Notation and conventions

Every article in Ketbook uses the symbols below. A page that needs something else defines it where it first appears.

States and configurations

Symbol	Meaning
$N$	number of lattice sites, or of particles in continuum problems
$\boldsymbol{\sigma}=(\sigma_1,\dots,\sigma_N)$	a basis configuration; for spin- $\tfrac12$ in the $S^z$ basis, $\sigma_i=\pm1$
$\Psi_\theta(\boldsymbol{\sigma})=\langle\boldsymbol{\sigma}\vert\Psi_\theta\rangle$	unnormalized amplitude produced by the network with parameters $\theta$
$\theta\in\mathbb R^{N_p}$ or $\mathbb C^{N_p}$	the $N_p$ variational parameters
$p_\theta(\boldsymbol{\sigma})\propto\lvert\Psi_\theta(\boldsymbol{\sigma})\rvert^2$	the normalized sampling distribution
$E_0,E_1$	exact ground-state and first-excited energies of $H$ in the sector considered
$e=E/N$	energy per site

Estimators

Symbol	Meaning
$N_s$	number of Monte Carlo samples used for one estimate
$\langle\cdot\rangle$	expectation over $p_\theta$ ; $\mathbb E_{p_\theta}$ when the distribution must be explicit
$E_{\mathrm{loc}}(\boldsymbol{\sigma})=\sum_{\boldsymbol{\sigma}'}H_{\boldsymbol{\sigma}\boldsymbol{\sigma}'}\Psi_\theta(\boldsymbol{\sigma}')/\Psi_\theta(\boldsymbol{\sigma})$	local energy
$E_\theta=\langle E_{\mathrm{loc}}\rangle$	variational energy
$\operatorname{Var}_\theta(H)=\langle\lvert E_{\mathrm{loc}}\rvert^2\rangle-\lvert E_\theta\rvert^2$	energy variance of the state
$O_k(\boldsymbol{\sigma})=\partial_{\theta_k}\log\Psi_\theta(\boldsymbol{\sigma})$	log-derivative with respect to parameter $k$
$\bar X=X-\langle X\rangle$	a centred quantity
$\tau_{\mathrm{int}}$ , $N_{\mathrm{eff}}=N_s/2\tau_{\mathrm{int}}$	integrated autocorrelation time and effective sample size

Optimization

Symbol	Meaning
$F_k$	energy gradient, $2\operatorname{Re}\langle\bar O_k^\bar E_{\mathrm{loc}}\rangle$ for real $\theta$ and $\langle\bar O_k^\bar E_{\mathrm{loc}}\rangle$ for holomorphic complex $\theta$
$S_{kk'}=\langle\bar O_k^*\bar O_{k'}\rangle$	quantum geometric tensor restricted to the variational manifold
$\eta$	learning rate, equal to the imaginary-time step in stochastic reconfiguration
$\lambda$	regularization strength
$X\in\mathbb C^{N_s\times N_p}$ , $\varepsilon\in\mathbb C^{N_s}$	centred, $\sqrt{N_s}$ -normalized log-derivative matrix and local-energy vector, so that $S=X^\dagger X$ and $F=X^\dagger\varepsilon$

Hamiltonians

Spin operators are $\mathbf S_i=\tfrac12\boldsymbol{\sigma}_i$ with $\hbar=1$ . A Hamiltonian written with Pauli matrices has energies four times larger for bilinear terms; benchmark definitions always state which is meant.
$\langle i,j\rangle$ runs over nearest-neighbour bonds, $\langle\!\langle i,j\rangle\!\rangle$ over next-nearest-neighbour bonds, each undirected bond counted once.
Lattice sizes are written $L\times L$ with $N=L^2$ ; periodic boundary conditions in all directions unless stated.
Fermionic operators $c^\dagger_{i\sigma}$ , $n_{i\sigma}=c^\dagger_{i\sigma}c_{i\sigma}$ ; the Hubbard hopping is $-t$ with $t>0$ .

Citations

References are given as arXiv identifiers, which resolve to every version of a paper and to its journal record. A quantitative claim cites the table, equation or figure it comes from.