Quantum Renyi entropy by optimal thermodynamic integration paths

Despite being a well-established operational approach to quantify entanglement, Renyi entropy calculations have been plagued by their computational complexity. We introduce here a theoretical framework based on an optimal thermodynamic integration scheme, where the Renyi 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.

Automated summary

In this paper, a theoretical framework based on an optimal thermodynamic integration scheme is introduced for efficiently calculating Renyi entropy. This approach avoids the computational complexity and slow convergence issues and provides low-variance estimates. The method is demonstrated in the one-dimensional quantum Ising model and applied to evaluate entanglement entropy in the formic acid dimer.