Abstract
Pseudo-entropy is an interesting quantity with a simple gravity dual, which generalizes entanglement entropy such that it depends on both an initial and a final state. Here we reveal the basic properties of pseudo-entropy in quantum field theories by numerically calculating this quantity for a set of two-dimensional free-scalar field theories and the Ising spin chain. We extend the Gaussian method for pseudo-entropy in free-scalar theories with two parameters: mass m and dynamical exponent z. This computation finds two novel properties of pseudo-entropy which we conjecture to be universal in field theories, in addition to an area law behavior. One is a saturation behavior and the other one is nonpositivity of the difference between pseudo-entropy and averaged entanglement entropy. Moreover, our numerical results for the Ising chain imply that pseudo-entropy can play a role as a new quantum order parameter which detects whether two states are in the same quantum phase or not.
Highlights
We reveal the basic properties of pseudo-entropy in quantum field theories by numerically calculating this quantity for a set of twodimensional free-scalar field theories and the Ising spin chain
Introduction.—Entanglement entropy in quantum many-body systems plays significant roles in various subjects of theoretical physics, such as condensed matter physics [1,2,3], particle physics [4,5,6,7,8], and gravitational physics [9,10,11,12]
In the anti–de Sitter/conformal field theory (AdS/CFT) correspondence, [13], entanglement entropy is equal to the area of a minimal surface [14,15]
Summary
Introduction.—Entanglement entropy in quantum many-body systems plays significant roles in various subjects of theoretical physics, such as condensed matter physics [1,2,3], particle physics [4,5,6,7,8], and gravitational physics [9,10,11,12]. We reveal the basic properties of pseudo-entropy in quantum field theories by numerically calculating this quantity for a set of twodimensional free-scalar field theories and the Ising spin chain. This computation finds two novel properties of pseudo-entropy which we conjecture to be universal in field theories, in addition to an area law behavior.
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