Multi-critical topological transition at quantum criticality.

Area of Science:

• Condensed Matter Physics
• Topological States of Matter
• Quantum Phase Transitions

Background:

• Investigating topological quantum phase transitions between gapless phases is a key area in condensed matter physics.
• Understanding these transitions is crucial for developing new quantum materials and technologies.

Purpose of the Study:

• To investigate and characterize topological quantum phase transitions between gapless phases.
• To analyze the distinct universality classes of these gapless phases.
• To explore a model Hamiltonian applicable to systems with gapless excitations.

Main Methods:

• Utilized the transverse field Ising model with three-spin interaction in one dimension.
• Analyzed topological invariants (winding numbers) to characterize phases.
• Calculated and analyzed Wannier state correlation functions.
• Performed energy dispersion analysis to study Lorentz invariance.

Main Results:

• Observed a topological transition between gapless phases on a critical line.
• Identified two multi-critical points: one trivial, one active (Lifshitz universality class).
• Confirmed the topological transition via correlation functions and energy dispersion analysis.
• Demonstrated the breakdown of Lorentz invariance at the multi-critical point.

Conclusions:

• The study successfully characterized topological quantum phase transitions between distinct gapless phases.
• A Lifshitz-type multi-critical point governs the transition, with implications for universality classes.
• The developed model and methods are applicable to systems where conventional topological concepts fail.