Entanglement measures in the quantum Rabi model

Abstract

Although quantum criticality is commonly believed to occur in many-body systems in the thermodynamic limit, it is newly realized that the quantum Rabi model (QRM) undergoes quantum phase transitions (QPTs) from a normal phase to a superradiant phase provided the energy barrier between two local-minima states is infinite. In this work, we study QPTs of the QRM from quantum information perspective of entanglement, i.e., von Neumann entropy. We find that the pronounced maximums of the derivative of von Neumann entropy can identify the critical point of the QRM with good accuracy. Consequently, a logarithmic diverging behavior for the derivative of von Neumann entropy is observed, and the critical exponents can be extracted via finite-frequency scaling. Interestingly, large frequency scaling for linear entropy at the critical point is also discovered, and combining with analytic derivations, the corresponding critical exponent is distilled. As an extension, the numerical calculations of von Neumann entropy confirm that the anisotropic QRM with finite anisotropy is of the same universality class as the standard QRM, but the Jaynes–Cummings model belongs to a different universality class. The simple structure of the QRM offers a promising platform to demonstrate the universal scaling behavior of the entanglement measures for QPTs.