Strong Zero Modes from Geometric Chirality in Quasi-One-Dimensional Mott Insulators

Area of Science:

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

Background:

• Strong zero modes enable quantum systems to preserve local information away from the ground state.
• Z_n chiral quantum clock models and Z_n parafermions are known examples exhibiting strong zero modes.

Purpose of the Study:

• To demonstrate the origin of Z_n chiral clock models and their strong zero modes from geometric chirality in fermionic Mott insulators.
• To investigate the presence and robustness of strong zero modes in a specific Z_3 chiral clock model perturbed by a realistic lattice interaction.

Main Methods:

• Utilized bosonization techniques combined with general symmetry considerations to link fermionic Mott insulators (three-leg ladders for n=3) to Z_3 chiral clock models.
• Introduced a concrete lattice model and analyzed its mapping to the Z_3 chiral clock model, including perturbation by the Uimin-Lai-Sutherland Hamiltonian.
• Investigated the dynamics of clock operator correlators at the edge of the perturbed model to demonstrate the presence of strong zero modes.

Main Results:

• Established a direct link between geometric chirality in fermionic Mott insulators and the emergence of Z_n chiral clock models with strong zero modes.
• Showed that a perturbed Z_3 chiral clock model, arising from a realistic lattice setup, still hosts strong zero modes.
• Demonstrated that edge correlators in the perturbed model remain stable for exponentially long times, even at infinite temperature, confirming robust strong zero modes.

Conclusions:

• Geometric chirality in fermionic Mott insulators provides a physical mechanism for realizing quantum systems with strong zero modes.
• The Z_3 chiral clock model, derived from fermionic ladders and perturbed by superexchange, serves as a concrete platform for studying robust strong zero modes.
• Strong zero modes offer a promising avenue for robust quantum information encoding in practical, high-temperature quantum many-body systems.