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  How does the geometry of tensor network depend on choice of logical state?

+ 5 like - 0 dislike

I  am currently studying tensor networks, constructed from perfect tensors, introduced in article http://arxiv.org/abs/1503.06237

I would like to consider tensor network, which is  holographic code. So as a setup we have some particular state on the boundary, state in the bulk(logical state)  and tensor network which realizes  map between two corresponding Hilbert spaces. 

I believe that for different bulk states one should obtain different geometries of corresponding tensor networks. (I am particularly interested in considering vacuum and thermal CFT on the boundary)

I am trying to check this fact by means of calculating  length of geodesic which corresponds to some region on the boundary.

 My problem is that (according to my understanding) algorithm introduced in the aforementioned article gives the same result for all cases.  According to it length of geodesic is a function only of number of cutted inplane lines along curve and their dimensionality.

Lengths of these geodesics can't be the same because these two tensor networks correspond to different geometries of the bulk.

asked Mar 16, 2016 in Theoretical Physics by Yaroslav (25 points) [ revision history ]
recategorized Mar 21, 2016 by Arnold Neumaier

Papers with sentences like the one including "residual region ... composed of randomly chosen perfect tensors" somehow scare me...  However, the maths used in this one are not limited to the given interpretation.
Could you please provide more details about your application of the algorithm?

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