netket.observable.Renyi2EntanglementEntropy

class netket.observable.Renyi2EntanglementEntropy

Bases: AbstractObservable

Rényi2 bipartite entanglement entropy of a state \(| \Psi \rangle\) between partitions A and B.

Inheritance

__init__(hilbert, partition)

Constructs the operator computing the Rényi2 entanglement entropy of a state \(| \Psi \rangle\) for a partition with partition A:

\[S_2 = -\log_2 \text{Tr}_A [\rho^2]\]

where \(\rho = | \Psi \rangle \langle \Psi |\) is the density matrix of the system and \(\text{Tr}_A\) indicates the partial trace over the partition A.

The Monte Carlo estimator of S_2 [Hastings et al., PRL 104, 157201 (2010)] is:

\[S_2 = - \log \langle \frac{\Psi(\sigma,\eta^{\prime}) \Psi(\sigma^{\prime},\eta)}{\Psi(\sigma,\eta) \Psi(\sigma^{\prime},\eta^{\prime})} \rangle\]

where the mean is taken over the distribution \(\Pi(σ,η) \Pi(σ',η')\), \(\sigma \in A\), \(\eta \in \bar{A}\) and \(\Pi(\sigma, \eta) = |\Psi(\sigma,\eta)|^2 / \langle \Psi | \Psi \rangle\).

Parameters:

• hilbert (None) – hilbert space of the system.

• partition (array) – list of the indices identifying the degrees of freedom in one partition of the full system. All indices should be integers between 0 and hilbert.size

Returns:

Rényi2 operator for which computing the expected value.

Attributes

hilbert

The hilbert space associated to this observable.

partition

list of indices for the degrees of freedom in the partition

Methods