Phase separation as an instability of the Tomonaga-Luttinger liquid

TL;DR

This paper investigates the behavior of the Tomonaga-Luttinger liquid near phase separation in a one-dimensional $t$-$J$ model, revealing universal properties and phase transition characteristics through analytical and numerical methods.

Contribution

It provides a detailed analysis of the asymptotic behavior near phase separation, highlighting universal properties of the $c=1$ conformal field theory in this context.

Findings

Compressibility diverges as $(J_c-J)^{-1}$ near the transition.

Drude weight remains constant and drops discontinuously to zero at the phase boundary.

Finite size analysis confirms the theoretical predictions.

Abstract

Asymptotic behavior of the Tomonaga-Luttinger liquid in the vicinity of the phase-separated region is investigated in the one-dimensional $t$-$J$ model, to study the universal property of the $c=1$ conformal field theory with U(1) symmetry near the $K\to\infty$ instability. On the analogy of the spinless fermion, we discuss that the compressibility behaves as $\kappa\propto (J_c-J)^{-1}$, and that the Drude weight is constant and changes to zero discontinuously at the phase boundary. This speculation is confirmed by analyzing the finite size effect from the result of the exact diagonalization.