Number

Baryon Number

These measure the local and global baryon number.

tdg.observable.number.n(ensemble)

The fermionic estimator of the local number density, one per site per configuration.

Seems to be positive (semi-)definite.

tdg.observable.number.N(ensemble)

The total number, one per configuration. Computed via fermion contractions; the sum of n() on sites.

Bosonic Estimators

Because we do the Hubbard-Stratanovich transformation in the number channel we can use a Ward-Takahashi-like identity to estimate the number density from the auxiliary field.

tdg.observable.number.n_bosonic(ensemble)

Using Ward-Takahashi identities one finds the bosonic estimator

\[\left\langle\tilde{n} = - \frac{1}{\tilde{\beta}} \tilde{V}^{-1} \sum_t A_t\right\rangle\]

of the local number density, one per site per configuration.

Note

Has substantially greater variance than the fermionic estimator n(), especially at low particle numbers.

tdg.observable.number.N_bosonic(ensemble)

The total number, one per configuration.

The sum of n_bosonic() on sites.

Density-density two-point functions

tdg.observable.nn.nn(ensemble)

The convolution of n with n \(n*n\), which plays an important role in the density-density fluctuation correlator.

Configurations slowest, then (linearized) sites.

tdg.observable.nn.density_density_fluctuations(ensemble)

A derived quantity, \(\left\langle n*n \right\rangle - \left\langle n \right\rangle * \left\langle n \right\rangle\).

Bootstraps first, then relative coordinate.