Phonons under confinement: Coarse-grained U(1) charge and a new transport mechanism
Abstract
An important feature of solid-state or cold atom systems in low dimensions is the restricted oscillations of ionic/atomic degrees of freedom in the confining directions, for which the conventional phonon from canonical quantization is not an ideal description. In this work we propose a general recipe to introduce this feature to otherwise unrestricted systems by mapping displacement fields to spin degrees of freedom, dubbed soft-corization. In the strong-confinement limit S=1/2, we demonstrate the validity of the approach with a harmonic chain; the results lead to a gapped fermionic model showing the absence of acoustic modes as a signature of the confinement of the entire chain. Despite the non-conserved total particle number in the presence of nearest-neighbor parings, the model holds a coarse-grained U(1) symmetry with conserved polarization charge in the absence of nearest-neighbor hopping. This enables a new transport mechanism via "dimer-tumbling" instead of single-particle hopping. We then introduce a short-range interaction via anharmonicity; for energy scales slightly above the gap, it leads to a (quantum) phase transition to a nonreciprocal state carrying polarization charge current and heat current with spontaneous time reversal symmetry breaking (TRSB) of the type T̂2=+1. The non-reciprocity can be probed by measuring the change of inductance due to gauge fields in and out of the ordered phase.
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BibTeX
@misc{gao2026phonons,
title = {{Phonons under confinement: Coarse-grained $U(1)$ charge and a new transport mechanism}},
author = {Yuan Gao and K. A. Muttalib},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.14232},
eprint = {2607.14232},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.14232},
}
RIS
TY - UNPB
TI - Phonons under confinement: Coarse-grained U(1) charge and a new transport mechanism
AU - Yuan Gao
AU - K. A. Muttalib
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2607.14232
UR - https://arxiv.org/abs/2607.14232
AB - An important feature of solid-state or cold atom systems in low dimensions is the restricted oscillations of ionic/atomic degrees of freedom in the confining directions, for which the conventional phonon from canonical quantization is not an ideal description. In this work we propose a general recipe to introduce this feature to otherwise unrestricted systems by mapping displacement fields to spin degrees of freedom, dubbed soft-corization. In the strong-confinement limit S=1/2, we demonstrate the validity of the approach with a harmonic chain; the results lead to a gapped fermionic model showing the absence of acoustic modes as a signature of the confinement of the entire chain. Despite the non-conserved total particle number in the presence of nearest-neighbor parings, the model holds a coarse-grained U(1) symmetry with conserved polarization charge in the absence of nearest-neighbor hopping. This enables a new transport mechanism via "dimer-tumbling" instead of single-particle hopping. We then introduce a short-range interaction via anharmonicity; for energy scales slightly above the gap, it leads to a (quantum) phase transition to a nonreciprocal state carrying polarization charge current and heat current with spontaneous time reversal symmetry breaking (TRSB) of the type T̂^2=+1. The non-reciprocity can be probed by measuring the change of inductance due to gauge fields in and out of the ordered phase.
ER -