Topological bound states in interacting Su-Schrieffer-Heeger rings

Area of Science:

• Condensed Matter Physics
• Topological Matter
• Quantum Many-Body Physics

Background:

• The Su-Schrieffer-Heeger (SSH) model describes topological phases in one-dimensional systems.
• Topological edge states are a hallmark of non-trivial topological invariants like Zak's phase.
• Understanding two-particle behavior is crucial for exploring complex quantum phenomena.

Purpose of the Study:

• Investigate the nature of two-particle states in an SSH chain with periodic boundary conditions.
• Identify and characterize emergent topological states in a many-body context.
• Differentiate the effects of nearest-neighbor versus Hubbard interactions on topological states.

Main Methods:

• Mapping the two-particle SSH system to a single particle in a 2D lattice with potential walls.
• Calculating the energy spectrum of two-body states using center-of-mass and relative coordinates.
• Analyzing the localization properties of emergent bands in the relative coordinate space.

Main Results:

• Two additional in-gap bands, beyond expected doublon bands, were found in the two-particle spectrum.
• These in-gap bands correspond to topological states localized at the edges of the relative distance coordinate.
• The presence of these topological bound states is specific to nearest-neighbor interactions, not Hubbard interactions.

Conclusions:

• Topological states can manifest intrinsically in many-body systems, localized in internal coordinates.
• These many-body topological states have no direct single-particle counterpart in effective models.
• Nearest-neighbor interactions play a critical role in the emergence of these novel topological phenomena in SSH chains.