Spectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice

We employ a variational Monte Carlo approach to efficiently obtain the dynamical structure factor for the spin-$1/2J_1\text{−}{J}_2$ Heisenberg model on the square lattice. Upon increasing the frustrating ratio $J_2/J_1$, the ground state undergoes a continuous transition from a Néel antiferromagnet to a ${\mathbb{Z}}_2$ gapless spin liquid. We identify the characteristic spectral features in both phases and highlight the existence of a broad continuum of excitations in the proximity of the spin-liquid phase. The magnon branch, which dominates the spectrum of the unfrustrated Heisenberg model, gradually loses its spectral weight, thus releasing nearly deconfined spinons, whose signatures are visible even in the magnetically ordered state. Our results provide an important example on how magnons fractionalize into deconfined spinons across a quantum critical point.

Figure 1

Dynamical spin structure factor of the spatially anisotropic Heisenberg model with $J_2=0$. Different values of the interchain couplings are reported: $J_1^{\perp }/J_1^{\parallel }=0.1$ (upper left), 0.3 (upper right), 0.5 (lower left), and 0.7 (lower right). The square cluster contains $N=22\times 22$ sites. Spectral functions have been convoluted with normalized Gaussians with a standard deviation $0.1J_1^{\parallel }$.

Figure 2

Variational results for the ground-state magnetization of the $J_1\text{−}{J}_2$ Heisenberg model. The results are obtained in the thermodynamic limit, by extrapolating the isotropic spin-spin correlations at the maximum distance in the $L\times L$ clusters with $L$ ranging from 10 to 22. The exact result for the unfrustrated Heisenberg model, obtained by quantum Monte Carlo [40, 41], is also reported for comparison (red star).

Figure 3

Dynamical spin structure factor of the $J_1\text{−}{J}_2$ Heisenberg model. Different values of the frustrating ratio are reported: $J_2/J_1=0$ (upper left), 0.3 (upper right), 0.45 (lower left), and 0.55 (lower right). The antiferromagnetic parameter ${\mathrm{\Delta }}_{\mathrm{AF}}$ is finite in the first three cases, while it is vanishing for the last one. The square cluster contains $N=22\times 22$ sites. Spectral functions have been convoluted with normalized Gaussians with a standard deviation $0.1J_1$.