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.
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.
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.
Bosonic excitations within long-range ordered, but strongly inhomogeneous phases have been studied in quite some detail. My thesis focuses instead on understanding the insulating, localized phase of disordered bosonic systems. In particular I study localization properties of strongly interacting bosons and spin systems in a disorder potential at zero temperature. I focus on simple, prototypical spin models (Ising model and XY model) in random fields on a Cayley tree with large connectivity. Regarding the nature of the quantum phase transition in strong disorder I find the following results: i) With a uniformly distributed disorder non-extensive excitations in the disordered phase are all localized. ii)Moreover, I find that the order arises due to a collective condensation, which is qualitatively distinct from a Bose Einstein condensation of single particle excitations into a delocalized state. In particular, in non-frustrated Bose glasses, I do not find evidence for a boson mobility edge in the Bose glass. These results are qualitatively different from claims in the recent literatures . Considering that (many body) localization of bosons is a kind of quantum glass transition, it is an interesting question to ask what phenomena occur, if the ingredients for more conventional (classical) glassy physics are added to a disordered bosons system, namely: random, frustrated interactions between the bosons. One can still think about such a system as bosons in a disordered potential, where the disordered potential is, at least partly, self-generated by random frustrated interactions between the bosons. This question takes us to the study of another type of disordered systems: glassy systems. Those are typically characterized by low temperature phases with an inhomogeneous density or magnetization pattern, which is extremely long-lived due to the occurrence of non-trivial ergodicity breaking. I study a solvable model of hard core bosons (pseudospins) subject to disorder and frustrating interactions. This solvable model provides insight into the possibility of coexistence of super uidity and glassy density order, as well as into the nature of the coexistence phase (the superglass). In particular, for the considered mean field model I prove the existence of a superglass phase. This complements the numerical evidence for such phases provided by quantum Monte Carlo investigations in finite dimensions and on random graphs. Those were, however, limited to finite temperature, and could thus not fully elucidate the structure of the phases at T = 0. In contrast, my analytical approach allows one to understand the quantum phase transition between glassy superfluid and insulator, and the non-trivial role played by glassy correlations. When the frustrated interactions are strong enough, the superfluid order may be destroyed. As I will show in a mean field model, this happens within the glass phase of the system, where a disorder induced superfluid-insulator phase transition takes place to give way to a frustrated Bose glass. The glassy background on top of which this happens leads to many interesting phenomena which seem not to have been noticed before. To understand the nature of the glassy superfluid-insulator quantum phase transition at zero temperature and the transport properties on the insulating, Bose glass side of the transition is the goal of the third part of my thesis. To address the above questions, I studied an exactly solvable model of a glassy superfluid-insulator quantum phase transition on a Bethe lattice geometry with high connectivity. My main results can be summarized as follows: i) I found that the superfluid-insulator transition is shifted to stronger hopping. This is a result of the pseudo gap in the density of states of the glass state, which tends to strongly disfavor the onset of superfluidity. ii) In the glassy insulator, the discrete local energy levels become broadened due to the quantum fluctuations.The level-broadening process appears as a phase transition which has strong similarities with an Anderson localization transition, and has implications on many body localization. By using the locator expansion for bosons I found that, the glassy insulator has a finite mobility edge for the bosonic excitations, which, however, does not close upon approaching the SI quantum phase transition point. This finding helps to understand the nature of the superfluid-to-frustrated Bose glass transition: the superfluid emerges as a collective phase ordering phenomenon at zero temperature, and not as a condensation in to a single particle delocalized state, in contrast to opposite predictions in the recent literatures. The existence of a mobility edge in the insulator suggests the possibility of phononless, activated transport in the bosonic insulator, which might be a candidate explanation for the experimentally seen activated transport, which has remained a mystery for a long time.
Quantum magnets represent an ideal playground for the controlled realization of novel quantum phases and of quantum phase transitions.The Hamiltonian of the system can be indeed manipulated by applying a magnetic field or pressure on the sample.When doping the system with non-magnetic impurities, novel inhomogeneous phases emerge from the interplay between geometric randomness and quantum fluctuations.In this paper we review our recent work on quantum phase transitions and novel quantum phases realized in disordered quantum magnets.The system inhomogeneity is found to strongly affect phase transitions by changing their universality class, giving the transition a novel, quantum percolative nature.Such transitions connect conventionally ordered phases to unconventional, quantum disordered ones -quantum Griffiths phases, magnetic Bose glass phases -exhibiting gapless spectra associated with low-energy localized excitations.
The Bose glass (BG) phase is the Griffiths region of the disordered Bose–Hubbard model (BHM), characterized by finite, quasi-superfluid clusters within a Mott insulating background. We propose to utilize this characterization to identify the complete zero-temperature phase diagram of the disordered BHM in d ⩾ 2 dimensions by analysing the geometric properties of what we call superfluid (SF) clusters, which are defined to be clusters of sites with non-integer expectation values for the local boson occupation number. The Mott insulator phase then is the region in the phase diagram where no SF clusters exist, and the SF phase the region where SF clusters percolate—the BG phase is inbetween: SF clusters exist, but do not percolate. This definition is particularly useful in the context of local mean field (LMF) or Gutzwiller–Ansatz calculations, where we show that an identification of the phases on the basis of global quantities such as the averaged SF order parameter and the compressibility is misleading. We apply the SF cluster analysis to the LMF ground states of the two-dimensional disordered BHM to produce its phase diagram and find (a) an excellent agreement with the phase diagram predicted on the basis of quantum Monte Carlo simulations for the commensurate density n = 1 and (b) large differences to stochastic mean field and other mean field predictions for fixed disorder strength. The relation of the percolation transition of the SF clusters with the onset of non-vanishing SF stiffness indicating the BG to SF transition is discussed.
The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension dc which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on 4He absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.