Double-layer Heisenberg antiferromagnet at finite temperature: Brueckner theory and quantum Monte Carlo simulations

The double-layer Heisenberg antiferromagnet with intra- and interlayer couplings J and $J_{\perp }$ exhibits a zero-temperature quantum phase transition between a quantum disordered dimer phase for $g>\mathrm{}{g}_c$ and a Néel phase with long-range antiferromagnetic order for $g<\mathrm{}{g}_c,$ where ${g=J}_{\perp }/J$ and $g_c\approx \mathrm{2.5.}$ We consider the behavior of the system at finite temperature for $g>~g_c$ using two different and complementary approaches; an analytical Brueckner approximation and numerically exact quantum Monte Carlo simulations. We calculate the temperature-dependent spin excitation spectrum (including the triplet gap), dynamic and static structure factors, the specific heat, and the uniform magnetic susceptibility. The agreement between the analytical and numerical approaches is very good. For $\overrightarrow{T}0$ and $\overrightarrow{g}{g}_c,$ our analytical results for the specific heat and the magnetic susceptibility coincide with those previously obtained within the nonlinear σ model approach for $\overrightarrow{N}\infty .$ Our quantum Monte Carlo simulations extend to significantly lower temperatures than previously, allowing us to obtain accurate results for the asymptotic quantum critical behavior. We also obtain an improved estimate for the critical coupling: $g_c=2.525\mathrm{}\pm \mathrm{0.002.}$