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arXiv:2411.05671 · Physical review. B./Physical review. B

Dynamics of edge modes in monitored Su-Schrieffer-Heeger models

Giulia Salatino, Gianluca Passarelli, Angelo Russomanno, Giuseppe E. Santoro, Procolo Lucignano, Rosario Fazio

Published Jun 2, 2025• 3 citations
arXivHTMLPDF

Abstract

We investigate the effect of dissipation on the dynamics of edge modes in the monitored Su-Schrieffer-Heeger (SSH) model. Our study considers both a linear observable and a nonlinear entanglement measure, namely the two-point correlation function and the Disconnected Entanglement Entropy (DEE), as diagnostic tools. While dissipation inevitably alters the entanglement properties observed in the closed system, statistical analysis of quantum trajectories reveals that by protecting the chain's edges from dissipation, it is possible to recover characteristic features analogous to those found in the unitary limit. This highlights the fundamental role of spatial dissipation patterns in shaping the dynamics of edge modes in monitored systems.

DOI
10.1103/z4sw-zj8z

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We investigate the effect of dissipation on the dynamics of edge modes in the monitored Su-Schrieffer-Heeger (SSH) model. Our study considers both a linear observable and a nonlinear entanglement measure, namely the two-point correlation function and the Disconnected Entanglement Entropy (DEE), as diagnostic tools. While dissipation inevitably alters the entanglement properties observed in the closed system, statistical analysis of quantum trajectories reveals that by protecting the chain's edges from dissipation, it is possible to recover characteristic features analogous to those found in the unitary limit. This highlights the fundamental role of spatial dissipation patterns in shaping the dynamics of edge modes in monitored systems.
We investigate the dynamics of entanglement in dissipative fermionic and bosonic Su-Schrieffer-Heeger (SSH) models and discover that they exhibit a revival dynamics of entanglement when the decoherence channel preserves the chiral symmetry. This behavior is only observable in the topological phase, and the visibility of the revival diminishes to zero at the phase boundary. Furthermore, the revival acquires a universal character, meaning that the entire time-evolution profile remains independent of system size, provided that the size exceeds the localization length of the edge modes associated with the topological phase. Our findings suggest that the universal entanglement revival originates from the topological properties of the SSH model. These dynamical properties may be experimentally accessible, for instance, by utilizing photonic quantum computers.
We investigate phase transitions in the extended Su-Schrieffer-Heeger (SSH) model with next-nearest-neighbor hoppings and an imaginary staggered chemical potential. In the presence of small non-Hermiticity, exceptional points emerge in pairs from the gap-closing momenta near the topological phase boundaries of the Hermitian limit. Utilizing the Krylov spread complexity and entanglement entropy, we analyze two dynamical protocols: (i) preparing the non-Hermitian ground state via a unitary transformation, and (ii) evolving the system under the non-Hermitian Hamiltonian. We show that the spread complexity, and long-time spread complexity as well as entanglement entropy can effectively signal phase transitions in the first and second protocols, respectively. To unravel the detailed structure of the transitions, we introduce the momentum-resolved complexity that identifies the characteristic modes and tracks their evolution with the driving parameter. In the regime where the system possesses a purely imaginary spectrum, we further identify dynamical phases based on the saturation behavior of the spread complexity. The entanglement entropy is also found to exhibit similar saturation behavior, thereby providing a more experimentally accessible probe of the dynamical phases.
We show that mutual statistics between quantum particles can be tuned to generate emergent novel few-particle quantum mechanics for the boundary modes of symmetry-protected topological phases of matter. As a concrete setting, we study a system of pseudofermions, defined as quantum particles with tunable algebra, which lie on two distinct Su-Schrieffer-Heeger (SSH) chains. We find that as the mutual statistics of the particles are tuned---the boundary modes present in the two chains gets nontrivially entangled showing a sudden jump in their mutual entanglement entropy. We further show that such tuning of statistics engenders a first-order transition between two topologically nontrivial phases which differ in the behavior of interchain entanglement. Using a combination of analytical and numerical techniques and effective modeling, we uncover the rich physics that this system hosts. The results are of particular relevance in context of the study of the effective low-energy quantum mechanics of topological edge modes in one hand and their recent realization in ultracold atoms on the other. This then provides for controlled manipulation of such low-energy modes.
We investigate quantum correlations and entanglement in a non-Hermitian quantum system modeled by a 2D stacked Su–Schrieffer–Heeger (SSH) lattice incorporating nonreciprocal hopping amplitudes and balanced on-site gain and loss. Focusing on the interplay between non-Hermiticity, topology, and open-boundary conditions, we analyze how these factors shape bipartite entanglement properties, characterized through the entanglement spectrum and entanglement negativity ( E N ). By examining the complex energy spectrum under open boundary conditions, we identify critical points associated with the closing of complex energy gaps, which significantly influence entanglement structure and signal topological phase transitions. Our findings reveal that boundary-localized non-Bloch modes and nonreciprocal couplings can induce highly tunable and unconventional entanglement features, absent under periodic boundary conditions. These results highlight the breakdown of conventional bulk-boundary correspondence and underscore the utility of entanglement measures in diagnosing non-Hermitian topological phases. Beyond advancing the fundamental understanding of quantum correlations in open systems, our study suggests potential pathways to engineer quantum devices and topological materials where gain, loss, and nonreciprocity are intrinsic elements.
Entanglement entropy (EE) provides a powerful probe of quantum phases, yet its role in identifying topological phase transitions in disordered systems remains underexplored. We introduce an exact EE-based framework that captures topological phase transitions even in the presence of disorder. Specifically, for a class of Su-Schrieffer-Heeger (SSH) model variants, we show that the difference in EE between half-filled and near-half-filled ground states,ΔSA, vanishes in the topological phase but remains finite in the trivial phase, a direct consequence of edge-state localization. This behavior persists even in the presence of quasiperiodic or binary disorder. By analyzing domain-wall configurations in the SSH chain, we further show how subsystem tuning allows one to distinguish genuine topological zero-energy eigenstates from trivial localized states. Exact phase boundaries, derived from Lyapunov exponents via transfer matrices, agree closely with numerical results fromΔSAand the topological invariant𝓠, with instances whereΔSAoutperforms𝓠. Our results highlight EE as a robust diagnostic tool and a potential bridge between quantum information and condensed matter approaches to topological matter.
Recent experimental advances in creating dissipative couplings provide a new route for engineering exotic lattice systems and exploring topological dissipation. Using the spatial lattice of atomic spin waves in a vacuum vapor cell, where purely dissipative couplings arise from diffusion of atoms, we experimentally realize a dissipative version of the Su-Schrieffer-Heeger (SSH) model. We construct the dissipation spectrum of the topological or trivial lattices via electromagnetically induced-transparency spectroscopy. The topological dissipation spectrum is found to exhibit edge modes within a dissipative gap. We validate chiral symmetry of the dissipative SSH couplings and also probe topological features of the generalized dissipative SSH model. This work paves the way for realizing non-Hermitian topological quantum optics via dissipative couplings.