Quantum Rényi entropy by optimal thermodynamic integration paths

Despite being a well-established operational approach to quantify entanglement, Rényi entropy calculations have been plagued by their computational complexity. We introduce here theoretical framework based on an optimal thermodynamic integration scheme, where the can be efficiently evaluated using regularizing paths. This avoids slowly convergent fluctuating contributions and leads low-variance estimates. In this way, large system sizes high levels of entanglement in model or first-principles Hamiltonians are within our reach. demonstrate one-dimensional quantum Ising perform evaluation formic acid dimer, discovering that its two shared protons entangled even above room temperature.Received 29 December 2021Accepted 9 June 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L032002Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasChemical Physics & ChemistryEntanglement entropyPath integralsQuantum phase transitionsTechniquesMonte Carlo methodsCondensed Matter, Materials Applied PhysicsQuantum InformationStatistical