Topological Domain-Wall Pump with Z_{2} Spontaneous Symmetry Breaking

Area of Science:

• Condensed Matter Physics
• Quantum Information Science
• Topological Phases of Matter

Background:

• Topological pumps are crucial for understanding quantum transport phenomena.
• Symmetry-protected topological phases offer robust quantum states.
• Domain walls in condensed matter systems can host exotic properties.

Purpose of the Study:

• To propose a novel domain-wall pump based on an extended cluster model of S=1/2 spins.
• To investigate the topological properties and symmetry protection of the proposed pump.
• To explore the potential of these systems as topologically protected qubits.

Main Methods:

• Utilizing an extended cluster model with local U(1) gauge invariance.
• Defining current and gauge fields on sites, deviating from conventional link-based approaches.
• Analyzing ground state properties, including degeneracy and gap, under Z2 invariance and boundary magnetic fields.
• Characterizing symmetry protection via Z2 Berry phase and spatial inversion.
• Investigating topological pumping through inversion symmetry-breaking paths.

Main Results:

• The proposed domain-wall pump exhibits a gapped, doubly degenerate ground state protected by Z2 invariance.
• Spontaneous symmetry breaking leads to a symmetry-protected ground state characterized by a Z2 Berry phase.
• The topological pump induces a nontrivial bulk Chern number and singular edge state behavior.
• Generalization to multispin interactions is explicitly provided.

Conclusions:

• The developed domain-wall pump demonstrates robust topological properties.
• The system provides a platform for realizing symmetry-protected topological phases.
• The extended quantum degrees of freedom serve as prominent, topologically protected qubits.