Localized Majorana-Like Modes in a Number-Conserving Setting: An Exactly Solvable Model

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Topological Materials

Background:

• Interacting fermion systems are crucial for understanding emergent quantum phenomena.
• Topological phases of matter host exotic excitations, such as Majorana fermions.
• Two-wire geometries offer unique platforms for studying quantum transport and edge states.

Purpose of the Study:

• To introduce and analyze a novel model of interacting fermions in a two-wire geometry.
• To investigate the existence and properties of nonlocal zero-energy Majorana-like edge excitations.
• To characterize the topological phase and its boundaries within the model's phase diagram.

Main Methods:

• Development of a number-conserving framework for the fermion model.
• Exact solution on a specific line by varying fermion density.
• Numerical analysis using the density matrix renormalization group (DMRG) away from the solvable line.
• Calculation of entanglement spectrum and braiding operators to identify topological properties.

Main Results:

• Identification of a topologically nontrivial ground state wave function on an exactly solvable line.
• Characterization of topological properties via degenerate entanglement spectrum and exponentially localized braiding operators.
• Observation of a gap in the single-particle spectrum despite a gapless Hamiltonian.
• Computation of correlations between edge modes and superfluid correlations.

Conclusions:

• The model supports a sizable topological phase with nonlocal Majorana-like edge excitations.
• The exactly solvable line serves as a boundary for this topological phase.
• The findings contribute to the understanding of topological phases in interacting fermion systems and potential applications in topological quantum computing.