Depletion in fermionic chains with inhomogeneous hoppings Articles uri icon

publication date

  • December 2022

start page

  • 224204-1

end page

  • 224204-10


  • 22


  • 106

International Standard Serial Number (ISSN)

  • 2469-9950

Electronic International Standard Serial Number (EISSN)

  • 2469-9969


  • 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√∂dinger 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.


  • Materials science and engineering
  • Physics


  • conformal field theory; dirac equation; quantum fields in curved spacetime; 1-dimensional spin chains; free-electron model; quantum spin chains; semiclassical methods