Thermal pure matrix product state and thermal mixed quantum states.

Title: Thermal pure matrix product state and thermal mixed quantum states.
Speaker: Prof. Chisa Hotta (UTokyo)
Start Date/Time: 2024-05-29 / 9:00 a.m. (Taipei time) = [10:00 a.m. (Janpan time)] 
End Date/Time: 2024-05-29 / 10:30 a.m. 
Host: Prof. Chia-Min Chung (NSYSU)

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We would like to discuss the classification of thermal states and the variability of their representation that depends on the numerical tools and available resources. A key idealized scenario within all possible choices of thermal quantum states is the thermal pure state, which relies on the concept of typicality in statistical physics. Given a suitably random initial state and ample computational resources, we can construct such a typical state using the standard imaginary time evolution technique. The resultant pure state exhibits a substantial amount of von Neumann entanglement entropy following the volume law, whose density is equivalent to the thermal entropy density.
However, in practical situations, achieving such a state is often infeasible due to various constraints. To compensate for the loss of entanglement entropy, we resort to random sampling averages, akin to an ensemble average. The closer the entanglement approaches the volume law, the less reliant we are on these random averages. Our approach involves using matrix product states, which we call TPQ-MPS, to design quantum states capable of storing entropy.
We will show some details of how we have qualified the thermal state and how we applied TPQ-MPS to the two dimensional Kitaev model.
If the time allows, we may present some on-going variational approach to obtain the thermal state.

Related papers:
A Iwaki, A Shimizu, C Hotta, Phys. Rev. Research 3, L022015 (2021)
A Iwaki, C Hotta, Phys. Rev. B 106, 094409 (2022)
A Iwaki, C Hotta, Journal of Physics: Conference Series 2207, 012031 (2022)
M Gohlke, A Iwaki, C Hotta, SciPost Physics 15, 206 (2023)
A Iwaki, C Hotta, arXiv:2403.10018