The quantum information of a fermion on the torus

Concepts from quantum information theory have become increasingly important in our understanding of entanglement in QFTs. A prominent example of this is the entanglement (or modular) Hamiltonian, which determines the entanglement spectrum. Using complex analysis, we determine this operator for the chiral fermion at finite temperature on the circle, and show that it exhibits surprising new features. This simple system illustrates how a modular flow can transition from complete locality to complete non-locality as a function of temperature, thus bridging the gap between previously known limits. We derive the first exact results for the entanglement entropy on the torus, and determine the analytic continuation of the Renyi entropies on the complex plane. Finally, we provide some explicit novel examples of modular flow.

References

https://arxiv.org/abs/1905.05768

https://arxiv.org/abs/1906.02207