Measurement

ED_sectors.k_eigvals — Function.

k_eigvals(H,k)

Computes the k lowest-energy eigenvalues for the given Hamiltonian H.

Note

This is a simple wrapper for Julia's eigs function, which uses the Lanczos algorithm. While this works with either sparse or full matrices for H, sparse matrices are much faster. The cost of the algorithm increases with k and should be only used when $k \ll \operatorname{dim}(H)$. If you only need the ground state, then just use k=1.

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ED_sectors.k_eigsys — Function.

k_eigsys(H, k)

Computes the k lowest-energy eigenvalues and eigenvectors for the given Hamiltonian H.

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ED_sectors.expectation — Function.

expectation(psi, O)
	expectation_rho(rho, O)

For a state psi, computes the expectation value $\left<\psi|O|\psi\right>$ and operator O. This is a simple wrapper for dot(psi, O*psi) and works for any type of matrix O.

For a density matrix rho, computes the expectation value $\operatorname{Tr}[\rho O]$.

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ED_sectors.reduce_density_matrix — Function.

reduce_density_matrix(phi, l)

Computes the reduced density matrix for the state psi by tracing out all but the first l spins.

Basis restriction

At present this only works when the basis has no symmetries. Support for reduced density matrices with symmetries is coming soon.

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ED_sectors.entanglement_entropy — Function.

entanglement_entropy(psi, l; epsilon = 10e-15)

Computes the entanglement entropy $S(l/L)$ for a state psi. Removes eigenvalues smaller than a numerical cutoff because they often give underflow errors.

This uses reduce_density_matrix, so it only works without symmetries.

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ED_sectors.measure_EE — Function.

measure_EE(psi, basis)

Computes the entanglement entropy at all cuts in a wavefunction psi in a basis basis.

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