Realizing All so(N)_{1} Quantum Criticalities in Symmetry Protected Cluster Models

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Statistical Mechanics

Background:

• Generalized cluster models exhibit complex quantum behaviors.
• Understanding quantum criticality is crucial for developing new materials and technologies.
• Conformal field theories (CFTs) provide powerful frameworks for describing critical phenomena.

Purpose of the Study:

• To demonstrate the emergence of so(N)₁ universality class quantum criticalities in one-dimensional generalized cluster models.
• To establish a duality between cluster models and nonlocally coupled transverse field Ising chains.
• To identify local representations for primary fields in so(N)₁ CFTs.

Main Methods:

• Perturbing one-dimensional generalized cluster models with Ising or Zeeman terms.
• Analyzing the low-energy spectrum of N linearly dispersing fermions.
• Constructing an explicit duality between cluster models and transverse field Ising chains.
• Investigating the symmetry protection mechanisms of cluster models.

Main Results:

• All so(N)₁ universality class quantum criticalities emerge from perturbed cluster models.
• The low-energy spectrum of N fermions precisely matches so(N)₁ CFT predictions.
• Cluster models are dual to nonlocally coupled transverse field Ising chains.
• Symmetry protection of cluster models is linked to Ising symmetries.
• Local representations for so(N)₁ CFT primary fields are identified.
• The su(2)₂ ≃ so(3)₁ Wess-Zumino-Witten model emerges in a specific spin-1/2 model.

Conclusions:

• Perturbed one-dimensional generalized cluster models provide a platform for realizing so(N)₁ quantum criticalities.
• The established duality offers new insights into the nature of quantum criticality and symmetry protection.
• The findings enable the construction of specific models exhibiting rich quantum phenomena, relevant for experimental realization.