Jastrow

Jastrow wavefunctions, introduced in (1) in the context of continuous space models, are implemented in two ways in NetKet.

Jastrow

The Jastrow machine does not have hidden units, and is defined by:

for arbitrary local quantum numbers . The total number of variational parameters of this long-range Jastrow operator is , and all parameters are taken complex-valued. This wavefunction needs less input parameters compared to the RBM wavefunction, since the hidden layer is not present. In the language of neural networks a Jastrow machine can be seen as a fully visible RBM, with all the intra-layer connections active.

Parameter Possible values Description Default value
InitFile String If specified, matrix parameters are loaded from the given file None
InitRandom Boolean Whether to initialize the parameters with random gaussian-distributed values True
SigmaRand Float If InitRandom is chosen, this is the standard deviation of the gaussian 0.1

Example

pars['Machine']={
    'Name'           : 'Jastrow',
}

JastrowSymm

This type of Jastrow wavefunction is constructed to be invariant under specific permutations of the graph indices. In particular, , where is the -th permutation of the index , and assuming a total of distinct permutations.

Let us consider the case of a N=20 spin chain, under periodic boundary conditions. The total number of parameters is , corresponding to the full upper triangle (excluding the diagonal, always set to ) to the matrix. However it is true that, if permutation symmetry holds, the parameter controlling the interaction between quantum operator and must be equal to , and so on. Therefore, in this case, the effective number of independent parameter is no longer but . In the general case, this number is automatically computed inside the class by checking the symmetry table associated with the graph.

Parameter Possible values Description Default value
InitFile String If specified, matrix parameters are loaded from the given file None
InitRandom Boolean Whether to initialize the parameters with random gaussian-distributed values True
SigmaRand Float If InitRandom is chosen, this is the standard deviation of the gaussian 0.1

Example

pars['Machine']={
    'Name'           : 'JastrowSymm',
}

References


  1. W. L. McMillan, Phys. Rev. 138, A442 (1965), Ground State of Liquid