The paper investigates the quantum Mpemba effect in a two-dimensional free-fermion lattice, focusing on the entanglement asymmetry as a measure of symmetry breaking. The authors analyze the ground state and the time evolution of the entanglement asymmetry after a quench to a Hamiltonian that preserves the particle number symmetry. They find that the quantum Mpemba effect is strongly influenced by the size of the system in the transverse dimension, with the effect either enhancing or spoiling the phenomenon depending on the initial states. The study extends the criteria for the occurrence of the quantum Mpemba effect from one-dimensional systems to two-dimensional systems, providing a deeper understanding of the non-equilibrium dynamics in quantum many-body systems.The paper investigates the quantum Mpemba effect in a two-dimensional free-fermion lattice, focusing on the entanglement asymmetry as a measure of symmetry breaking. The authors analyze the ground state and the time evolution of the entanglement asymmetry after a quench to a Hamiltonian that preserves the particle number symmetry. They find that the quantum Mpemba effect is strongly influenced by the size of the system in the transverse dimension, with the effect either enhancing or spoiling the phenomenon depending on the initial states. The study extends the criteria for the occurrence of the quantum Mpemba effect from one-dimensional systems to two-dimensional systems, providing a deeper understanding of the non-equilibrium dynamics in quantum many-body systems.