[論文レビュー] Entanglement signatures of quantum criticality in Floquet non-Hermitian topological systems

Siyuan Cheng, Rui Xie+3 more|arXiv (Cornell University)|Jan 6, 2026

Quantum many-body systems被引用数 0

ひとこと要約

要約: The paper uses entanglement entropy and entanglement spectrum to diagnose topological phase transitions in the one-dimensional Floquet non-Hermitian SSH model, locating transitions via peaks and logarithmic scaling with central charge c=1, and showing robustness to non-Hermiticity and next-nearest-neighbor hopping.

ABSTRACT

The entanglement entropy can be an effective diagnostic tool for probing topological phase transitions. In one-dimensional single particle systems, the periodic driving generates a variety of topological phases and edge modes. In this work, we investigate the topological phase transition of the one-dimensional Floquet Su-Schrieffer-Heeger model using entanglement entropy, and construct the phase diagram based on entanglement entropy. The entanglement entropy exhibits pronounced peaks and follows the logarithmic scaling law at the phase transition points, from which we extract the central charge $c=1$. We further investigate the entanglement spectrum to accurately distinguish the different topological phases. In addition, the coupling between zero and $π$ modes leads to characteristic splittings in the entanglement spectrum, signaling their hybridization under periodic driving. These results remain robust in non-Hermitian regimes and in the presence of next-nearest-neighbor hopping, demonstrating the reliability and universality of entanglement entropy as a diagnostic for topological phase transitions.

研究の動機と目的

• Motivate entanglement entropy as a diagnostic for topological phase transitions in driven 1D systems.
• Characterize topological zero modes, π modes, and hybrid phases via entanglement entropy and spectrum.
• Establish robustness of entanglement signatures under non-Hermitian terms and extended hopping.
• Extract universal quantities such as the central charge from finite-size scaling of S_A.
• Investigate how driving frequency and coupling between edge modes affect entanglement properties.

提案手法

• Study the 1D Floquet SSH model with periodic driving of intracell hopping, H(k,t)=[d_x+λ cos(ω t)]σ_x+d_y σ_y.
• Use Floquet formalism to obtain quasienergy spectrum and edge-mode structure under PBC and OBC.
• Compute entanglement entropy S_A from the single-particle correlation matrix C_ij for noninteracting fermions.
• Analyze entanglement spectrum and identify two-fold degeneracy at ξ=0.5 for edge modes; observe splitting in coexistence phases.
• Extract central charge c from finite-size scaling S_A(N)= (c/3) ln N + a near critical points.
• Extend to non-Hermitian cases with H(k,t)=[d_x+λ cos(ω t)]σ_x+[d_y+iγ]σ_y and include t3 (NNN hopping); redefine ground state via biorthogonal framework and use |L⟩,|R⟩ states to form ρ_A and compute S_A.

実験結果

リサーチクエスチョン

• RQ1 How does periodic driving generate zero, π, and hybrid edge modes in the Floquet SSH model?
• RQ2 Can entanglement entropy and entanglement spectrum reliably diagnose topological phase transitions in Floquet non-Hermitian systems?
• RQ3 What is the universal scaling (central charge) at these Floquet-critical transitions?
• RQ4 Are entanglement diagnostics robust to non-Hermitian terms and next-nearest-neighbor hopping?
• RQ5 How do driving frequency and edge-mode coupling affect entanglement signatures?

主な発見

• Entanglement entropy shows pronounced peaks at topological phase transitions.
• Entanglement entropy scales logarithmically with system size at critical points, yielding central charge c=1.
• Entanglement spectrum reveals two-fold degeneracy at ξ=0.5 in phases with a single edge-mode type and splits in the coexistence phase due to zero-π mode coupling.
• Periodic driving creates a distinct π-mode phase in addition to zero-mode and hybrid phases.
• Non-Hermitian strength and next-nearest-neighbor hopping preserve the ability of entanglement measures to diagnose transitions; phase boundaries shift due to breakdown of conventional bulk-boundary correspondence.
• Finite-size scaling confirms c=1 at the transition points in both Hermitian and non-Hermitian settings.