Phonons under confinement: Finite Hilbert space, coarse-grained $U(1)$ charge and a new transport mechanism
Year: 2026
Type: preprint
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 dimer current and heat current with spontaneous time reversal symmetry breaking of the type $\hat{T}^2=+1$. The non-reciprocity can be probed by measuring the change of inductance due to gauge fields in and out of the ordered phase.
Source: arXiv (Cornell University)
Authors: Gao, Yuan, Muttalib, K. A.
Institution: University of Florida
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169513583