Entanglement enhancement in two-dimensional spin system coupled to a thermal dissipative environment in an inhomogeneous magnetic field.

Recently there has been great interest in studying unconventional magnetism in spin systems in the absence and presence of dissipative effects. Furthermore, many of the newly engineered quantum systems such as cold atoms in optical lattices, optical microcavities, trapped ions and superconducting circuits, represent great experimental framework for studying dissipative effects in driven many-body quantum systems. In this work, we study the time evolution and the asymptotic steady state of the bipartite quantum entanglement and spin relaxation in a finite two-dimensional triangular Heisenberg spin -1/2 lattice under the influence of dissipative Lindblad environment at zero and finite temperature. We show how a particular inhomogeneous magnetic field setup, where the gradient is directed toward the central spin, can significantly enhance the bipartite and global bipartite entanglement among the nearest neighbor spins and boost their thermal robustness in the completely anisotropic (Ising) system and even the beyond nearest neighbors in the partially anisotropic system, signaling a long range quantum correlation and consequently a critical behavior across the system.