In condensed matter physics, the Kitaev chain or Kitaev–Majorana chain is a simplified model for a topological superconductor. It models a one dimensional lattice featuring Majorana bound states. The Kitaev chain has been used as a toy model of semiconductor nanowires for the development of topological quantum computers. The model was first proposed by Alexei Kitaev in 2000.

The tight binding Hamiltonian of a Kitaev chain considers a one dimensional lattice with N site and spinless particles at zero temperature, subjected to nearest neighbour hopping interactions, given in second quantization formalism as

where ${\displaystyle \mu }$ is the chemical potential, ${\displaystyle c_{j}^{\dagger },c_{j}}$ are creation and annihilation operators, ${\displaystyle t\geq 0}$ the energy needed for a particle to hop from one location of the lattice to another, ${\displaystyle \Delta =|\Delta |e^{i\theta }}$ is the induced superconducting gap (p-wave pairing) and ${\displaystyle \theta }$ is the coherent superconducting phase. This Hamiltonian has particle-hole symmetry, as well as time reversal symmetry.

The Hamiltonian can be rewritten using Majorana operators, given by

which can be thought as the real and imaginary parts of the annihilation operator ${\displaystyle c_{j}={\tfrac {1}{2}}(\gamma _{j}^{\rm {A}}+i\gamma _{j}^{\rm {B}})}$. These Majorana operators are Hermitian operators, and anticommutate,

Using these operators the Hamiltonian can be rewritten as

where ${\displaystyle \omega _{\pm }=|\Delta |\pm t}$.

In the limit ${\displaystyle t=|\Delta |\to 0}$, we obtain the following Hamiltonian