Nonunitary spin-charge separation in a one-dimensional fermion gas

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory

Background:

• Investigating the behavior of quantum systems at low temperatures is crucial for understanding emergent phenomena.
• The one-particle dynamical correlation function provides insights into the fundamental properties of interacting particles.

Purpose of the Study:

• To determine the infrared (IR) asymptotic behavior of the one-particle dynamical correlation function for a gas of impenetrable spin 1/2 fermions at near-zero temperatures.
• To explore signs of spin-charge separation and its implications for the system's properties.

Main Methods:

• Exact analytical calculations were performed to derive the correlation function.
• The study focused on the asymptotic behavior in the infrared limit and at infinitesimal temperatures.

Main Results:

• The correlation function exhibits characteristics of spin-charge separation.
• The charge part displays scaling behavior, while the spin part shows exponential spatial decay.
• Anomalous dimensions in the charge sector were found to deviate from predictions of unitary conformal field theories.
• The fermion spectral weight demonstrates a power-law divergence at low energies, with a specific anomalous exponent of -1/2.

Conclusions:

• The findings suggest a novel form of spin-charge separation in this fermionic system.
• The observed anomalous dimensions challenge existing theoretical frameworks, particularly unitary conformal field theories.
• The power-law divergence of spectral weight indicates unique low-energy excitations in the system.