Quantum field theory for the chiral clock transition in one spatial dimension

Area of Science:

• Condensed Matter Physics
• Quantum Phase Transitions
• Ultracold Atomic Gases

Background:

• The N-state chiral clock model exhibits complex quantum phase transitions.
• This model shares universality with experiments on ordered Rydberg states in ultracold atoms.
• Understanding these transitions is key to quantum simulation and novel quantum states.

Purpose of the Study:

• To investigate the quantum phase transition in the 1D N-state chiral clock model.
• To analyze the transition's universality class and critical behavior.
• To connect theoretical models with experimental observations in ultracold atomic systems.

Main Methods:

• Lattice duality transformation to map the clock model to a Bose gas model.
• Renormalization group analysis in an expansion of 2-d and 4-N.
• Numerical density-matrix renormalization group (DMRG) studies.

Main Results:

• A direct phase transition is identified for N=3, from a gapped phase with broken Z_N symmetry to a gapped phase with restored Z_N symmetry.
• The transition exhibits a dynamical critical exponent z ≠ 1, precluding description by relativistic quantum field theory.
• A renormalization group fixed point is found at two-loop order, supporting the direct phase transition scenario.
• Numerical DMRG studies provide evidence for the direct transition and estimate critical exponents z and ν.

Conclusions:

• The N-state chiral clock model in d=1 provides a platform for studying non-relativistic quantum phase transitions.
• The duality to a Bose gas offers a powerful tool for theoretical analysis.
• Experimental realization with ultracold atoms can probe these unique quantum phenomena.