Fidelity-mediated analysis of the transverse-field XY chain with the long-range interactions: anisotropy-driven multi-criticality

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 transversefield-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 XXsymmetric 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

“…In Ref. [307], the QPT of the anisotropic LRTFAXYM was studied with exact diagonalisation, and the critical point was determined for β = 1/2, which coincides perfectly with the value from pCUT+MC (see Figure 31). For all β > 0, Adelhardt et al [31] identified the same three regimes for the universality of the QPT as for the ferromagnetic LRTFIM.…”

“…[31], and the data point "ED" is from Ref. [307]. The anisotropy parameter β is tuned from β = 1 (Ising) to β = 0 (isotropic XY).…”

“…The data points "pCUT+MC" are improved results from Ref [31],. and the data point "ED" is from Ref [307]…”