Bose and Mott glass phases in dimerized quantum antiferromagnets

Abstract

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 not previously described by any analytic theory for this model 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. The disordered Bose-Hubbard model is an ideal system for the thorough study of the effects of disorder on strongly interacting quantum systems. Ultracold atoms in optical lattices [1][2][3][4][5] perhaps offer the most direct experimental system in which to realize Bose-Hubbard physics, however the small system sizes and destructive nature of many measurements limit the efficacy of experiments. Dimerized quantum antiferromagnets present a compelling alternative environment due to an exact mapping to a lattice gas of bosons with hard-core repulsion [6][7][8]. These systems consist of lattices of pairs of spins (dimers) which, in the ground state, are all in a singlet configuration. This state can be viewed as an 'empty' lattice while a local triplet excitation can be thought of as a site occupied by a spin-1 boson ('triplon').Condensation of these bosons corresponds to exotic magnetically ordered states seen in materials such as [18][19][20]. These systems provide excellent experimental setups to probe quantum critical behavior through field-and pressuretuning, and have motivated some notable theoretical works based on bond-operator techniques [21][22][23][24].Recent experiments on disordered quantum antiferromagnets have seen evidence for novel glassy phases, particularly in bromine-doped dichloro-tetrakis-thioureanickel (DTN) [25] where both Bose and Mott glass phases of bosonic quasiparticles have been observed. Such phases have also been seen in other materials [26][27][28][29] and in quantum Monte Carlo simulations [30][31][32][33][34].Motivated by these experimements, in this Letter we present an analytic treatment of dimerized quantum antiferromagnets with weak intra-dimer bond disorder us- ing the hard-core boson formalism. We perform a strong coupling expansion [35,36] combined with a replica disorder average to derive an effective field theory. From a renormalization group (RG) analysis we obtain the phase boundaries between the gapped magnetic states -or in boson language, incompressible Mott ins...

Finding the phase diagram of strongly correlated disordered bosons using quantum quenches

“…Despite intense analytical [56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72] and numerical [73][74][75][76][77][78][79][80][81][82][83][84] study, many questions as to the nature of the BG remain. Various theoretical proposals have been put forward suggesting ways to observe the BG in experiments [70,[83][84][85][86][87][88][89].…”

Self-consistent T-matrix approach to gap renormalization in quantum magnets with bond disorder

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Quench Spectroscopy of a Disordered Quantum System

“…where âj and â † j are, respectively, the annihilation and creation operators of a boson on site j, V j = ∆ j − µ, with ∆ j a site-dependent random potential and µ the chemical potential. The applications of the DBHM range from disordered superfluid Helium [5] to magnetic systems [33][34][35][36][37][38]. It has also been emulated in ultracold-atom systems [39,40], where the disorder can be generated by a speckle pattern [41,42], a bichromatic quasiperiodic potential [43,44], impurities [45][46][47] or by a spatial light modulator [48,49].…”