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

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 the 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 is an element of 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 is an element of R + i pi.

Automated summary

This study focuses on the exact elementary excitations in a U(1) symmetry broken quantum integrable system, specifically the twisted J1-J2 spin chain with various spin interactions. The energy spectrum is quantified using zero roots of the transfer matrix, leading to the determination of ground state energy and elementary excitations in the thermodynamic limit. Additionally, nearly degenerate states and the possibility of gapless low-lying excitations and quantum phase transitions are observed in certain regimes of the system.