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arXiv:cond-mat/0104161

The phase diagram of the one-dimensional quantum sine-Gordon system ($β^{2}=4π)$ with a linear spatial modulation

Zhiguo Wang, Yumei Zhang

Published Apr 10, 2001• 0 citations
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Abstract

The one-dimensional quantum sine-Gordon system with a linear spatial modulation is investigated in a special case, $β^{2}$ =4$π$. The model is tranformed into a massive Thirring model and then is exactly diagonalized, the energy spetrum of the model is obtained. Our result clearly demonstrates that cancelling the cosine term without any considering is unadvisable.

DOI
10.48550/arxiv.cond-mat/0104161

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The phase diagram of the one-dimensional quantum sine-Gordon system (β2=4π)β^{2}=4π)β2=4π) with a linear spatial modulation
The one-dimensional quantum sine-Gordon system with a linear spatial modulation is investigated in a special case, β2β^{2}β2 =4πππ. The model is tranformed into a massive Thirring model and then is exactly diagonalized, the energy spetrum of the model is obtained. Our result clearly demonstrates that cancelling the cosine term without any considering is unadvisable.
A new procedure of trial variational wave functional is proposed for investigating the mass renormalization and the local structure of the ground state of a one-dimensional quantum sine-Gordon model with linear spatial modulation, whose ground state differs from that without modulation. The phase diagram obtained in parameters plane shows that the vertical part of the boundary between soliton lattice phase and incommensurate (IC) phase with vanishing gap sticks at , the IC phase can only appear for and the IC phase regime is enlarged with increasing spatial modulation in the case of definite parameter . The transition is of the continuous type on the vertical part of the boundary, while it is of the first order on the boundary for .
The commensurate-incommensurate (C-IC) phase transition in the one dimensional quantum sineGordon model at zero temperature is exactly solved with the use of the Bethe ansatz technique for the lattice massive Thirring model. The energy difference between C and IC phases is derived based on the same ground state which is valid in the whole parameter region. It is due to the fact that there is no change in the ground state of the lattice massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model. It is proved in the whole parameter region that the IC phase can be realized with the soliton density proportional to x f E s (Es: formation energy of soliton), when Es becomes negative.
A new procedure of trial variational wave functional is proposed for invostigating the mass reuormalizationand the local structure of the ground state of a one-dimensional quantum sine-Gorrdonm model with linear spatial modu-lation, whose ground state differs from that without modulation. Thc phase diagram obtained in parameters (αA 2,β2)plane shows that the vertical part of the boundary between soliton lattice phase and iucommensurate (IC) phase withvanishing gap sticks at β2 = 4, the IC phase can only appear forβ2 ＞ 47r and thc IC phase regime is enlarged withincreasing spatial modulation in the case of definite parameter αA-2. The transition is of the continuous type on thevertical part of the boundary, while it is of the first order on the boundary forβ2 ＞ 47r.