Many-body characterization of particle-conserving topological superfluids

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Topological Phases of Matter

Background:

• Distinguishing trivial from topological superfluids in interacting systems with conserved particle number is challenging.
• Existing models often lack exact solvability or particle number conservation.
• Topological superconductivity is crucial for fault-tolerant quantum computing.

Purpose of the Study:

• To introduce a number-conserving, interacting model that is exactly solvable.
• To identify unique signatures of topological superconductivity in interacting systems.
• To define and analyze many-body Majorana operators and topological invariants.

Main Methods:

• Development of the Richardson-Gaudin-Kitaev chain, an integrable, number-conserving variation of the Kitaev model.
• Exact solution for periodic and antiperiodic boundary conditions.
• Derivation of a closed-form expression for an interacting topological invariant.

Main Results:

• Identification of fermion parity switches as a distinct characteristic of topological superconductivity in interacting systems.
• Definition of many-body Majorana operators by tuning flux to a fermion parity switch.
• Demonstration that the transition out of the topological phase is of third order.

Conclusions:

• The Richardson-Gaudin-Kitaev chain provides a powerful framework for studying topological phases in interacting systems.
• Fermion parity switches offer a robust signature for topological superconductivity.
• The model facilitates the exploration of Majorana zero modes and topological invariants in a controllable, interacting setting.