Finite temperature negativity Hamiltonians of the massless Dirac fermion

A bstract The negativity Hamiltonian, defined as the logarithm of a partially transposed density matrix, provides an operatorial characterisation mixed-state entanglement. However, so far, it has only been studied for matrices corresponding to subsystems globally pure states. Here, we consider genuine example mixed state one-dimensional massless Dirac fermions in system at finite temperature and size. As subsystems, arbitrary set disjoint intervals. structure Hamiltonian resembles one entanglement same geometry: addition local term proportional stress-energy tensor, each point is non-locally coupled infinite but discrete other points. when lengths non-transposed intervals coincide, remarkably simplifies retrieve mild non-locality ground Hamiltonian. We also conjecture exact expression associated twisted partial transpose, which Hermitian fermionic matrix. finally obtain continuum limit both bi-local operators from numerical computations free-fermionic chains.