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首页> 外文期刊>Physical review, D >Continuous quantum phase transition in the fermionic mass solutions of the Nambu–Jona-Lasinio model
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Continuous quantum phase transition in the fermionic mass solutions of the Nambu–Jona-Lasinio model

机译：Nambu-jons-lasinio模型的Fermionic质量溶液中的连续量子相变

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Recently, quantum simulators have been constructed to investigate experimentally the most prominent theoretical four-point many-body system described by the Hubbard model. By varying the coupling strength of the four-point interaction in relation to the kinetic term, it is possible to analyze the phase structure of the model. This intriguing fact leads us to ask the question as to whether similar Hamiltonians with four-point interactions can also be studied as a function of their four-point coupling strength. In this paper, we reexamine the Nambu–Jona-Lasinio model, regarding it generally beyond the context of quantum chromodynamics. Essentially, it is a model in which particle-antiparticle pairing leads to a Bardeen-Cooper-Schrieffer-like condensate, with the result that chiral symmetry is broken dynamically in the strong-coupling regime, where G Λ 2 is larger than a critical value, i.e., G Λ 2 > G c Λ 2 . To study the behavior of the system, it is necessary to move from this regime to a hypothetical regime of weak coupling, altering the coupling strength of the interaction arbitrarily. In order to do this, the gap equation must be regarded as complex and its Riemann surface structure must be known. We do this and obtain a continuous quantum phase transition characterized by the development of a complex order parameter (the dynamically generated mass) from the second sheet of the Riemann surface associated with the gap equation, as we move into the weak-coupling regime. The power-law behavior of the order parameter in the vicinity of the phase transition point is demonstrated to be independent of the choice of the regularization scheme with the critical exponent as β ≈ 0.55 . At the same time, the isovector pseudoscalar modes retain their feature as Goldstone modes and still have zero mass, while the isoscalar scalar meson follows the behavior of the order parameter and gains a width. Energetically, this mode is not favored over the normal, uncondensed mode but would have to be accessed through an excitation process.
机译：最近，已经建立了量子模拟器来实验研究了船站模型描述的最突出的理论四点多体系。通过改变与动力学术语相关的四点相互作用的耦合强度，可以分析模型的相位结构。这种有趣的事实导致我们询问关于具有四点相互作用的类似Hamiltonians是否可以作为它们的四点耦合强度的函数进行研究。在本文中，我们重新审视Nambu-jona-lasinio模型，通常超出量子色动力学的背景。基本上，它是一种模型，其中粒子 - 抗粒子配对导致Bardeen-Cooper-Schrieffer样冷凝物，其结果是在强耦合状态下动态断开手性对称性，其中Gλ2大于临界值，即Gλ2> gcλ2。为了研究系统的行为，有必要从该制度从这个制度转变为弱耦合的假设制度，任意改变相互作用的耦合强度。为此，必须将间隙方程视为复杂的并且必须知道其riemann表面结构。我们这样做并获得具有与与间隙方程相关联的riemann表面的第二片材的复杂订单参数（动态产生的质量）的开发的连续量子相转变，其特征在于与间隙方程相关联，当我们进入弱耦合状态时。阶段转换点附近的订单参数的幂律行为被证明是与正则化方案的选择无关，以临界指数为β≈0.55。与此同时，ISoVector伪张显示模式将其特征保留为Goldstone模式并且仍然具有零质量，而Isoscalar Scalar Meson遵循订单参数的行为并获得宽度。在良好状态下，这种模式不受正常，无责任模式的偏好，但必须通过激励过程访问。

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