Thermal critical points from competing singlet formations in fully frustrated bilayer antiferromagnets

We examine the ground-state phase diagram and thermal phase transitions in a plaquettized fully frustrated bilayer spin-1/2 Heisenberg model. Based on a combined analysis from sign-problem free quantum Monte Carlo simulations, perturbation theory, and free-energy arguments, we identify a first-order quantum phase transition line that separates two competing quantum-disordered ground states with dominant singlet formations on interlayer dimers and plaquettes, respectively. At finite temperatures, this line extends to form a wall of first-order thermal transitions, which terminates in a line of thermal critical points. From a perturbative approach in terms of an effective Ising model description, we identify a quadratic suppression of the critical temperature scale in the strongly plaquettized region. Based on free-energy arguments we furthermore obtain the full phase boundary of the low-temperature dimer-singlet regime, which agrees well with the quantum Monte Carlo data.

Figure 1

(a) The pFFB lattice with interlayer dimer bonds $J_D$ (thick, red), plaquette bonds $J_P$ (thick, blue) and interplaquette bonds $J$ (thin, black). (b) The effective spin-1 model for the pFFB within the dimer spin triplet regime.

Figure 2

Dimer triplet density $n_{\text{D}}$ (top panel) and AFM structure factor $S(\pi ,\pi )$ (bottom panel) of the pFFB model as a function of $J/J_{\text{D}}$ and $J_{\text{P}}/J_{\text{D}}$ at a fixed temperature of $T/J_{\text{D}}=0.1$ as obtained from QMC for $L=12$. Black lines denote the boundaries of the AFM phase as obtained from the effective spin-1 model description. Red (white) lines denotes the first-order quantum phase transition line obtained from the free-energy comparison (perturbation theory in the regime $J\ll J_{\text{P}}\approx J_{\text{D}}$). The different regions are labeled by the corresponding ground-state phases. The inset shows two constant-$J_{\text{P}}/J_{\text{D}}$ cuts of $S(\pi ,\pi )$.

Figure 3

Energy levels of a single plaquette $E_{⊠}$ as a function of $J_{\text{P}}/J_{\text{D}}$, splitting into two singlets, three triplets, and one quintuplet of different dimer triplet density $n_{\text{D}}$.

Figure 4

Sketch (not to scale) of the finite temperature phase diagram showing the wall of discontinuities (red) of the finite-temperature first-order transitions in the pFFB model. Near the decoupled plaquette limit, the dependence of the critical temperature $T_c$ (bold red line) on the interplaquette coupling is quadratic. Its behavior for small $J_{\text{P}}$ is purely indicative based only on its limiting value $T_c=0$ at $J_{\text{P}}=0$. The black lines represent the $T=0$ continuous transitions of the AFM phase to the PS and tubes phases, which are expected to terminate at the wall of discontinuities.

Figure 5

Energy per site $E_{\text{CD}}^{S=1}$ of the $S=1$ Heisenberg model on the columnar dimer lattice (inset) parametrized by the angle $\theta$ for different system sizes $L$. The temperature was scaled as $T=1/2L$ to probe ground-state properties. Black vertical lines denote the boundaries of the central AFM regime from Ref. [17].

Figure 6

Dimer triplet density $n_{\text{D}}$ (top panels) and AFM structure factor $S(\pi ,\pi )$ (bottom panels) of the pFFB model as functions of $J$ and $J_{\text{P}}$ at fixed temperatures $T/J_{\text{D}}=0.2$ (left panels) and $T/J_{\text{D}}=0.3$ (right panels) on a system with $L=12$.