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四川大学学报：自然科学版

泛函积分与sine-Gordon-Thirring模型的相结构

邹伯夏, 颜骏, Tao Wang

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

本文研究了具有杂质耦合的一维量子sine-Gordon-Thirring模型的相结构.应用微扰和非微扰泛函积分方法推导了有限温度下的的有效势,分析了弱耦合和强耦合情况下的共存相的稳定性.发现当费米子为排斥势(g>0)时不能形成稳定相,费米子为吸引势(g<0)时,可以形成稳定相.

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Chinese Science Bulletin (Chinese Version)•Sep 1, 2011•1 citation
本文研究了具有杂质耦合的一维量子sine-Gordon-Thirring模型的相结构.应用微扰和非微扰泛函积分方法推导了有限温度下的的有效势,分析了弱耦合和强耦合情况下的共存相的稳定性.发现当费米子为排斥势(g>0)时不能形成稳定相,费米子为吸引势(g<0)时,可以形成稳定相.
We introduce and study the properties of a periodic model interpolating between the sine-- and the sinh--Gordon theories in 1+11+11+1 dimensions. This model shows the peculiarities, due to the preservation of the functional form of their potential across RG flows, of the two limiting cases: the sine-Gordon, not having conventional order/magnetization at finite temperature, but exhibiting Berezinskii-Kosterlitz-Thouless (BKT) transition; and the sinh-Gordon, not having a phase transition, but being integrable. The considered interpolation, which we term as {\em sn-Gordon} model, is performed with potentials written in terms of Jacobi functions. The critical properties of the sn-Gordon theory are discussed by a renormalization-group approach. The critical points, except the sinh-Gordon one, are found to be of BKT type. Explicit expressions for the critical coupling as a function of the elliptic modulus are given.
For any k -state model among the Gordon-Generalization (GG) hierarchy (J. Phys. Soc. Jpn. 55 (1986) 1092 and 2166), a systematic procedure to obtain the parametrized Boltzmann weights is presented. An exact expression for the free energy of the general k -state model in the GG hierarchy is explicitly given. The procedure is successfully applied to determine the parametrization for the 5-state model in the GG hierarchy. It is concluded that each k -state model in the GG hierarchy is exactly solvable.
针对目前大维数量子寄存器生成的困难性, 研究了基于小维数量子寄存器实现大维数量子Fourier 变换的方法. 首先, 定义了t 比特半经典量子Fourier 变换, 从几率幅的角度证明该变换可以实现量子Fourier 变换, 且所需2 位量子门的规模显著降低, 并设计了该变换的量子实现线路. 然后基于t 比特半经典量子Fourier 变换, 将经典固定窗口法与Shor 算法实现方法相融合, 重新设计了Shor 整数分解量子算法的实现线路, 与Parker 等人的实现线路相比, 计算资源大体相同(所需的基本量子门均为所需量子寄存器的维数前者较后者多t -1维), 而实现速度提高了t2 倍, t 是窗口宽度.