Antiferromagnetic order in systems with doublet $S_{\mathrm{tot}}=1/2$ ground states

Abstract

We use projector Quantum Monte-Carlo methods to study the $S_{\mathrm{tot}}=1/2$ doublet ground states of two dimensional $S=1/2$ antiferromagnets on a $L\times L$ square lattice with an odd number of sites $N_{\mathrm{tot}}=L^2$. We compute the ground state spin texture ${\Phi }^z(\vec{r})=<S^z(\vec{r}){>}_{\uparrow }$ in $|G{>}_{\uparrow }$, the $S_{\mathrm{tot}}^z=1/2$ component of this doublet, and investigate the relationship between $n^z$, the thermodynamic limit of the staggered component of this ground state spin texture, and $m$, the thermodynamic limit of the magnitude of the staggered magnetization vector of the same system in the singlet ground state that obtains for even $N_{\mathrm{tot}}$. We find a univeral relationship between the two, that is independent of the microscopic details of the lattice level Hamiltonian and can be well approximated by a polynomial interpolation formula: $n^z\approx (1/3-\frac{a}{2}-\frac{b}{4})m+a{m}^2+b{m}^3$, with $a\approx 0.288$ and $b\approx -0.306$. We also find that the full spin texture ${\Phi }^z(\vec{r})$ is itself dominated by Fourier modes near the antiferromagnetic wavevector in a universal way. On the analytical side, we explore this question using spin-wave theory, a simple mean field model written in terms of the total spin of each sublattice, and a rotor model for the dynamics of $\vec{n}$. We find that spin-wave theory reproduces this universality of ${\Phi }^z(\vec{r})$ and gives $n^z=(1-\alpha -\beta /S)m+(\alpha /S)m^2+\mathcal{O}(S^{-2})$ with $\alpha \approx 0.013$ and $\beta \approx 1.003$ for spin-$S$ antiferromagnets, while the sublattice-spin mean field theory and the rotor model both give $n^z=1/3m$ for $S=1/2$ antiferromagnets. We argue that this latter relationship becomes asymptotically exact in the limit of infinitely long-range {\em unfrustrated} exchange interactions.

11 two-column pages; 9 eps figures

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• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
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• Ground state of the S = 1/2 Heisenberg spin chain with random ferro- and antiferromagnetic couplings
• Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(\pi ,\pi )$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets
• High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice