Abstract
The quantum XY spin chain with the interactions decaying as a power law 1∕r1+σ of the distance between spins r was investigated with the exact diagonalization method. Here, the constituent spin is set to S=1, which enables us to incorporate the biquadratic interactions so as to realize the order–disorder transition with the O(2) symmetry maintained. Thereby, in the ordered phase, we resolved the Higgs mass mH out of the Goldstone-excitation continuum by specifying Higgs-particle’s quantum numbers to adequate indices. We then turn to the analysis of the critical amplitude ratio mH∕Δ (Δ: paramagnetic gap in the disordered phase). As the power of the algebraic decay σ increases, the amplitude ratio mH∕Δ gets enhanced gradually in agreement with the ϵ(=4−D)-expansion-renormalization-group result; here, we resort to the σ↔D relation advocated recently in order to establish a relationship between the renormalization-group result and ours.
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