Criticality of the Higgs mass for the long-range quantum XY Chain: Amplitude ratio between the Higgs and paramagnetic gaps

摘要

The quantum XY spin chain with the interactions decaying as a power law 1/r(1+sigma) 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 m(H) 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 m(H)/Delta (Delta: paramagnetic gap in the disordered phase). As the power of the algebraic decay sigma increases, the amplitude ratio m(H)/Delta gets enhanced gradually in agreement with the epsilon(= 4 - D)-expansion-renormalization-group resu here, we resort to the sigma <-> D relation advocated recently in order to establish a relationship between the renormalization-group result and ours. (C) 2019 Elsevier B.V. All rights reserved.