Effective thermodynamics of reduced density matices
| Project/Area Number |
22K14007
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 13030:Magnetism, superconductivity and strongly correlated systems-related
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| Research Institution | Kindai University |
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Principal Investigator |
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| Project Period (FY) |
2022-04-01 – 2024-03-31
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| Project Status |
Discontinued (Fiscal Year 2022)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2023: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2022: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | Thermodynamics / Tensor network / Noise correlations / Hubbard model / Dynamics / Quantum chaos / Bose gases / Non-equilibrium Dynamics / Irreversibility / Quantum quench |
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| Outline of Research at the Start |
The unitary non-equilibrium dynamics of closed many-body systems will be investigated. The thermodynamics of the full system is described solely by the work distribution, but as the system energy is described by a sum of few-body operators, the effective thermodynamics of reduced density matrices (RDMs), where effective heat and work terms can be defined with the remaining system acting as the environment, is a natural way to gain further insight. These concepts will be investigated using the Bose-Hubbard model which can be tuned between integrable and chaotic regimes through the interaction.
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| Outline of Annual Research Achievements |
In this financial year I have achieved several required steps for implementing my proposal and published one paper related to the required techniques, with another paper having been submitted for publication.
Implementing the effective heat and work for a model with finite interactions requires the evaluation of the second-order density matrix. This is a rather involved process in the tensor network (TN) approach, however, during the last year I implemented this in ITensor and used it for my work on noise correlations in SU(N) systems which was recently published in PRA. In the last year I have also co-authored a manuscript, submitted to scipost, on quantum chaos in Bose-mixtures. Here we found interesting chaotic regimes, depending on the symmetry between interactions. This is closely related to the thermodynamic properties of the system and suggests potential parameter regimes of interest for investigating effective thermodynamics in systems with two distinguishable components.
Additionally, I have implemented the calculation of effective heat and work for the Bose-Hubbard model (BHM) using exact diagonalization (ED). I have also implemented Hubbard model quench dynamics using the TN Suzuki-Trotter approach in order to study correlation spreading. Preliminary investigations of the effective heat and work in the BHM using ED suggests that the behavior for different types of quenches in strongly chaotic and weakly chaotic regimes are qualitatively different.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The project is progressing relatively smoothly. Most of the required numerical calculations have been implemented and I have published a related paper showcasing one of the required techniques. Simulation of the effective heat and work using ED for the Bose-Hubbard model have been implemented. Additionally, both the 4-point correlation function and BHM dynamics have been implemented using the TN approach in ITensor, which means that the basic ingredients for calculating the effective thermodynamics using this approach is in place as well.
The ED calculations suggest that the qualitative behavior strongly depends on the interactions in the BHM as well as the type of quench. For example for an interaction quench the one-body reduced system energy is dominated by effective heat transfer, while the two-body interaction energy is dominated by effective work. This corresponds to the intuitive notion that any work performed in the system must be dominated by the interaction potential which is the one that is physically changed. In the strongly chaotic regime such a quench also leads to a relatively stable heat and work over time and it becomes simpler to investigate the average properties. Meanwhile a global quench such as changing the frequency of a harmonic trapping potential shows a much more mixed picture, with both effective heat and work contributing to the one-body and interaction energy, and being less stable over time even in the chaotic regime.
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| Strategy for Future Research Activity |
In the next financial year I plan to finish the work on the Bose-Hubbard model. I will further investigate the qualitative differences uncovered between interaction and trap quenches in the chaotic and less chaotic regions. I will also investigate how the effective one- and two-body heat/work relates to standard quantities such as the irreversible work. Additionally the relation to effective temperatures that can be assigned to the many-body state as well as the von Neuman entropy of the one and two-body density matrices will be investigated.
The initial work will be performed using ED techniques. I will then then attempt to look at larger system sizes in the same parameter regimes using the tensor network approach. If the ED results shows that large time-scales are required to properly investigate the effective heat and work it may be less practical to solve using the TN Suzuki-Trotter approach due to the growth of spatial entanglement entropy with time. Even in that case the ED results alone are likely to be of sufficient interest and can also be used to identify regimes suitable for larger system investigation in the TN approach.
Investigating the thermodynamics of the reduced states and their relation to one-body and interaction energies in a minimal continuum few-body Bose 2+2 mixture, using a similar setup and techniques as in my recently co-authored manuscript https://arxiv.org/abs/2301.04818 would also be a potentially interesting direction, if time permits.
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Report
(1 results)
Research Products
(3 results)
