One dimensional chains of free fermions belong to the simplest many body systems, where many physical quantities can be computed with ease. In quantum information theory free fermionic circuits are also distinguished: they lead to classical simulability of quantum states. Recently a new class of models was discovered[1,2], which have a hidden free fermionic structure, despite being apparently interacting. The hidden free fermions are obtained with a construction that is distinct from the well known Jordan-Wigner transformation. We review the progress in this topic, focusing on selected models and their properties.

 

[1]: B Pozsgay, arXiv:2402.02984

[2]: P Fendley, B Pozsgay, SciPost Phys. 16, 102 (2024)