Bosonization in $R$-paraparticle Luttinger models

• URL: http://arxiv.org/abs/2508.20429v2
• Date: Wed, 10 Sep 2025 07:10:05 GMT
• Title: Bosonization in $R$-paraparticle Luttinger models
• Authors: Dennis F. Salinel, Kristian Hauser A. Villegas,
• Abstract summary: We introduce the parafermion-paraboson classification in $R$-paraparticles in terms of their average occupation numbers.<n>The notion of $p$-order in $R$-parafermions is also redefined as the maximum number of particles that can occupy a quantum state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $R$-parafermion signatures in one-dimensional systems.

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