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arXiv:cond-mat/0512023 · Journal of Physics B Atomic Molecular and Optical Physics

Bose–Einstein condensation versus localization of bosonic quasiparticles in disordered weakly-coupled dimer antiferromagnets

Tommaso Roscilde, Stephan Haas

Published May 2, 2006• 10 citations
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Abstract

We investigate the field-induced insulator-to-superfluid transition of bosonic quasiparticles in S = 1/2 weakly-coupled dimer antiferromagnets. In the presence of realistic disorder due to site dilution of the magnetic lattice, we show that the system displays an extended Bose-glass phase characterized by the localization of the hard-core quasiparticles.

DOI
10.1088/0953-4075/39/10/s15

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We investigate the field-induced insulator-to-superfluid transition of bosonic quasiparticles in S = 1/2 weakly-coupled dimer antiferromagnets. In the presence of realistic disorder due to site dilution of the magnetic lattice, we show that the system displays an extended Bose-glass phase characterized by the localization of the hard-core quasiparticles.
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.
We numerically investigate the phase diagram of two-dimensional site-diluted coupled dimer systems in an external magnetic field. We show that this phase diagram is characterized by the presence of an extended Bose glass, not accessible to mean-field approximation, and stemming from the localization of two distinct species of bosonic quasiparticles appearing in the ground state. On the one hand, nonmagnetic impurities doped into the dimer-singlet phase of a weakly coupled dimer system are known to free up local magnetic moments. The deviations of these local moments from full polarization along the field can be mapped onto a gas of bosonic quasiparticles, which undergo condensation in zero and very weak magnetic fields, corresponding to transverse long-range antiferromagnetic order. An increasing magnetic field lowers the density of such quasiparticles to a critical value at which a quantum phase transition occurs, corresponding to the quasiparticle localization on clusters of local magnets (dimers, trimers, etc.) and to the onset of a Bose glass. Strong finite-size quantum fluctuations hinder further depletion of quasiparticles from such clusters, and thus lead to the appearance of pseudoplateaus in the magnetization curve of the system. On the other hand, site dilution hinders the field-induced Bose-Einstein condensation of triplet quasiparticles on the intact dimers, and it introduces instead a Bose glass of triplets. A thorough numerical investigation of the phase diagram for a planar system of coupled dimers shows that the two above-mentioned Bose glass phases are continuously connected, and they overlap in a finite region of parameter space, thus featuring a two-species Bose glass. The quantum phase transition from Bose glass to magnetically ordered phases in two dimensions is marked by novel universal exponents ($z\ensuremath{\approx}2$, $\ensuremath{\beta}\ensuremath{\approx}0.9$, and $\ensuremath{\nu}\ensuremath{\approx}1$). Hence we conclude that doped quantum antiferromagnets in a field represent an ideal setting for the study of fundamental dirty-boson physics.
We examine the effects of disorder on dimerized quantum antiferromagnets in a magnetic field, using the mapping to a lattice gas of hard-core bosons with finite-range interactions. Combining a strong-coupling expansion, the replica method, and a one-loop renormalization-group analysis, we investigate the nature of the glass phases formed. We find that away from the tips of the Mott lobes, the transition is from a Mott insulator to a compressible Bose glass, however the compressibility at the tips is strongly suppressed. We identify this finding with the presence of a rare Mott glass phase and demonstrate that the inclusion of replica symmetry breaking is vital to correctly describe the glassy phases. This result suggests that the formation of Bose and Mott glass phases is not simply a weak localization phenomenon but is indicative of much richer physics. We discuss our results in the context of both ultracold atomic gases and spin-dimer materials.
A quantum particle cannot in general diffuse through a disordered medium because of its wavelike nature, but interacting particles can escape localization by collectively percolating through the system. For bosonic particles this phenomenon corresponds to a quantum transition from a localized insulator phase —the Bose glass— to a superfluid phase, in which particles condense into an extended state. Here, we construct a universal phase diagram of disordered bosons in doped quantum magnets for which bosonic quasiparticles are represented by magnetized states (spin triplets) of the quantum spins, condensing into a magnetically ordered state. The appearance of a Bose glass leads to strong measurable signatures in the onset of superfluidity of the spin-triplet gas, exhibiting a complex crossover from low-temperature quantum percolation to a conventional condensation transition at intermediate temperatures.
Site dilution of spin-gapped antiferromagnets leads to localized free moments, which can order antiferromagnetically in two and higher dimensions. Here we show how a weak magnetic field drives this order-by-disorder state into a novel disordered-local-moment (DLM) phase, characterized by the formation of local singlets between neighboring moments and by localized moments aligned antiparallel to the field. This disordered phase is characterized by the absence of a gap, as is the case in a Bose glass. The associated field-driven quantum phase transition is consistent with the universality of a superfluid-to-Bose-glass transition. The robustness of the DLM phase and its prominent features, in particular a series of pseudo-plateaus in the magnetization curve, makes it accessible and relevant to experiments.
A spin-wave approach of the zero temperature superfluid-insulator transition for two-dimensional hard-core bosons in a random potential μ=±W is developed. While at the classical level there is no intervening phase between the Bose-condensed superfluid (SF) and the gapped disordered insulator, the introduction of quantum fluctuations leads to a much richer physics. Upon increasing the disorder strength W, the Bose-condensed fraction disappears first, before the SF. Then a gapless Bose-glass phase emerges over a finite region until the insulator appears. Furthermore, in the strongly disordered SF regime, a mobility edge in the spin-wave excitation spectrum is found at a finite frequency Ω(c) decreasing with W, and presumably vanishing in the Bose-glass phase.