Abstract
Entanglement, the “spooky action at a distance”, symbolized by the famous Bell pair of two qubits has emerged as the most fundamental aspect of quantum mechanics in the last decade. Entanglement, having no classical analogue, allows to distill the truly quantum nature of non-trivial many-body states. However, computation of various measures of entanglement, e.g. entanglement entropy, unlike thermal entropy, is much more challenging within well-known techniques of quantum many-body physics like path integrals and associated perturbative and non-perturbative approximations. I will discuss a new path integral approach, on a par with standard coherent state path integrals, for calculating entanglement of interacting fermions. I will discuss application of the method for interacting fermionic systems described by large-N models related to the Sachdev-Ye-Kitaev (SYK) model. I will elucidate the connection between Rényi entanglement entropy and residual entropy of the non Fermi liquid (NFL) ground state in the SYK model and extract sharp signatures of quantum phase transition in the entanglement entropy across an NFL to fermi liquid (FL) transition. Furthermore, I will discuss the application of method to obtain nontrivial system-size scaling of entanglement in an interacting diffusive metal.
Reference:
A. Haldar, S. Bera, S. Banerjee, Phys. Rev. Research 2, 033505 (2020).