Symmetry-respecting real-space renormalization for the quantum Ashkin-Teller model

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Statistical Mechanics

Background:

• The quantum Ashkin-Teller model is a one-dimensional quantum spin chain.
• It exhibits a line of criticality with continuously varying critical exponents.
• Previous studies showed a simple real-space renormalization-group (RG) approach is effective for the quantum transverse-field Ising model.

Purpose of the Study:

• To investigate the critical behavior of the quantum Ashkin-Teller model using a simple real-space RG approach.
• To explore the generality of this RG method for models with richer critical structures.
• To compare RG predictions with conformal field theory (CFT) and numerical simulations.

Main Methods:

• Employed a simple real-space renormalization-group approach exploiting on-site symmetry.
• Applied the method to the one-dimensional quantum Ashkin-Teller model.
• Compared the predicted correlation length critical exponent with CFT results and numerical simulations.

Main Results:

• The real-space RG approach yields predictions for the correlation length critical exponent in broad agreement with CFT along the criticality line.
• Near the special Ising point, the RG method's accuracy is comparable to intensive numerical simulations.
• The accuracy of the RG approach decreases as the model deviates from the simpler Ising case.

Conclusions:

• The simple real-space RG approach is a surprisingly accurate and efficient tool for studying critical phenomena in quantum spin chains like the Ashkin-Teller model.
• This method provides a valuable and computationally less demanding alternative to sophisticated numerical techniques for certain critical exponent predictions.
• The study validates the utility of this RG approach for models with complex critical behaviors beyond the Ising universality class.