We investigate the behavior of quantum coherence of the ground states of 2D Heisenberg XY model and 2D Ising model with transverse field on square lattices, by using the method of Quantum Renormalization Group (QRG). We show that the non-analytic behavior of quantum coherence near the critical point, can detect quantum phase transition (QPT) of these models. We also use the scaling behavior of maximum derivative of quantum coherence, with system size, to find the critical exponent of coherence for both models and also the length exponent of the Ising model. The results are in close agreement with the ones obtained from entanglement analysis, that is while quantum coherence needs less computational calculations in comparison to entanglement approaches.We investigate the behavior of quantum coherence of the ground states of 2D Heisenberg XY model and 2D Ising model with transverse field on square lattices, by using the method of Quantum Renormalization Group (QRG). We show that the non-analytic behavior of quantum coherence near the critical point, can detect quantum phase transition (QPT) of these models. We also use the scaling behavior of maximum derivative of quantum coherence, with system size, to find the critical exponent of coherence for both models and also the length exponent of the Ising model. The results are in close agreement with the ones obtained from entanglement analysis, that is while quantum coherence needs less computational calculations in comparison to entanglement approaches.

arXiv:2208.00158Jul 30, 20220 citations

Ground state of the two-dimensional antiferromagnetic Heisenberg model studied using an extended Wigner-Jordon transformation

Y. R. Wang

A two-dimensional (2D) Wigner-Jordon transformation which maps spin variables into spinless fermion variables is found and is used to study the 2D spin-1/2 antiferromagnetic Heisenberg model. The transformation generates a fictitious gauge field in the XY component of the Heisenberg model, and hence induces an in-phase orbital current in the Ising component flowing around each elementary plaquette of the underlying lattice. The ground state of the Heisenberg model in a 2D square lattice is found to be an in-phase N\'eel flux phase, i.e., a coexisting state of the flux phase with in-phase orbital currents and a long-range antiferromagnetic spin order. The zero-temperature mean-field energy of the in-phase N\'eel flux state, ${\mathit{E}}_{0}$ =-0.33J per bond, is only 1% higher than the best-estimated ground-state energy, -0.334J per bond.A two-dimensional (2D) Wigner-Jordon transformation which maps spin variables into spinless fermion variables is found and is used to study the 2D spin-1/2 antiferromagnetic Heisenberg model. The transformation generates a fictitious gauge field in the XY component of the Heisenberg model, and hence induces an in-phase orbital current in the Ising component flowing around each elementary plaquette of the underlying lattice. The ground state of the Heisenberg model in a 2D square lattice is found to be an in-phase N\'eel flux phase, i.e., a coexisting state of the flux phase with in-phase orbital currents and a long-range antiferromagnetic spin order. The zero-temperature mean-field energy of the in-phase N\'eel flux state, ${\mathit{E}}_{0}$=-0.33J per bond, is only 1% higher than the best-estimated ground-state energy, -0.334J per bond.

Physical review. B, Condensed matterFeb 1, 199192 citations

Disordered phase of a two-dimensional Heisenberg model with

S. Moukouri

arXiv:cond-mat/0510288Physics Letters ANov 30, 200514 citations

{\mathit{E}}_{0}

=-0.33J per bond, is only 1% higher than the best-estimated ground-state energy, -0.334J per bond.