality in open quantum matter

[Yu-BinLi]

Team

Team name	ybli
Members	ybli

Challenge

Row
Challenge	Reproduce effective central charges at the Nishimori and weak self-dual critical points in open quantum matter, with a finite-size Lyapunov-spectrum analysis.
Catalog issue	Addresses #122 — released by Guo-Yi Zhu, Hong Kong University of Science and Technology (Guangzhou).
Track	peps, chosen by the team because the issue explicitly includes tensor-network contraction.

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Results

Clean 2D Ising (validation, c = 1/2)

Quantity	Our result	Exact	Error
c_eff (Model C)	0.4999	0.5	0.02%
Delta_1	0.124	1/8 = 0.125	0.8%
Delta_2	0.996	1.0	0.4%

Nishimori RBIM (p = 0.8899, beta_N = 1.0449)

Quantity	Our result	Literature
c_eff (Model A)	0.49 ± 0.04	0.464(4)
c_eff(6,10) pair	0.466	0.464(4)
Delta_1	0.055 ± 0.001
Delta_2	1.632 ± 0.005

Data: 3150 samples across L = 4, 6, 8, 10, 12 (two independent runs).

Weak self-dual point of measured toric code (theta = pi/4, c_eff ~ 0.447)

Born-weight sampling via Walsh-Hadamard Transform (WHT) optimized sampler. Transfer matrix amplitude spectrum via dense SVD.

Quantity	Our result	Literature
c_eff (pair c(4,6), Ly=20)	0.446	0.447
c_eff (Ly=10 pairs)	0.43 - 0.48	0.447
Delta_1	0.164
Delta_2	0.270
Delta_3	0.271

c_eff = 0.45 +/- 0.05. The pair estimator c(4,6) = 0.446 from Ly=20 data matches the literature value 0.447 to within 0.2%. The 3-param fits are unstable due to non-standard finite-Ly corrections in the Born-correlated disorder; pair estimates partially cancel these corrections and are more reliable.

Delta_1 is remarkably stable (0.163-0.165 across L = 4, 6, 8, 10). Delta_2 and Delta_3 are nearly degenerate, suggesting multiplet structure consistent with the class-D Majorana network description. L = 12 is excluded from scaling dimensions due to SVD convergence failure on the 4096 x 4096 transfer matrix product.

Convention: Phi = -gamma_0 (amplitude / single-layer), matching the Ising convention where Phi = -log(Z)/Ly gives c = 1/2.

Data: two datasets at Ly = 10L (200/100/100/50/12 samples for L = 4-12) and Ly = 20L (50 samples per L, 30 for L = 12).

Cross-model comparison

Quantity	Ising (exact)	Nishimori	Self-dual	Lit. (self-dual)
c_eff	0.500	0.49(4)	0.45(5)	0.447
Delta_1	0.125	0.055(1)	0.164	-
Delta_2	1.000	1.63(5)	0.270	-

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Method

Born-weighted random transfer-matrix products with Lyapunov spectrum extraction:

1. For each disorder realization m, build row transfer matrices T_y
2. Compute Lyapunov spectrum via Householder QR (no translation invariance needed)
3. Leading exponent gamma_0 gives free energy per row; gaps gamma_0 - gamma_m give scaling dimensions
4. Finite-size scaling: Phi_L = aL - pialphac/(6L) + corrections

For the self-dual point, the Born sampling uses a Walsh-Hadamard Transform (WHT) to achieve O(N log N) per-row cost instead of O(N^2), enabling exact Born sampling up to L = 12.

How to reproduce

Run tests (49 tests, all pass)

julia -e 'include("tracks/peps/solutions/ybli/test/runtests.jl")'

Clean Ising benchmark

julia tracks/peps/solutions/ybli/scripts/benchmark_ising.jl

Nishimori RBIM (using included cluster data)

The raw CSV data for 3150 samples is in scripts/results/. To re-run the fit:

julia -e '
include("tracks/peps/solutions/ybli/src/OpenCriticality.jl")
using .OpenCriticality
using Printf, Statistics

Ls = [4, 6, 8, 10, 12]
results_dir = "tracks/peps/solutions/ybli/scripts/results"
mean_neg_g0 = Float64[]
for L in Ls
    neg_g0s = Float64[]
    for suffix in ["", "_run2"]
        f = "$results_dir/nishimori_dense_L$(L)$(suffix).csv"
        isfile(f) || continue
        for line in readlines(f)[2:end]
            push!(neg_g0s, -parse(Float64, split(line, ",")[2]))
        end
    end
    push!(mean_neg_g0, mean(neg_g0s))
end
c = fit_central_charge(Ls, mean_neg_g0, 1.0; model=:A)[1]
println("c_eff = ", c)
'

Generate fresh cluster data

# Slurm submission
julia tracks/peps/solutions/ybli/scripts/nishimori_cluster.jl --generate
sbatch slurm/array_job.sh

# Or run locally for small L
julia tracks/peps/solutions/ybli/scripts/nishimori_cluster.jl

Weak self-dual point

# Run sampling + SVD analysis (Ly = 10*L by default)
julia tracks/peps/solutions/ybli/scripts/self_dual_optimized.jl 4 200

# For larger L, use Julia 1.12+ and longer Ly
julia tracks/peps/solutions/ybli/scripts/self_dual_optimized.jl 8 50 10

# Run the full analysis (reads both Ly=10 and Ly=20 datasets)
julia tracks/peps/solutions/ybli/scripts/analyze_self_dual_final.jl

Full details in RESULTS.md.

References

• Issue #122
• arXiv:2502.14034
• cond-mat/0106023
• cond-mat/0010143
• arXiv:2606.12132