General Formula for the Green's Function Approach to the Spin-1/2 Antiferromagnetic Heisenberg Model

Abstract

A wide range of analytical and numerical methods are available to study quantum spin systems. However, the complexity of spin correlations and interactions limits their applicability to specific temperature ranges. The analytical approach utilizing Green's function has proved advantageous, as it allows for formulation without restrictions on the presence of long-range order and facilitates estimation of the spin excitation spectrum and thermodynamic quantities across the entire temperature range. In this work, we present a generalized formulation of the Green's function method that can be applied to diverse spin systems. As specific applications, we consider the hypercubic lattice and the $J_1$-$J_2$ model. For the cubic lattice case, the Green's function approach provides a good estimation for the transition temperature. Regarding the $J_1$-$J_2$ model, we include nematic correlations in the analysis and find no signature of such correlations, though accurate numerical calculations are required in the presence of strong frustration. Although our focus is on the spin one-half antiferromagnetic Heisenberg model on an arbitrary lattice, the Green's function approach can be generalized to incorporate other interactions and higher spin values.

10 pages, 9 figures

References in corpus (4)

• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Gapless spin liquid and valence-bond solid in the $J_1-J_2$ Heisenberg model on the square lattice: insights from singlet and triplet excitations
• Thermal Ising transition in the spin-1/2 J1-J2 Heisenberg model
• Quantum Heisenberg model on a sawtooth-chain lattice: Rotation-invariant Green's function method

Cited by in corpus (3)

• Phase diagram of the $J_1$-$J_2$ quantum Heisenberg model for arbitrary spin
• Static and Dynamical Spin Correlations in the Kitaev Model at Finite Temperatures via Green's Function Equation of Motion
• Spin-Spin Correlations in the Kitaev Model at Finite Temperatures: Approximate and Exact Results via Green's Function Equation of Motion