Vanishing stabilizer Rényi entropy in the ground state of the Majumdar-Ghosh model

Abstract

The Majumdar-Ghosh model is a quantum Heisenberg spin model that has a nearest-neighbor and next-nearest-neighbor interaction. Its ground states consist of decoupled Bell state dimers and are therefore stabilizer states. In this paper, we provide a direct calculation of the stabilizer Rényi entropy to prove that the nonstabilizerness of the ground state of the Majumdar-Ghosh model is zero for all possible chain lengths. To do so, we evaluate the expectation value of all Pauli string operators and use a combinatoric argument to prove that the stabilizer Rényi entropy vanishes identically.