Quantum to classical crossover in the 2D easy-plane XXZ model

Abstract

Ground-state and thermodynamical properties of the spin-1/2 two-dimensional easy-plane XXZ model are investigated by both a Green's-function approach and by Lanczos diagonalizations on lattices with up to 36 sites. We calculate the spatial and temperature dependences of various spin correlation functions, as well as the wave-vector dependence of the spin susceptibility for all anisotropy parameters ∆. In the easy-plane ferromagnetic region (−1 < ∆ < 0), the longitudinal correlators of spins at distance r change sign at a finite temperature T0(∆, r). This transition, observed in the 2D case for the first time, can be interpreted as a quantum to classical crossover.

Magnetic order in the quasi-two-dimensional easy-planeXXZmodel

“…As can be seen in the inset, the effects of spin anisotropy on the longitudinal and transverse LRO are opposite: We have ∂m zz /∂∆ > 0, whereas ∂m +− /∂∆ < 0 which agrees, at R z = 0, with the Monte Carlo data [14] and the results of Ref. [13].…”

“…Taking for e(∆, 1) the exact diagonalization (ED) data on lattices with up to 36 sites (without finite-size scaling) from Ref. [13], we obtain lim Rz→0 ∆ c (R z ) ≡ ∆ 0 = 0.958. On the other hand, taking the Monte Carlo (MC) data from Ref.…”

“…Therefore, we make the reasonable assumption R z,0 = 0. To fulfill the requirements ∆ 0 = 1 and R z,0 = 0 simultaneously, so that the phase boundary touches the critical point (∆, R z ) = (1, 0), as input for e ′ we use a linear combination of the ED [13] and Monte Carlo data [14], e ′ = xe ′ ED + (1 − x)e ′ MC . We find that the above requirements may be fulfilled, if x is chosen as x=0.44.…”

“…[9]) yield reasonable results only at sufficiently low temperatures, since the temperature-dependent SRO is not adequately taken into account. To provide a good description of magnetic SRO at arbitrary temperatures, a Green's-function theory based on the projection method was developed for the spatially anisotropic Heisenberg models [9][10][11] and for the 1D [12] and 2D easy-plane XXZ models [13].…”

“…In the limiting cases ∆ = 1 and R z = 0 the model (1) reduces to the models studied in Refs. [9] and [13], respectively. Our Green's-function theory outlined in the Appendix is based on an approximate time evolution of spin operators, e.g., − Sz q = (ω zz q ) 2 S z q , resulting from a decoupling of three-spin operator products which is improved by the introduction of vertex parameters.…”