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

Amplitude ratio between the Higgs and paramagnetic gaps

Research output: Contribution to journalArticle

Abstract

The quantum XY spin chain with the interactions decaying as a power law 1∕r 1+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 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 ∕Δ (Δ: paramagnetic gap in the disordered phase). As the power of the algebraic decay σ increases, the amplitude ratio m H ∕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.

Original languageEnglish
Article number121395
JournalPhysica A: Statistical Mechanics and its Applications
Volume527
DOIs
Publication statusPublished - Aug 1 2019

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Criticality
Higgs
Renormalization Group
Spin Chains
Diagonalization
Interaction
Range of data
Power Law
Continuum
Excitation
Decay
Symmetry
quantum numbers
interactions
continuums
expansion
symmetry
decay
excitation
Relationships

Keywords

  • Critical amplitude ratio
  • Critical exponent
  • Long-range interactions
  • Quantum XY spin model

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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title = "Criticality of the Higgs mass for the long-range quantum XY chain: Amplitude ratio between the Higgs and paramagnetic gaps",
abstract = "The quantum XY spin chain with the interactions decaying as a power law 1∕r 1+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 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 ∕Δ (Δ: paramagnetic gap in the disordered phase). As the power of the algebraic decay σ increases, the amplitude ratio m H ∕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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N2 - The quantum XY spin chain with the interactions decaying as a power law 1∕r 1+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 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 ∕Δ (Δ: paramagnetic gap in the disordered phase). As the power of the algebraic decay σ increases, the amplitude ratio m H ∕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∕r 1+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 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 ∕Δ (Δ: paramagnetic gap in the disordered phase). As the power of the algebraic decay σ increases, the amplitude ratio m H ∕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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