TY - JOUR

T1 - Criticality of the Higgs mass for the long-range quantum XY chain

T2 - Amplitude ratio between the Higgs and paramagnetic gaps

AU - Nishiyama, Yoshihiro

N1 - Publisher Copyright:
© 2019 Elsevier B.V.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - 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.

AB - 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.

KW - Critical amplitude ratio

KW - Critical exponent

KW - Long-range interactions

KW - Quantum XY spin model

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U2 - 10.1016/j.physa.2019.121395

DO - 10.1016/j.physa.2019.121395

M3 - Article

AN - SCOPUS:85065399931

SN - 0378-4371

VL - 527

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

M1 - 121395

ER -