Fermionic non-Gaussianity quantifies a quantum state's deviation from a classically tractable free-fermionic description, constituting a necessary resource for computational quantum advantage. Here we use fermionic antiflatness (FAF) to measure this deviation across ergodic and many-body localized (MBL) regimes. We focus on the paradigmatic disordered spin- $1\!/2$ XXZ chain and its impurity variant with local interactions. Across highly excited eigenstates, FAF evolves from typical-state behavior at weak disorder to strongly suppressed values deep in the MBL regime, with volume-law scaling in the XXZ chain and an area-law bound in the impurity setting. Rare long-range cat-like eigenstates exhibit a pronounced enhancement of FAF, making it a sensitive diagnostic of mechanisms proposed to destabilize MBL. Starting from product states, we find that in the MBL regime FAF grows slowly in time, approaching saturation via a power-law relaxation. Overall, our results show that MBL suppresses fermionic non-Gaussianity, and the associated complexity beyond free fermions, while ergodicity restores it, motivating explorations of fermionic non-Gaussianity in other ergodicity-breaking phenomena.Fermionic non-Gaussianity quantifies a quantum state's deviation from a classically tractable free-fermionic description, constituting a necessary resource for computational quantum advantage. Here we use fermionic antiflatness (FAF) to measure this deviation across ergodic and many-body localized (MBL) regimes. We focus on the paradigmatic disordered spin-$1\!/2$ XXZ chain and its impurity variant with local interactions. Across highly excited eigenstates, FAF evolves from typical-state behavior at weak disorder to strongly suppressed values deep in the MBL regime, with volume-law scaling in the XXZ chain and an area-law bound in the impurity setting. Rare long-range cat-like eigenstates exhibit a pronounced enhancement of FAF, making it a sensitive diagnostic of mechanisms proposed to destabilize MBL. Starting from product states, we find that in the MBL regime FAF grows slowly in time, approaching saturation via a power-law relaxation. Overall, our results show that MBL suppresses fermionic non-Gaussianity, and the associated complexity beyond free fermions, while ergodicity restores it, motivating explorations of fermionic non-Gaussianity in other ergodicity-breaking phenomena.

quant-pharXiv:2602.00245Feb 3, 20260 citations

Non-Equilibrium Steady States in Quantum Spin Chains

Gunter Markus Schutz

Jan 1, 20170 citations

Preparation of non-ergodic states in quantum spin chains

A. O. García Rodríguez, G. G. Cabrera

We test the time evolution of quite general initial states in a model that is exactly solvable, $i.e.$ a semi-infinite $XY$ spin chain with an impurity at the boundary. The dynamics is portrayed through the observation of the site magnetization along the chain, focusing on the long-time behavior of the magnetization, which is estimated using the stationary phase method. Localized states are split off from the continuum for some regions of the impurity parameter space. Bound states are essential for the non-ergodic behavior reported here. When two impurity states exist, the quantum interference between them leads to magnetization oscillations which settle over very long times with the absence of damping. The frequency of the remanent oscillation is recognized as being the Rabi frequency of the localized levels.We test the time evolution of quite general initial states in a model that is exactly solvable, $i.e.$ a semi-infinite $XY$ spin chain with an impurity at the boundary. The dynamics is portrayed through the observation of the site magnetization along the chain, focusing on the long-time behavior of the magnetization, which is estimated using the stationary phase method. Localized states are split off from the continuum for some regions of the impurity parameter space. Bound states are essential for the non-ergodic behavior reported here. When two impurity states exist, the quantum interference between them leads to magnetization oscillations which settle over very long times with the absence of damping. The frequency of the remanent oscillation is recognized as being the Rabi frequency of the localized levels.

arXiv:1703.03446Mar 9, 20170 citations

Entanglement of Impurities in Spin Chains

Erik Schwartz Sørensen, Nicolas Laflorencie, Ming-Shyang Chang +1 more

Bulletin of the American Physical SocietyMar 13, 20080 citations

1\!/2

XXZ chain and its impurity variant with local interactions. Across highly excited eigenstates, FAF evolves from typical-state behavior at weak disorder to strongly suppressed values deep in the MBL regime, with volume-law scaling in the XXZ chain and an area-law bound in the impurity setting. Rare long-range cat-like eigenstates exhibit a pronounced enhancement of FAF, making it a sensitive diagnostic of mechanisms proposed to destabilize MBL. Starting from product states, we find that in the MBL regime FAF grows slowly in time, approaching saturation via a power-law relaxation. Overall, our results show that MBL suppresses fermionic non-Gaussianity, and the associated complexity beyond free fermions, while ergodicity restores it, motivating explorations of fermionic non-Gaussianity in other ergodicity-breaking phenomena.

We test the time evolution of quite general initial states in a model that is exactly solvable,

i.e.

a semi-infinite

XY

spin chain with an impurity at the boundary. The dynamics is portrayed through the observation of the site magnetization along the chain, focusing on the long-time behavior of the magnetization, which is estimated using the stationary phase method. Localized states are split off from the continuum for some regions of the impurity parameter space. Bound states are essential for the non-ergodic behavior reported here. When two impurity states exist, the quantum interference between them leads to magnetization oscillations which settle over very long times with the absence of damping. The frequency of the remanent oscillation is recognized as being the Rabi frequency of the localized levels.