Elementary excitations in an integrable twisted J1-J2 spin chain in the thermodynamic limit

TL;DR

This paper investigates the elementary excitations of a twisted J1-J2 spin chain with complex interactions using transfer matrix zero roots, revealing ground state properties, nearly degenerate states, and quantum phase transitions in the thermodynamic limit.

Contribution

It introduces a novel approach using zero roots of the transfer matrix to analyze excitations, providing analytical results for the ground state and excitations in an integrable model.

Findings

Identification of zero root patterns and their relation to excitations

Discovery of nearly degenerate states in ferromagnetic regimes

Observation of gapless excitations and phase transitions in antiferromagnetic regimes

Abstract

The exact elementary excitations in a typical U(1) symmetry broken quantum integrable system, that is the twisted J1-J2 spin chain with nearest-neighbor, next nearest neighbor and chiral three spin interactions, are studied. The main technique is that we quantify the energy spectrum of the system by the zero roots of transfer matrix instead of the traditional Bethe roots. From the numerical calculation and singularity analysis, we obtain the patterns of zero roots. Based on them, we analytically obtain the ground state energy and the elementary excitations in the thermodynamic limit. We find that the system also exhibits the nearly degenerate states in the regime of $\eta\in \mathbb{R}$, where the nearest-neighbor couplings among the z-direction are ferromagnetic. More careful study shows that the competing of interactions can induce the gapless low-lying excitations and quantum phase transition in the antiferromagnetic regime with $\eta\in \mathbb{R}+i\pi$.