Rényi entanglement entropy in complex quantum systems
ORAL
Abstract
Despite being a well-established operational approach to quantify entanglement, R'enyi entropy calculations have been plagued by their computational complexity [1-3]. We introduce a theoretical framework based on an optimal thermodynamic integration scheme, where the R'enyi entropy can be efficiently evaluated using regularizing paths [4]. This approach avoids slowly convergent fluctuating contributions and leads to low-variance estimates. In this way, large system sizes and high levels of entanglement in model or first-principles Hamiltonians are within our reach. We demonstrate it in the one-dimensional quantum Ising model and perform the first evaluation of entanglement entropy in the formic acid dimer, by discovering that its two shared protons are entangled even above room temperature.
[1] G. Carleo and M. Troyer, Solving the quantum many-body problem with artificial neural
networks, Science (80-. ). 355, 602 (2017), arXiv:1606.02318.
[2] M. B. Hastings, I. Gonz ´alez, A. B. Kallin, and R. G. Melko, Measuring Rényi entanglement
entropy in quantum Monte Carlo simulations, Phys. Rev. Lett. 104, 157201 (2010).
[3] J. DEmidio, Entanglement Entropy from Nonequilibrium Work, Phys. Rev. Lett. 124, 110602
(2020), arXiv:1904.05918.
[4] M. Srdinsek, M. Casula, and R. Vuilleumier, Quantum Rényi entropy by optimal thermody-
namic integration paths, Phys. Rev. Research 4, L032002 (2022).
[1] G. Carleo and M. Troyer, Solving the quantum many-body problem with artificial neural
networks, Science (80-. ). 355, 602 (2017), arXiv:1606.02318.
[2] M. B. Hastings, I. Gonz ´alez, A. B. Kallin, and R. G. Melko, Measuring Rényi entanglement
entropy in quantum Monte Carlo simulations, Phys. Rev. Lett. 104, 157201 (2010).
[3] J. DEmidio, Entanglement Entropy from Nonequilibrium Work, Phys. Rev. Lett. 124, 110602
(2020), arXiv:1904.05918.
[4] M. Srdinsek, M. Casula, and R. Vuilleumier, Quantum Rényi entropy by optimal thermody-
namic integration paths, Phys. Rev. Research 4, L032002 (2022).
*We are thankful for the support of the HPCaVe computational platform of Sorbonne University, where the main calculations were performed. We are grateful for the environment provided by ISCD and its MAESTRO junior team. This work was partially supported by the European Centre of Excellence in Exascale Computing TREX-Targeting Real Chemical Accuracy at the Exascale, funded by the European Union's Horizon 2020 Research and Innovation program under Grant Agreement No. 952165.
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Publication: M. Srdinsek, M. Casula, and R. Vuilleumier, Quantum Rényi entropy by optimal thermody-
namic integration paths, Phys. Rev. Research 4, L032002 (2022).
Presenters
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Miha Srdinsek
- Sorbonne University