Non-Hermitian fractional quantum Hall states

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Topological Phases of Matter

Background:

• Non-Hermitian systems are crucial for understanding open quantum systems, such as cold atoms with dissipation.
• Topological phases of matter exhibit unique properties protected by symmetry.
• Fractional quantum Hall (FQH) states are a prominent example of topological order.

Purpose of the Study:

• To demonstrate the emergence of a topological ordered phase in non-Hermitian systems.
• To investigate the possibility of realizing a fractional quantum Hall (FQH) state in systems with non-Hermitian interactions.
• To explore the role of many-body translational symmetry and repulsive interactions in the formation of non-Hermitian FQH states.

Main Methods:

• Consideration of non-Hermitian Hamiltonians with two-body interactions, relevant to dissipative cold atom systems.
• Analysis of topological degeneracy as an indicator of topological order.
• Calculation of the many-body Chern number for the ground state multiplet.

Main Results:

• Demonstration of a topological ordered phase in non-Hermitian systems.
• Observation of a fractional quantum Hall (FQH) state emerging from non-Hermitian two-body interactions.
• Identification of robust topological degeneracy due to many-body translational symmetry.
• Emergence of the FQH state even without repulsive interactions, linked to a continuous quantum Zeno effect.

Conclusions:

• Non-Hermitian systems with two-body interactions can host a fractional quantum Hall (FQH) state.
• Topological degeneracy in these systems is robust against non-Hermiticity.
• The FQH state can emerge without repulsive interactions, highlighting novel mechanisms for topological order in open quantum systems.