Rényi entanglement entropy in complex quantum systems

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.

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