Quantum Localization in Bilayer Heisenberg Antiferromagnets with Site Dilution

The field-induced antiferromagnetic ordering in systems of weakly coupled $S=1/2$ dimers at zero temperature can be described as a Bose-Einstein condensation of triplet quasiparticles (singlet quasiholes) in the ground state. For the case of a Heisenberg bilayer, it is here shown how the above picture is altered in the presence of site dilution of the magnetic lattice. Geometric randomness leads to quantum localization of the quasiparticles or quasiholes and to an extended Bose-glass phase in a realistic disordered model. This localization phenomenon drives the system towards a quantum-disordered phase well before the classical geometric percolation threshold is reached.

Figure 1

Field dependence of the uniform magnetization $m_u^z$, transverse staggered magnetization $m_s^x$, and superfluid density ${\rm Y}$ at $T=0$ for the bilayer antiferromagnet with $J/J^{\prime }=4$ in the clean limit ($p=0$).

Figure 2

Ground-state phase diagram of the site-diluted bilayer Heisenberg antiferromagnet with $J/J^{\prime }=4$.

Figure 3

(a),(b) Real-space images of the dimer magnetization $m_i=⟨S_{i,1}^z+S_{i,2}^z⟩$ on intact dimers in a $40\times 40\times 2$ bilayer with $J/J^{\prime }=4$, dilution $p=0.1$, and at inverse temperature $\beta J=256$, for (a) $h=0.56$ and (b) $h=0.6$. The radius of the dots is proportional to the dimer magnetization. The magnetization of unpaired spins is omitted for clarity. The most visible localized states are highlighted in (a), while the backbone of the percolating magnetized network is highlighted in (b). (c) Superfluid density as a function of the field for the specific sample considered.

Figure 4

Zero-temperature field scan in the site-diluted bilayer Heisenberg antiferromagnet with $J/J^{\prime }=4$ and $p=0.2$. Inset: scaling of the order parameter $m_s^x$ in the different phases of the system; from top to bottom, $h=0.75$ ($XY$ ordered), 0.05 (order by disorder), 1.85 (high-field Bose glass), 0.35 (quantum disordered), and 0.6 (low-field Bose glass).

Figure 5

Finite-temperature phase diagram for the site-diluted bilayer Heisenberg antiferromagnet with $J/J^{\prime }=4$ and dilution $p=0.2$. Inset: temperature dependence of the transverse structure factor for the same model with $L=32$.