Magic phase transitions in monitored gaussian fermions

TL;DR

This paper explores how continuous monitoring influences the nonstabilizerness (magic) of Gaussian fermionic systems, revealing a hidden complexity transition in subleading corrections that standard entanglement measures cannot detect.

Contribution

It introduces a scalable method to track magic in monitored fermionic systems and uncovers a novel measurement-induced complexity transition in subleading terms.

Findings

Leading volume-law magic remains robust across measurement rates.

A sharp transition occurs in subleading logarithmic corrections.

Magic diagnostics reveal hidden dynamical features not seen by entanglement.

Abstract

Monitored quantum systems, where unitary dynamics compete with continuous measurements, exhibit dynamical transitions as the measurement rate is varied. These reflect abrupt changes in the structure of the evolving wavefunction, captured by complementary complexity diagnostics that include and go beyond entanglement aspects. Here, we investigate how monitoring affects magic state resources, the nonstabilizerness, of Gaussian fermionic systems. Using scalable Majorana sampling techniques, we track the evolution of stabilizer R\'enyi entropies in large systems under projective measurements. While the leading extensive (volume-law) scaling of magic remains robust across all measurement rates, we uncover a sharp transition in the subleading logarithmic corrections. This measurement-induced complexity transition, invisible to standard entanglement probes, highlights the power of magic-based diagnostics in revealing hidden features of monitored many-body dynamics.