Momentum Occupancy

The momentum occupancies are like the corresponding fermion bilinears but are not site-local but momentum-local.

Warning

These are NOT the fourier transforms of n() and spin()! Should you want those quantities, just measure them and take the fourier transform.

tdg.observable.momentum_occupancy.n_momentum(ensemble)

The expectation value of \(\frac{1}{V}\tilde{\psi}^\dagger_{k} \tilde{\psi}_{k}\) summed over spins.

This is a lattice discretization of \(\frac{1}{L^2} \psi^\dagger(k) \psi(k)\) and it has good continuum and infinite-volume limits and is dimensionless.

Configurations first, then momentum \(k\).

tdg.observable.momentum_occupancy.spin_momentum(ensemble)

The expectation value of \(\frac{1}{2V} \tilde{\psi}^\dagger_{k} \sigma^i \tilde{\psi}_{k}\)

This is a lattice discretization of \(\frac{1}{2L^2} \psi^\dagger(k) \sigma^i \psi(k)\) and it has good continuum and infinite-volume limits and is dimensionless. It should be 0 unless the external field \(h\) is nonzero.

Configurations first, then momentum \(k\), then spin index \(i\). The spin direction matches the index of tdg.PauliMatrix[1:] so that 0 is in the x direction, for example.