Entanglement and its extension, Renyi entropy, are useful in measuring the quantum information encoded in a quantum state and are at the heart of the quantum theories, encompassing the quantum mechanics, quantum field theories, quantum gravity and quantum information science. These entropies have been extensively studied recently in the literature.
Quantum fields can be manipulated by the background gauge fields, such as electric and magnetic fields. In the quantum world, gauge potentials are more useful. The time and space components of the 1+1 dimensional gauge potential are called a chemical potential and current, respectively. They are our primary physical objects.
With analytic and exact computations of the entanglement and Renyi entropies on quantum field theories in 1+1 dimensions with finite chemical potential (or finite charge density) at zero temperature to verify that they do not depend on chemical potential for the field theory systems with Dirac fermions in the presence of current and/or chemical potential.
We have obtained a general formula for the entropies that can be applied in the presence of chemical potential and current. With this formula, we are able to investigate the properties of the entropies in various limits, including small and large temperature as well as large system size. We hope to provide a complete picture in a near future.