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Abstract Symmetry-protected topological phases1–4cannot be described by any local order parameter and are beyond the conventional symmetry-breaking model5. They are characterized by topological boundary modes that remain stable under symmetry respecting perturbations1–4,6–8. In clean, gapped systems without disorder, the stability of these edge modes is restricted to the zero-temperature manifold; at finite temperatures, interactions with mobile thermal excitations lead to their decay9–11. Here we report the observation of a distinct type of topological edge mode12–14, which is protected by emergent symmetries and persists across the entire spectrum, in an array of 100 programmable superconducting qubits. Through digital quantum simulation of a one-dimensional disorder-free stabilizer Hamiltonian, we observe robust long-lived topological edge modes over up to 30 cycles for a wide range of initial states. We show that the interaction between these edge modes and bulk excitations can be suppressed by dimerizing the stabilizer strength, leading to an emergent U(1) × U(1) symmetry in the prethermal regime of the system. Furthermore, we exploit these topological edge modes as logical qubits and prepare a logical Bell state, which exhibits persistent coherence, despite the system being disorder-free and at finite temperature. Our results establish a viable digital simulation approach15–18to experimentally study topological matter at finite temperature and demonstrate a potential route to construct long-lived, robust boundary qubits in disorder-free systems.
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Extrinsic geometry and gappable edges in rotationally invariant topological phases
Recent work on Abelian topological phases with rotational symmetry has raised the question of whether rotational symmetry can protect gapless propagating edge modes. Here we address this issue by considering the coupling of topological phases to the extrinsic geometry of the background. First, we analyze an effective hydrodynamic theory for an Abelian topological phase with vanishing Hall conductance. After integrating out the bulk hydrodynamic degrees of freedom, we identify charge neutral, rotationally invariant-mass terms by coupling the propagating boundary modes to the extrinsic geometry. This allows us to integrate out the edge modes and we find a gapped theory described by a local induced action that depends on the extrinsic geometry of the boundary, regardless of the shift. Finally, we apply these ideas to a microscopic theory and find the explicit bulk terms which respect gauge and rotational symmetry and open a gap in the edge spectrum.
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- PAR ID:
- 10693814
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 112
- Issue:
- 15
- ISSN:
- 2469-9950
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1103/wwb5-19b3
