Quantum Rényi entropy by optimal thermodynamic integration paths

Abstract

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