Certified, self-generated, beyond-ED real-time dynamics of the 3+1D compact-U(1) deconfinement quench — with an exact SU(2) representability foundation.
A trapped-flux state in 3+1D compact lattice gauge theory is quenched from the confined into the Coulomb regime and evolved in real time. The exact-diagonalization (ED) anchor certifies the early window on state spaces up to the (3,3,3)-per sector (5.66×10¹⁸ basis states); a gauge-equivariant neural quantum state (NQS; Carleo & Troyer, Science 355, 602, 2017) carries the trajectory into the regime the anchor cannot reach and past what matrix-product methods can store. Every NQS result is scored step-by-step against this ED reference.
| Pillar | What | Code |
|---|---|---|
| ED anchor | Gauss-projected basis, sparse H, Krylov real-time evolution, Gate-0 significance | src/cqed/, scripts/ed/ |
| Quench physics | flux-melt crossover, strings, entanglement, DQPT, scrambling, radiation | scripts/dynamics/ |
| NQS method | ansätze, samplers, p-tVMC / SR projection, error-feedback MC | src/nqs/, scripts/nqs/ |
| Beyond ED | self-generated certified trajectory past the ED / MPS reach | scripts/beyond_ed/ |
| SU(2) foundation | exact NQS representability of a non-Abelian gauge theory | scripts/su2_nqs_representability.py, scripts/su2_2d/ |
Beyond classical. At the physically hardest step (t=1), the state's entanglement puts it out of reach of matrix-product methods, while the NQS stores it in kilobytes.
| quantity (t=1, g²=1.0) | value |
|---|---|
| MPS bond dim χ(F=0.999) | 2,177 (= 76% of the full Schmidt rank, 2,865) |
| MPS memory F=0.999 | 5.46 GB |
| NQS parameters / memory | 9,624 params / 0.15 MB |
| MPS / NQS memory | 3.5×10⁴× |
The advantage is real everywhere in the Gate-0 window but not uniform — quoted as a range, χ(F=0.999)=1,237–2,177 and MPS/NQS=1.1–3.5×10⁴× across g²=1.0–1.4. Rigorous for ED and the whole MPS/DMRG/TEBD family. Figure: figures/fig_classical_advantage.png.
SU(2) representability. A plain complex RBM reproduces exact SU(2) real-time dynamics to machine precision, establishing the ansatz for a non-Abelian theory.
| system | states | RBM | fidelity |
|---|---|---|---|
| N=2 open (j=1/2 string) | 5 | nh=8, 124 real params | 1−F ≲ 1e-10 across the trajectory |
| N=4 open (j=1 adjoint flux) | 42 | nh=8, 232 real params | F > 0.999 everywhere |
Physics. The confinement→Coulomb quench is a clean ergodic (ETH) crossover, not a transition; its one phenomenon is the flux melt (electric-field tension σ_E ∝ 1/g²), with local flux contrast volume-stable across nine orders of magnitude in sector size in the certified early window. Figures: figures/fig_melt_law.png, figures/fig_confinement_melt_curve.png.
QuantDynam/
├── src/
│ ├── cqed/ ED engine: Gauss-projected basis, sparse H, Krylov
│ │ evolution, observables, baselines, thermal reference
│ └── nqs/ NQS: ansätze, samplers, p-tVMC / SR projection,
│ error-feedback MC propagation
├── scripts/
│ ├── ed/ Gate-0 scan, truncation, thermal, ED-free validation
│ ├── dynamics/ quench physics: strings, entanglement, DQPT,
│ │ scrambling, flux melt, defects, radiation
│ ├── gen/ generational coupling / melt-law scans
│ ├── nqs/ NQS drivers: pilots, samplers, SR projection, headline runs
│ ├── beyond_ed/ beyond-ED self-generated trajectory drivers (+ GPU)
│ ├── method/ hardware-export / benchmark utilities
│ ├── su2_2d/ 2+1D SU(2) Kogut-Susskind ED engine + MPS-hardness audit
│ ├── figures/ figure builders (seaborn, publication style)
│ └── su2_*.py SU(2) foundation + self-generation pipeline
├── results/ run outputs (JSON), grouped by theme
│ (benchmark/ beyond_ed_paper/ nqs/ kz/ ramps/ radiation/ …)
├── configs/ experiment configs
├── figures/ publication figures (PNG, 300 dpi); supplement/ = SI
├── environment.yml conda environment (Python 3.14, NQS stack)
├── requirements.txt pip pins (CPU core)
├── requirements-gpu.txt pip pins (CUDA box: jax[cuda12])
├── LICENSE
└── README.md
conda env create -f environment.yml
conda activate quantdynam
# or, into an existing environment:
pip install -r requirements.txt # CPU / Apple-silicon
pip install -r requirements-gpu.txt # CUDA box (jax[cuda12])Tested on macOS / Apple-silicon and Linux CUDA (Python 3.14). Anything that imports the engine runs with PYTHONPATH=src.
# ED anchor: the Gate-0 quench scan (ED vs mean-field vs Gaussian nulls, thermal T_eff)
PYTHONPATH=src python scripts/ed/gate0_scan.py \
--dims 2,2,2 --periodic 0,0,0 --emax 1 \
--g2 0.5,0.7,1.0,1.4,2.0,3.0 --tmax 15 --nt 151 \
--out results/cube_emax1.json
# NQS trajectory scored against ED at every step (GCNN ansatz)
PYTHONPATH=src python scripts/nqs/headline_gcnn.py --sector 322_perX --gcnn 4x22
# beyond-ED self-generated trajectory (GPU box)
PYTHONPATH=src python scripts/beyond_ed/beyond_ed_nqs_gpu.py
# SU(2) exact-representability battery
PYTHONPATH=src python scripts/su2_nqs_representability.py
# publication figures (seaborn; writes PNG + PDF to figures/)
PYTHONPATH=src python scripts/figures/plot_melt_law.py
PYTHONPATH=src python scripts/figures/plot_confinement_melt_curve.pyGate 0 (significance: ED beats Gaussian + mean-field nulls in a quench window) → Gate 1 (NQS capability: fidelity vs the ED reference) → scale → physics. Go/no-go criteria were fixed before results, and any change is logged with reasoning; each NQS trajectory is scored step-by-step against the ED reference within the exact-certified window before it is trusted beyond it.
@misc{quantdynam2026,
title = {Real-Time Quantum Dynamics of the 3+1D Compact-QED Deconfinement
Quench via Gauge-Equivariant Neural Quantum States},
author = {Garg, Arnav},
year = {2026},
note = {Under review}
}MIT — see LICENSE.