TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.3.087
TI  - Brick wall quantum circuits with global fermionic symmetry
PY  - 2024/09/23
UR  - https://scipost.org/SciPostPhys.17.3.087
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 3
SP  - 087
A1  - Richelli, Pietro
AU  - Schoutens, Kareljan
AU  - Zorzato, Alberto
AB  - We study brick wall quantum circuits enjoying a global fermionic symmetry. The constituent 2-qubit gate, and its fermionic symmetry, derive from a 2-particle scattering matrix in integrable, supersymmetric quantum field theory in 1+1 dimensions. Our 2-qubit gate, as a function of three free parameters, is of so-called free fermionic or matchgate form, allowing us to derive the spectral structure of both the brick wall unitary $U_F$ and its, non-trivial, Hamiltonian limit $H_{\gamma}$ in closed form. We find that the fermionic symmetry pins $H_{\gamma}$ to a surface of critical points, whereas breaking that symmetry leads to non-trivial topological phases. We briefly explore quench dynamics for this class of circuits.
ER  -

@Article{10.21468/SciPostPhys.17.3.087,
	title={{Brick wall quantum circuits with global fermionic symmetry}},
	author={Pietro Richelli and Kareljan Schoutens and Alberto Zorzato},
	journal={SciPost Phys.},
	volume={17},
	pages={087},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.3.087},
	url={https://scipost.org/10.21468/SciPostPhys.17.3.087},
}