correlation length and charge sector

How do I use this algorithm? What does that parameter do?
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lww
Posts: 10
Joined: 09 Jan 2019, 13:27

correlation length and charge sector

Post by lww »

Correlation length in iDMRG is determined by the second largest eigenvalue \(\eta_2\) of transfer matrix. I looked into the source code and found the following code, which always returns eigenvalues within charge sector 0. Does that mean we should always use \(\eta_2\) from the same charge sector as dominant eigenvector, instead of the global one?

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T = TransferMatrix(self, self, charge_sector=0, form='B') 
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Johannes
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Joined: 21 Jul 2018, 12:52
Location: TU Munich

Re: correlation length and charge sector

Post by Johannes »

Good question, thanks for pointing that out.

The dominant eigenvector with eigenvalue 1 should always be in 0 charge sector: in canonical form the dominant eigenvector is just the identity, which has no charge. But I agree that it is not clear a priori (at least not to me) in which sector the next to dominant eigenvector is. For example, if correlations like \(<S^+_i S^-_j>\) decay much slower than \(<S^z_i S^z_j>\), it should be in the charge=+-1 sector.

To be on the save side, I've added an argument charge_sector to correlation_length now, so you can simply check it.
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