Mott Glass in Site-Diluted $S=1$ Antiferromagnets with Single-Ion Anisotropy

The interplay between site dilution and quantum fluctuations in $S=1$ Heisenberg antiferromagnets on the square lattice is investigated using quantum Monte Carlo simulations. Quantum fluctuations are tuned by a single-ion anisotropy $D$. In the clean limit, a sufficiently large $D>D_c=5.65(2)J$ forces each spin into its $m_S=0$ state, and thus destabilizes antiferromagnetic order. In the presence of site dilution, quantum fluctuations are found to destroy Néel order before the percolation threshold of the lattice is reached, if $D$ exceeds a critical value $D^{*}=2.3(2)J$. This mechanism opens up an extended quantum-disordered Mott-glass phase on the percolated lattice, characterized by a gapless spectrum and vanishing uniform susceptibility.

Figure 1

Phase diagram of the site-diluted $S=1$ SLHAF. The magnetic phases (and the corresponding bosonic ones) are indicated. $\mathrm{QD}=\mathrm{\text{quantum}}$ disordered. The mean-field (MF) line corresponds to the low-dilution limit $(D/J{)}_{c,p}=(D/J{)}_{c,0}(1-p)$.

Figure 2

(a) Ground-state correlation length of the $S=1$ anisotropic Heisenberg antiferromagnet on the chain as a function of the anisotropy. (b) Local susceptibility ${\chi }_{\mathrm{loc},i}={\int }_0^{\beta }d\tau ⟨S_i^z(0)S_i^z(\tau )⟩$ on a $40\times 40$ lattice at the percolation threshold $p=p^{*}$, with anisotropy below and above $(D/J{)}^{*}=2.2$. ${\chi }_{\mathrm{loc},i}=0$ corresponds to empty sites.

Figure 3

(a) Uniform susceptibility for various points in the Mott-glass phase, contrasted with the case of a point in the gapped phase for $p=0$ (system size: $L=36$). (b) Uniform magnetization upon application of a weak field in the Mott-glass phase at $p=0.2$, $D/J=4.4$. In the inset: different magnetization curves starting from the $XY$ ordered phase ($D/J=3$), Mott-glass phase ($D/J=4.4$), and QD gapped phase ($D/J=5.8$). For $D/J=3$ we have plotted $m/2$, and, for $D/J=5.8$, $h$ is rescaled by a factor of 3. Here $L=28$ and $p=0.2$.