Anyon Crystallization by Statistics
Abstract
We revisit the long-standing problem of the anyon gas. We study the solvable near-bosonic limit of a large number of anyons N at fixed N/k, where 1/k characterizes the statistical interaction. In this limit, the ground state is a crystal with order N/k lattice sites. The statistical interactions, mediated by a long-range gauge field, are completely screened within the crystalline phase. The resulting state is a conventional crystal without superfluidity. We characterize this anyon crystal by determining its unit-cell size, ground-state energy, acoustic excitations, angular momentum crossings, and other properties. Our results indicate a quantum phase transition between the crystal at k>kc and a superfluid at k<kc, with a critical value kc≃2−−5. These results imply that an anyon gas with only statistical interactions is not necessarily a superfluid, contrary to common lore. We also present a detailed analysis of the renormalization-group evolution of anyon--anyon interactions, identifying many new potential fixed points and elucidating finite-size effects.
Related
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BibTeX
@misc{komargodski2026anyon,
title = {{Anyon Crystallization by Statistics}},
author = {Zohar Komargodski and Xuzixiang Lou and Ivri Nagar and Domenico Orlando and Susanne Reffert and Amit Sever},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25249},
eprint = {2609.25249},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25249},
note = {CC0},
}
RIS
TY - UNPB
TI - Anyon Crystallization by Statistics
AU - Zohar Komargodski
AU - Xuzixiang Lou
AU - Ivri Nagar
AU - Domenico Orlando
AU - Susanne Reffert
AU - Amit Sever
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25249
UR - https://arxiv.org/abs/2609.25249
AB - We revisit the long-standing problem of the anyon gas. We study the solvable near-bosonic limit of a large number of anyons N at fixed N/k, where 1/k characterizes the statistical interaction. In this limit, the ground state is a crystal with order N/k lattice sites. The statistical interactions, mediated by a long-range gauge field, are completely screened within the crystalline phase. The resulting state is a conventional crystal without superfluidity. We characterize this anyon crystal by determining its unit-cell size, ground-state energy, acoustic excitations, angular momentum crossings, and other properties. Our results indicate a quantum phase transition between the crystal at k>k_c and a superfluid at k<k_c, with a critical value k_c≃2−−5. These results imply that an anyon gas with only statistical interactions is not necessarily a superfluid, contrary to common lore. We also present a detailed analysis of the renormalization-group evolution of anyon--anyon interactions, identifying many new potential fixed points and elucidating finite-size effects.
ER -