Transverse-field XY spin chain with the competing long-range interactions: multi-criticality around the XX-symmetric point

The transverse-field XY spin chain with competing antiferromagnetic long-range interactions, J(r) ? 1/r(a) (r: distance between spins), and the exponent a was investigated numerically. The main concern is to clarify the character of the transverse-field-driven phase transition for the small-a regime around the XX-symmetric point, ? = 0 (?: XY-anisotropy parameter). To cope with the negative-sign problem, we employed the exact-diagonalization method, which enables us to evaluate the fidelity susceptibility ?(F). Because the fidelity susceptibility does not assume any order parameter after a phase transition, it detects the multi-criticality around the XX-symmetric point in a systematic manner. As a preliminary survey, with ? = 0.5 and a = 2 fixed, we made the scaling analysis of ?(F). The scaling behavior of ?(F) shows that the transverse field-driven phase transition belongs to the 2D-Ising universality class. Thereby, with the properly crossover-scaled ?, the ?(F) data is cast into the crossover scaling formula for the small-a regime. The multi-critical exponents fed into the scaling formula are argued through referring to related studies.

Automated summary

The transverse-field XY spin chain with competing antiferromagnetic long-range interactions was numerically investigated to clarify the character of the transverse-field-driven phase transition. The fidelity susceptibility was used to detect the multi-criticality around the XX-symmetric point systematically. The results showed that the transverse field-driven phase transition belongs to the 2D-Ising universality class in the small-a regime.