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"""Make CSVs for numerical data.
Some data can be slow to process and it is better to write them into a CSV file before
plotting, so that we don't need to wait for a long time during plotting. Data included:
- Energy result from neural network and ED with different number of electrons in 1/3.
- Ground state energy, quasiparticle/quasihole energy, electron population on the LLL,
and overlap with the Laughlin wavefunction with different kappa in 1/3 filling.
"""
import os
from pathlib import Path
os.environ["JAX_PLATFORMS"] = "cpu"
import numpy as np
import pandas as pd
from deephall.loss import iqr_clip_real
from puwr import tauint
from uncertainties import ufloat, umath
DATA_PATH = Path(__file__).parent / "data"
def correct_energy(kinetic, potential, N, Q, R, nu, q=0, kappa=1):
# Remove background contribution
potential -= kappa * (N**2 - q**2) / 2 / R
# Density correction for potential energy
energy_in_au = (
(kinetic - N / 2 * Q / R**2 + potential) * np.sqrt(2 * Q * nu / N) / N
)
# Normalize potential in the unit of 1/ell
energy_in_ell = energy_in_au * R / np.sqrt(Q) / kappa
return energy_in_ell
def ed_energy(ed_output, N, Q, R, nu, q=0):
return correct_energy(N / 2, ed_output / 2, N, Q, R, nu, q)
def energy_vs_n():
data = {"n": [6, 7, 8, 9, 10, 11, 12], "energy": [], "std": [], "ed": []}
for n in data["n"]:
flux = 3 * (n - 1)
netobs_ckpt = DATA_PATH / f"n{n}l{flux}/k1/energy-100k/netobs_ckpt_001999.npz"
with netobs_ckpt.open("rb") as f, np.load(f) as npf:
energy = correct_energy(
npf["values/kinetic"],
npf["values/potential"],
*(n, flux / 2, np.sqrt(flux / 2)),
nu=1 / 3,
).real
mean, std, *_ = tauint([[iqr_clip_real(energy, scale=3)]], 0)
data["energy"].append(mean)
data["std"].append(std)
ed_n = [6, 7, 8, 9, 10, 11]
ed_output = [
7.7432698280425,
10.121045415564,
12.725298638045,
15.542042784237,
18.559733276244,
21.768350529899,
]
data["ed"] = [
ed_energy(e, n, 3 * (n - 1) / 2, np.sqrt(3 * (n - 1) / 2), 1 / 3)
for n, e in zip(ed_n, ed_output)
] + [np.nan]
return pd.DataFrame(data)
def llm_1_3():
data = {
"kappa": [0.5, 1, 3, 10],
"energy": [],
"energy_std": [],
"qp_energy": [],
"qp_energy_std": [],
"qh_energy": [],
"qh_energy_std": [],
"gap": [],
"gap_std": [],
"overlap": [],
"overlap_std": [],
"n_LLL": [],
"n_LLL_std": [],
}
for kappa in data["kappa"]:
netobs_ckpt = DATA_PATH / f"n6l14/k{kappa}/energy/netobs_ckpt_001999.npz"
with netobs_ckpt.open("rb") as f, np.load(f) as npf:
qp_energy = correct_energy(
npf["values/kinetic"],
npf["values/potential"],
*(6, 14 / 2, np.sqrt(14 / 2)),
nu=1 / 3,
kappa=kappa,
q=1 / 3,
).real
qp_energy_mean, qp_energy_std, *_ = tauint([[iqr_clip_real(qp_energy)]], 0)
data["qp_energy"].append(qp_energy_mean)
data["qp_energy_std"].append(qp_energy_std)
netobs_ckpt = DATA_PATH / f"n6l15/k{kappa}/energy/netobs_ckpt_001999.npz"
with netobs_ckpt.open("rb") as f, np.load(f) as npf:
energy = correct_energy(
npf["values/kinetic"],
npf["values/potential"],
*(6, 15 / 2, np.sqrt(15 / 2)),
nu=1 / 3,
kappa=kappa,
).real
energy_mean, energy_std, *_ = tauint([[iqr_clip_real(energy)]], 0)
data["energy"].append(energy_mean)
data["energy_std"].append(energy_std)
netobs_ckpt = DATA_PATH / f"n6l16/k{kappa}/energy/netobs_ckpt_001999.npz"
with netobs_ckpt.open("rb") as f, np.load(f) as npf:
qh_energy = correct_energy(
npf["values/kinetic"],
npf["values/potential"],
*(6, 16 / 2, np.sqrt(16 / 2)),
nu=1 / 3,
kappa=kappa,
q=1 / 3,
).real
qh_energy_mean, qh_energy_std, *_ = tauint([[iqr_clip_real(qh_energy)]], 0)
data["qh_energy"].append(qh_energy_mean)
data["qh_energy_std"].append(qh_energy_std)
gap_mean, gap_std, *_ = tauint(
[[6 * iqr_clip_real(qp_energy + qh_energy - 2 * energy)]], 0
)
data["gap"].append(gap_mean)
data["gap_std"].append(gap_std)
netobs_ckpt = DATA_PATH / f"n6l15/k{kappa}/overlap/netobs_ckpt_000199.npz"
with netobs_ckpt.open("rb") as f, np.load(f) as npf:
overlap_num_real, overlap_num_real_std, *_ = tauint(
[[npf["values/ratio"].real]], 0
)
overlap_num_imag, overlap_num_imag_std, *_ = tauint(
[[npf["values/ratio"].imag]], 0
)
overlap_den, overlap_den_std, *_ = tauint([[npf["values/ratio_square"]]], 0)
overlap = umath.sqrt(
(
ufloat(overlap_num_real, overlap_num_real_std) ** 2
+ ufloat(overlap_num_imag, overlap_num_imag_std) ** 2
)
/ ufloat(overlap_den, overlap_den_std)
)
data["overlap"].append(overlap.n)
data["overlap_std"].append(overlap.s)
netobs_ckpt = DATA_PATH / f"n6l15/k{kappa}/1rdm/netobs_ckpt_019999.npz"
with netobs_ckpt.open("rb") as f, np.load(f) as npf:
trace = np.trace(npf["values/one_rdm"], axis1=1, axis2=2)
mean, std, *_ = tauint([[trace.real]], 0)
data["n_LLL"].append(mean)
data["n_LLL_std"].append(std)
return pd.DataFrame(data)
if __name__ == "__main__":
energy_vs_n().to_csv(open(DATA_PATH / "energy_vs_n.csv", "w"), index=False)
llm_1_3().to_csv(open(DATA_PATH / "llm_1_3.csv", "w"), index=False)
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