Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics

Magic, or nonstabilizerness, is a crucial quantum resource, yet its dynamics in open quantum systems remain largely unexplored. We investigate magic in the open XXZ spin chain under either boundary gain and loss or bulk dephasing using the stabilizer Rényi entropy <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>M</a:mi> <a:mn>2</a:mn> </a:msub> </a:math> . To enable scalable simulations of large systems, we develop a unique, highly efficient algorithm for computing <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>M</b:mi> <b:mn>2</b:mn> </b:msub> </b:math> within the matrix product state formalism while maintaining constant bond dimension—an advancement over existing methods. For boundary driving, we uncover universal scaling laws, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>M</c:mi> <c:mn>2</c:mn> </c:msub> <c:mrow> <c:mo>(</c:mo> <c:mi>t</c:mi> <c:mo>)</c:mo> </c:mrow> <c:mo>∼</c:mo> <c:msup> <c:mi>t</c:mi> <c:mrow> <c:mn>1</c:mn> <c:mo>/</c:mo> <c:mi>z</c:mi> </c:mrow> </c:msup> </c:mrow> </c:math> , linked to the dynamical exponent <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>z</d:mi> </d:math> for several distinct universality classes. We also disentangle classical and quantum contributions to magic by introducing a mean-field approximation for magic, thus emphasizing the prominent role of quantum-critical fluctuations in nonstabilizerness. For bulk dephasing, dissipation can transiently enhance magic before suppressing it and drive it to a nontrivial steady-state value. These findings position magic as a powerful diagnostic tool for probing universality and dynamics in open quantum systems.