# Locked Subharmonic Oscillations in the Entanglement Spectrum of a Periodically Driven Topological Chain

**Authors:** Rishabh Jha  
**arXiv:** [2604.07442](https://arxiv.org/abs/2604.07442)  
**Date:** 2026-04-08  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2604.07442v1/

## Key points

- Study focuses on periodically driven quantum systems and their subharmonic response
- Analysis of physical observables in interacting scenarios
- Investigation into the entanglement spectrum of a number-conserving free-fermion system
- Two-step driven Su-Schrieffer-Heeger chain with symmetry-protected edge modes at quasienergies 0 and π
- Coherent superposition of edge sectors leads to alternating stroboscopic structures in subsystem correlation matrix
- Period-doubling response with Fourier weight concentrated at half the drive frequency observed in single-particle entanglement levels
- Off-diagonal edge-bond observable acts as a linear one-body comparator for the phenomenon
- Dissipation of effect when initial state is replaced or system transitions into topologically trivial phase lacking edge modes
- Zero-π Floquet topology and coherent nonequilibrium preparation are essential factors for inducing responses
- Entanglement spectroscopy highlighted as a precise probe for examining Floquet topological coherence within quantum systems under periodic driving conditions

## Summary

This study by Rishabh Jha focuses on periodically driven quantum systems and their subharmonic response, specifically analyzing physical observables in interacting scenarios. The research delves into the entanglement spectrum of a number-conserving free-fermion system, revealing a distinct subharmonic signature. The investigation centers on a two-step driven Su-Schrieffer-Heeger chain with a Floquet operator supporting symmetry-protected edge modes at quasienergies 0 and π. The key finding is that when the initial state comprises a coherent superposition of these edge sectors, the subsystem correlation matrix exhibits alternating stroboscopic structures. Additionally, tracking the overlap of single-particle entanglement levels reveals a robust period-doubling response with Fourier weight concentrated at half the drive frequency. Interestingly, while diagonal edge densities remain flat due to sublattice symmetry, an off-diagonal edge-bond observable serves as a linear one-body comparator for this phenomenon. This effect dissipates when replacing the initial state with a stroboscopically stationary Floquet eigenstate derived from similar topological mode content or when transitioning the system into a topologically trivial phase lacking edge modes. These results underscore zero-π Floquet topology as a necessary condition and emphasize coherent nonequilibrium preparation as an essential additional factor for inducing such responses. In summary, this research highlights entanglement spectroscopy as a precise probe for examining Floquet topological coherence within quantum systems under periodic driving conditions.