Non-Unitary Spin-Charge Separation in One-Dimensional Fermion Gas

TL;DR

This paper presents exact analysis of the one-particle correlation function in a one-dimensional impenetrable spin-1/2 fermion gas, revealing non-unitary spin-charge separation and anomalous spectral behavior.

Contribution

It uncovers non-unitary conformal field theory characteristics in the spin-charge separation of a 1D fermion gas, with exact asymptotic results.

Findings

Correlation function exhibits spin-charge separation with distinct scaling behaviors.

Charge part shows non-unitary conformal field theory scaling.

Spectral weight diverges as a power law with exponent -1/2.

Abstract

In this Letter we report exact results on the infrared asymptotics of one-particle dynamical correlation function of the gas of impenetrable spin 1/2 fermions at infinitesimal temperature. The correlation function shows signs of spin-charge separation with scaling behavior in the charge part and exponential decay as a function of the space coordinate in the spin part. Surprisingly, the anomalous dimensions in the charge part do not correspond to any unitary conformal field theory. We find that the fermion spectral weight has a power law divergency at low energy with the anomalous exponent $-1/2.$