Answering a question on finite temperature simulations with fermionic systems:
Dear Dr. ******,
the basic implementation for finite-T simulations are in the current release of openMPS, although they are not advertised right now. The reason for that is that the closed system simulations come with many convenient features, which are not available for the open/mixed systems including the finite-T simulations. I will summarize what algorithm is implemented and what you could currently simulate.
The finite-T simulations start with the identity scaled to a normalized density matrix. The imaginary time evolution cools this initial infinite-T states to the ground state for long enough imaginary time evolution. We use a locally purfied tensor network (LPTN) for the representation of the density matrix and the Time-Evolving-Block-Decimation (TEBD) for the imaginary time evolution.
For the fermions we have the following possibilities and restrictions:
1) Local measurements and the energy are possible.
2) Correlations and two-site reduced density matrices are calculated, I would need to check in detail if the density matrices are just an internal step or written to the output files. Since the 1d chain with fermions have to consider the Jordan-Wigner string terms, the correlations for f, fdagger terms are excluded. The number correlations n_i, n_j work.
3) One could measure nearest-neighbor f, fdagger correlations (string term is included on the second site)
4) No long-range interactions due to TEBD.
5) No number conservation for various reasons.
6) It would be relatively easy for me to double-check each measurement against our exact diagonalization for small systems for the thermal state exp(- beta H)
I hope that answers some of questions and you have a better picture what can be simulated and please let me know if you have any further questions. If you need certain measures, I can put them as well on the development list; There will be some new development in the upcoming year of my PhD.
Best regards,
Daniel Jaschke
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Answering a question on finite temperature simulations with fermionic systems:
Dear Dr. ******,
the basic implementation for finite-T simulations are in the current release of openMPS, although they are not advertised right now. The reason for that is that the closed system simulations come with many convenient features, which are not available for the open/mixed systems including the finite-T simulations. I will summarize what algorithm is implemented and what you could currently simulate.
The finite-T simulations start with the identity scaled to a normalized density matrix. The imaginary time evolution cools this initial infinite-T states to the ground state for long enough imaginary time evolution. We use a locally purfied tensor network (LPTN) for the representation of the density matrix and the Time-Evolving-Block-Decimation (TEBD) for the imaginary time evolution.
For the fermions we have the following possibilities and restrictions:
1) Local measurements and the energy are possible.
2) Correlations and two-site reduced density matrices are calculated, I would need to check in detail if the density matrices are just an internal step or written to the output files. Since the 1d chain with fermions have to consider the Jordan-Wigner string terms, the correlations for f, fdagger terms are excluded. The number correlations n_i, n_j work.
3) One could measure nearest-neighbor f, fdagger correlations (string term is included on the second site)
4) No long-range interactions due to TEBD.
5) No number conservation for various reasons.
6) It would be relatively easy for me to double-check each measurement against our exact diagonalization for small systems for the thermal state exp(- beta H)
I hope that answers some of questions and you have a better picture what can be simulated and please let me know if you have any further questions. If you need certain measures, I can put them as well on the development list; There will be some new development in the upcoming year of my PhD.
Best regards,
Daniel Jaschke