Depletion in fermionic chains with inhomogeneous hoppings

• URL: http://arxiv.org/abs/2209.10624v2
• Date: Mon, 27 Mar 2023 17:38:06 GMT
• Title: Depletion in fermionic chains with inhomogeneous hoppings
• Authors: Bego\~na Mula, Nadir Samos S\'aenz de Buruaga, Germ\'an Sierra, Silvia N. Santalla, Javier Rodr\'iguez-Laguna
• Abstract summary: Ground state of free-fermionic chain with inhomogeneous hoppings at half-filling can be mapped into the Dirac vacuum. We observe density modulations and depletion effects far from half-filling. We show that depletion effects can be compensated for all filling fractions by adding a chemical potential proportional to the hoppings.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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