标题： 在$R$-准粒子 Luttinger 模型中的玻色化 显示英文标题

标题： Bosonization in $R$-paraparticle Luttinger models

摘要： 我们重新引入了在$R$-parafermion粒子中根据其平均占据数的parafermion-paraboson分类，类似于Green的准统计。 $p$-阶在$R$-parafermions中的概念也被重新定义为可以占据量子态的最大粒子数。 给出了一个具有$m=2$个内部自由度的order-$2$ $R$ -parafermion的例子，它遵循一个不同于Pauli的排斥原理。 在玻色化背景下研究了相互作用的$R$-parafermions。 具体来说，我们证明了虽然密度波通常具有玻色子的性质，并且对于由Luttinger模型描述的任意一维$R$- parafermion 系统，风味-电荷分离自然发生，但风味波并不总是满足玻色统计。 进一步比较分区函数表明，只有$(p=1)$-有序$R$- parafermions 在低能极限下与玻色化过程相容。 基于这些结果，我们讨论了一维系统中 parafermion 特征的潜在实现。 显示英文摘要

摘要： We reintroduce the parafermion-paraboson classification in $R$-paraparticles in terms of their average occupation numbers, analogous to Green's parastatistics. The notion of $p$-order in $R$-parafermions is also redefined as the maximum number of particles that can occupy a quantum state. An example of an order-$2$ $R$-parafermion with $m=2$ internal degrees of freedom is presented, which obeys an exclusion principle that is not Pauli's. The interacting $R$-parafermions are studied in the context of bosonization. Specifically, we show that while density waves are generally bosonic in nature and that flavor-charge separation naturally occurs for any one-dimensional $R$-parafermion system described by the Luttinger model, flavor waves do not always satisfy bose statistics. Comparison of the partition functions further show that only $(p=1)$-ordered $R$-parafermions are compatible with the bosonization procedure in the low-energy limit. Based from these results, we discuss a potential realization of parafermion signatures in one-dimensional systems.