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

Abstract

The transverse-field XY spin chain with competing antiferromagnetic long-range interactions, J r ∝ 1 / r α (r: distance between spins), and the exponent α was investigated numerically. The main concern is to clarify the character of the transverse-field-driven phase transition for the small-α regime around the XX-symmetric point, η = 0 (η: XY-anisotropy parameter). To cope with the negative-sign problem, we employed the exact-diagonalization method, which enables us to evaluate the fidelity susceptibility χ 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 η = 0.5 and α = 2 fixed, we made the scaling analysis of χ F . The scaling behavior of χ F shows that the transverse-field-driven phase transition belongs to the 2D-Ising universality class. Thereby, with the properly crossover-scaled η, the χ F data is cast into the crossover scaling formula for the small-α regime. The multi-critical exponents fed into the scaling formula are argued through referring to related studies.

Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions

“…Since the expression for the gap ∆(λ) is linear in λ, the critical exponent is zν = 1, independent of the σ value. Using the expression for the dispersion (312), the knowledge about λ c , and the definition of the dynamic critical exponent (314), Adelhardt et al [31] evaluated z and, therefore, also ν as a function of σ. The results of their calculations are presented in Figure 30.…”

“…For β = 0, the critical exponents zν = 1 and critical values λ c = (2η(1 + σ)) −1 were determined analytically in Section 7.1, and it was shown that the universality class of the nearestneighbour isotropic chain remains for all σ > −1 [31]. A recent study [312] investigated the multicritical point using exact diagonalisation for comparably small system sizes. The critical points for β = 1/2 and β = 1/5 agree well with the exact limit and the pCUT+MC values.…”