Extracting the Luttinger parameter from a single wave function

TL;DR

This paper presents a novel method to determine the Luttinger parameter of Tomonaga-Luttinger liquids directly from a single wave function using conformal field theory, avoiding traditional data fitting.

Contribution

The authors introduce a universal approach to extract the Luttinger parameter from a single wave function via overlaps with crosscap states, validated through analytical and numerical models.

Findings

Method accurately extracts Luttinger parameters in finite systems

Overlaps with crosscap states are universal numbers

No data fitting or finite-size scaling needed

Abstract

The low-energy physics of Tomonaga-Luttinger liquids (TLLs) is controlled by the Luttinger parameter. We demonstrate that this parameter can be extracted from a single wave function for one-component TLLs with periodic boundary condition. This method relies on the fact that TLLs are described by conformal field theory in which crosscap states can be constructed. The overlaps between the crosscap states and the ground state as well as some excited states are proved to be universal numbers that directly reveal the Luttinger parameter. In microscopic lattice models, crosscap states are formed by putting each pair of antipodal sites into a maximally entangled state. Analytical and numerical calculations are performed in a few representative models to substantiate the conformal field theory prediction. The extracted Luttinger parameters are generally quite accurate in finite-size systems with moderate lengths, so there is no need to perform data fitting and/or finite-size scaling.