Calculating Purity of PurificationMPS

How do I use this algorithm? What does that parameter do?
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vmen
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Joined: 21 Nov 2023, 03:25

Calculating Purity of PurificationMPS

Post by vmen »

Hi,

If I have a purification MPS representing a finite temperature thermal mixed state \(\rho\), is there an efficient way I can compute the purity \(Tr[\rho^2]\) of the thermal state? I am not sure if there is even a way to compute moments of the actual thermal state from the pure MPS in the purified space. I really just need any quantity that is a monotone in purity of the represented thermal state, not necessarily the purity.

Any help is appreciated, thank you!
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Johannes
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Joined: 21 Jul 2018, 12:52
Location: TU Munich

Re: Calculating Purity of PurificationMPS

Post by Johannes »

The best idea I can come up with on the spot would be to contract Tr(rho^2) as a tensor network from left to right.
There's no function for that in TeNPy ritght now, but it shouldn't be hard to implement that.
Doing this is O(chi^5), though, so it's quite expensive compared to the usual O(chi^3) scaling we have in MPS.
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