[peps] ybli: criticality in open quantum matter

tracks/peps/solutions/ybli/README.md

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+# Criticality in open quantum matter
+
+## 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. |
+
+## Results
+
+See [RESULTS.md](RESULTS.md) for the full report with tables and analysis.
+
+### Clean Ising (validation, c = 1/2)
+
+- c_eff = 0.500 (Model C fit, error < 0.02%)
+- Delta_1 = 0.124 (exact: 1/8 = 0.125)
+- Delta_2 = 0.996 (exact: 1.0)
+
+### Nishimori RBIM (p = 0.8899)
+
+- c_eff = 0.49 +/- 0.04 (Model A, bootstrap)
+- c_eff(6,10) = 0.466 (pair estimator, matches literature 0.464(4))
+- Delta_1 = 0.055 +/- 0.001 (nearly marginal operator)
+- Delta_2 = 1.632 +/- 0.005
+- System sizes L = 4..12, 3150 total disorder samples
+
+### Weak self-dual point (c_eff ~ 0.447)
+
+- Toric code PEPS Born-weight sampling implemented
+- Exact Born sampler validated at L=4
+- MCMC sampler for larger L is functional
+- Full scaling analysis pending: see RESULTS.md section 3
+
+## Method
+
+The effective central charge c_eff is extracted from the finite-size scaling
+of the Born-weighted free energy:
+
+    Phi_L = -(1/Ly) * log Z_m
+
+where Z_m is the Born weight of configuration m. For each configuration,
+the leading Lyapunov exponent of the transfer-matrix product determines the
+free-energy density. The Lyapunov approach avoids boundary contamination
+from open boundary conditions.
+
+### Architecture
+
+```
+src/
+  OpenCriticality.jl      -- module entry point, exports
+  Conventions.jl          -- ModelConvention, free_energy_per_row
+  Models.jl               -- ClassicalIsing, NishimoriRBIM, MeasuredToricCode
+  Contraction.jl          -- dense_logZ, boundary_mps_logZ (log-space)
+  Lyapunov.jl             -- leading_lyapunov, lyapunov_spectrum (Householder QR)
+  Samplers.jl             -- DirectSampler, MetropolisSampler
+  FiniteSizeScaling.jl    -- fit_central_charge, bootstrap_c_eff, pair estimators
+test/
+  runtests.jl             -- 12 test sets, 49 tests (all pass)
+scripts/
+  benchmark_ising.jl      -- clean Ising c_eff extraction
+  nishimori_cluster.jl    -- cluster Lyapunov spectrum for Nishimori RBIM
+  nishimori_dense_run2.jl -- independent second run (different seeds)
+  nishimori_mps_only.jl   -- boundary MPS free energy for L=14,16
+  self_dual_born.jl       -- measured toric code Born-weight sampling
+  slurm_array.jl          -- Slurm array job template
+  results/                -- CSV data from cluster runs
+```
+
+## Reproduction
+
+### Prerequisites
+
+- Julia 1.10+ (tested on 1.12.6)
+- No external packages required (stdlib only: LinearAlgebra, Statistics, Random, Printf)
+- Optional: Slurm cluster for large-L runs
+
+### Run tests
+
+```bash
+julia -e 'include("tracks/peps/solutions/ybli/test/runtests.jl")'
+```
+
+### Clean Ising benchmark
+
+```bash
+julia tracks/peps/solutions/ybli/scripts/benchmark_ising.jl
+```
+
+Expected output: c_eff = 0.500 (Model C), matching exact c = 1/2.
+
+### Nishimori RBIM scaling
+
+The raw data (3150 samples, L=4..12) is included in `scripts/results/`.
+To re-run the finite-size scaling analysis:
+
+```bash
+julia -e '
+include("tracks/peps/solutions/ybli/src/OpenCriticality.jl")
+using .OpenCriticality
+using Printf, Statistics, LinearAlgebra
+
+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)
+'
+```
+
+To generate fresh data on a cluster:
+
+```bash
+# Submit Slurm job
+sbatch slurm_array_template.sh
+# Or run locally for small L
+julia tracks/peps/solutions/ybli/scripts/nishimori_cluster.jl
+```
+
+### Weak self-dual point
+
+```bash
+# L=4 (exact Born sampling)
+julia tracks/peps/solutions/ybli/scripts/self_dual_born.jl "4"
+
+# L=4,6 (L=6 uses MCMC)
+julia tracks/peps/solutions/ybli/scripts/self_dual_born.jl "4,6"
+```
+
+## Key technical decisions
+
+- **Transfer matrix**: symmetric form T = sqrt(Dh) * Tv * sqrt(Dh)
+- **Lyapunov extraction**: Householder QR with R_{ii} > 0 convention,
+  reorthogonalization when ||Q'Q - I|| > 1e-10
+- **Free energy from gamma_0**: Phi_L = -gamma_0 avoids boundary
+  contamination for disordered models
+- **Finite-size fit**: Model A (2-param) is most stable for L=4-12;
+  higher-order corrections require larger L
+- **Log-space normalization**: prevents overflow for large Ly
+
+## References
+
+- [Issue #122](https://github.com/QuantumBFS/quantum.harness/issues/122)
+- [arXiv:2502.14034](https://arxiv.org/abs/2502.14034)
+- [cond-mat/0106023](https://arxiv.org/abs/cond-mat/0106023)
+- [cond-mat/0010143](https://arxiv.org/abs/cond-mat/0010143)
+- [arXiv:2606.12132](https://arxiv.org/abs/2606.12132)