In using the Kitaev Wire Model to explore the features of the OSMPS tools, I was hoping to learn a little more about the quantum information tools available while waiting to see what's going on for the discrete symmetries and multi-flavor Fermionic MPS.
For the bond entropy, is this defined as the entanglement entropy between the left and right hand sides of the bond? From printing the array, it seems that the bond entropy gives an L+1 array with index 0 being the bond entropy between site zero and site 1 (zero for a pure state on sites 1 through L) - in general the jth element is the von Neumann entropy up to site j with the half after site j. Correct?
The reduced density matrices seem to be limited to one or two sites: https://openmps.sourceforge.io/mps_chapters/simulationdetails.html?highlight=densitymatrix_i#defining-observables
But is there anything particular stopping this from being extended to one to two regions? The single region is similar to the bond entropy - but from site i to j in one contiguous block. For a globally pure state, the von Neumann entropy of blocks from 1 to i-1 along with j+1 to L is the same as i to j .
I've attached a copy of this for the ground state search of the Ktiaev model without enforcing the global Z2 symmetry.
When I try to construct the mutual infromation of sites 1 and L by adding this myObservables.AddObservable('DensityMatrix_ij', [[1,L]])
to compute the Density matrix of the broundary sets at the opposite ends of the lattice, it seems to compute okay, but there's some issue with attempting to access this quantity after the calculation.
The main thing I am interested in is taking the mutual information of two disjoint regions. Like, say, region A from sites 1 to site 3 with region C from sites 8-10 on 10 site lattice. The main thing missing is the ability to compute the density matrix for AC by integrating out region B of sites 4-7.
In using the Kitaev Wire Model to explore the features of the OSMPS tools, I was hoping to learn a little more about the quantum information tools available while waiting to see what's going on for the discrete symmetries and multi-flavor Fermionic MPS.
For the bond entropy, is this defined as the entanglement entropy between the left and right hand sides of the bond? From printing the array, it seems that the bond entropy gives an L+1 array with index 0 being the bond entropy between site zero and site 1 (zero for a pure state on sites 1 through L) - in general the
jth element is the von Neumann entropy up to sitejwith the half after sitej. Correct?The reduced density matrices seem to be limited to one or two sites: https://openmps.sourceforge.io/mps_chapters/simulationdetails.html?highlight=densitymatrix_i#defining-observables
But is there anything particular stopping this from being extended to one to two regions? The single region is similar to the bond entropy - but from site
itojin one contiguous block. For a globally pure state, the von Neumann entropy of blocks from 1 toi-1along withj+1toLis the same asitoj.I've attached a copy of this for the ground state search of the Ktiaev model without enforcing the global Z2 symmetry.
When I try to construct the mutual infromation of sites 1 and L by adding this
myObservables.AddObservable('DensityMatrix_ij', [[1,L]])to compute the Density matrix of the broundary sets at the opposite ends of the lattice, it seems to compute okay, but there's some issue with attempting to access this quantity after the calculation.
all give errors.
The main thing I am interested in is taking the mutual information of two disjoint regions. Like, say, region A from sites
1to site3with region C from sites8-10on 10 site lattice. The main thing missing is the ability to compute the density matrix for AC by integrating out region B of sites4-7.Many thanks for all the help,
- Jared