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arXiv:cond-mat/0006273 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Spontaneous symmetry breaking in the finite lattice quantum sine-Gordon model

S. G. Chung

Published Sep 1, 2000• 6 citations
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Abstract

The spontaneous breaking of a global discrete translational symmetry in the finite lattice quantum sine-Gordon model is demonstrated by a density matrix renormalization group. A phase diagram in the coupling constant-inverse system size plane is obtained. Comparison of the phase diagram with a Woomany-Wyld finite-size scaling leads to an identification of the Berezinskii-Kosterlitz-Thouless transition in the quantum sine-Gordon model as the spontaneous symmetry breaking.

DOI
10.1103/physreve.62.3262

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The spontaneous breaking of a global discrete translational symmetry in the finite lattice quantum sine-Gordon model is demonstrated by a density matrix renormalization group. A phase diagram in the coupling constant-inverse system size plane is obtained. Comparison of the phase diagram with a Woomany-Wyld finite-size scaling leads to an identification of the Berezinskii-Kosterlitz-Thouless transition in the quantum sine-Gordon model as the spontaneous symmetry breaking.
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Abstract. The phase structure of the layered sine-Gordon (LSG) model is investigated in terms of symmetry considerations by means of differential renormalization group (RG) method using the local potential approximation. The RG analysis of the general N-layer model provides us with the possibility to consider the dependence of the vortex dynamics on the number of layers. The Lagrangians are distinguished according to the number of zero eigenvalues of their mass matrices where the number is found to be decisive with respect to the phase structure of the N-layer models, with neighbouring layers being coupled by terms quadratic in the field variables. It is shown that the LSG model with N layers undergoes a Kosterlitz–Thouless type phase transition at the critical value of the parameter β2 c = 8Nπ. In the limit of infinitely many layers the LSG model can be considered as the discretized version of the three-dimensional sine-Gordon model which has been shown to have a single phase within the local potential approximation. The infinite critical value of the parameter β2 c for the LSG model in the continuum limit (N → ∞) is consistent with the latter observation. PACS numbers: 11.10.Hi,11.10.Gh,11.10.Kk
We investigate a gap-formation mechanism of the one-dimensional Kondo-necklace model at zero temperature. An analytic treatment using the bosonization method shows that the model undergoes the Kosterlitz-Thouless transition at the critical coupling Jc=0{J}_{c}=0Jc​=0, which is described by the quantum sine-Gordon model. This result is contrary to the previous investigations on the ground-state phase transition, where some finite critical coupling values have been predicted. To clarify the validity of our analytic calculation result, we estimate the singlet-triplet gap by employing White's density matrix renormalization group method; the numerical calculation is carried out for the systems up to 200 sites with open boundary condition. As a result, we find that the excitation gap observed in the large JJJ region becomes smaller quickly with the decrease of JJJ. However, the data show the existence of a small gap for J> 0.25J>~0.25J> 0.25, which seems to support Jc=0{J}_{c}=0Jc​=0.