Depletion in fermionic chains with inhomogeneous hoppings
Abstract
The ground state of a free-fermionic chain with inhomogeneous hoppings at half-filling can be mapped into the Dirac vacuum on a static curved space-time, which presents exactly homogeneous occupations due to particle-hole symmetry. Yet, far from half-filling we observe density modulations and depletion effects. The system can be described by a 1D Schr\"odinger equation on a different static space-time, with an effective potential which accounts for the depleted regions. We provide a semiclassical expression for the single-particle modes and the density profiles associated to different hopping patterns and filling fractions. Moreover, we show that the depletion effects can be compensated for all filling fractions by adding a chemical potential proportional to the hoppings. Interestingly, we can obtain exactly the same density profiles on a homogeneous chain if we introduce a chemical potential which is inverse to the hopping intensities, even though the ground state is different from the original one.
Cite
@article{arxiv.2209.10624,
title = {Depletion in fermionic chains with inhomogeneous hoppings},
author = {Begoña Mula and Nadir Samos Sáenz de Buruaga and Germán Sierra and Silvia N. Santalla and Javier Rodríguez-Laguna},
journal= {arXiv preprint arXiv:2209.10624},
year = {2023}
}