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arXiv:cond-mat/9801048 · Physical review. B, Condensed matter

Vortices in coupled planes with columnar disorder and bosonic ladders

E. Orignac, Thierry Giamarchi

Published May 1, 1998• 37 citations
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Abstract

The phase diagram of two bosonic chains coupled by interchain hopping and interchain boson-boson repulsion is investigated by means of bosonization and renormalization-group techniques. It comprises two types of charge-density waves, a conventional superfluid phase, and a superfluid phase made of condensed boson pairs. The effect of a random potential on that system is also derived. Compared with the one-chain case, interchain hopping strongly stabilizes the conventional superfluid phase with respect to Anderson localization. By contrast, the superfluid phase made of condensed boson pairs is much more unstable with respect to Anderson localization than the superfluid phase of the one-chain system. An exact mapping of the two strongly correlated bosonic chains onto two coupled vortex planes gives us the phase diagram of the latter system without any further calculation. The vortex system exhibits two types of vortex lattice phase (one with entanglement and another one without entanglement), a normal phase and a phase with bound pairs of vortices. The results for Anderson localization of the bosons allow us to study vortex pinning by columnar defects or twin boundaries and obtain the correlation length of the pinned vortex lattice. We show that interplane vortex hopping strongly reduces vortex pinning by columnar defects but not by twin boundaries. We obtain the melting temperature of the entangled solid. We also derive the critical current by modified Larkin-Ovchinnikov arguments and find a very sharp decrease of critical currents when the system moves into the entangled phase in the case of columnar pins. For strong columnar pins, there is a transition into a pinned solid phase with dislocations. We argue that two multicritical points may exist in the phase diagram.

DOI
10.1103/physrevb.57.11713

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The phase diagram of two bosonic chains coupled by interchain hopping and interchain boson-boson repulsion is investigated by means of bosonization and renormalization-group techniques. It comprises two types of charge-density waves, a conventional superfluid phase, and a superfluid phase made of condensed boson pairs. The effect of a random potential on that system is also derived. Compared with the one-chain case, interchain hopping strongly stabilizes the conventional superfluid phase with respect to Anderson localization. By contrast, the superfluid phase made of condensed boson pairs is much more unstable with respect to Anderson localization than the superfluid phase of the one-chain system. An exact mapping of the two strongly correlated bosonic chains onto two coupled vortex planes gives us the phase diagram of the latter system without any further calculation. The vortex system exhibits two types of vortex lattice phase (one with entanglement and another one without entanglement), a normal phase and a phase with bound pairs of vortices. The results for Anderson localization of the bosons allow us to study vortex pinning by columnar defects or twin boundaries and obtain the correlation length of the pinned vortex lattice. We show that interplane vortex hopping strongly reduces vortex pinning by columnar defects but not by twin boundaries. We obtain the melting temperature of the entangled solid. We also derive the critical current by modified Larkin-Ovchinnikov arguments and find a very sharp decrease of critical currents when the system moves into the entangled phase in the case of columnar pins. For strong columnar pins, there is a transition into a pinned solid phase with dislocations. We argue that two multicritical points may exist in the phase diagram.
We study the phase diagram of flux lines in superconductors with columnar pins. Based on numerical exact diagonalization simulations on small clusters, we get two phases of vortices: A low-temperature pinned glass with diverging tilt modulus and a high-temperature delocalized entangled vortex liquid. For random potential disorder we find a new phase transition temperature TBG{T}_{\mathrm{BG}}TBG​ from a pinned Bose glass to an entangled liquid that reduces with increasing vortex density. This occurs primarily because vortices screen the disorder potential and generate an effective weaker random potential with increasing vortex density. For a fixed fraction of randomly placed attractive columnar pins, we find a Mott-insulating phase when the vortex density exactly matches the density of pins at the matching field ${B=B}_{\ensuremath{\varphi}}.$ We also find a transition from a strongly pinned Bose glass for $B<{B}_{\ensuremath{\varphi}}$ to a weakly pinned Bose glass for $B>{B}_{\ensuremath{\varphi}}$ as the vortex density is varied.
We consider hardcore bosons in two coupled chains of one dimensional lattices at half filling with repulsive intrachain interaction and interchain attraction. This can be mapped onto a coupled chain of spin-1/2 XXZXXZXXZ model with interchain ferromagnetic coupling. We investigate various phases of hardcore bosons (and related spin model) at zero temperature by a density matrix renormalization group method. Apart from the usual superfluid and density wave phases, pairing of interchain bosons leads to the formation of phases like pair superfluid and density wave of strongly bound pairs. We discuss the possible experimental realization of such correlated phases in the context of cold dipolar gas.
We study a bosonic ladder with two coupled chains using the finite-size density-matrix renormalization group method. We show that in a commensurate bosonic ladder the critical on-site interaction (UC)({U}_{C})(UC​) for the superfluid to Mott insulator transition gets larger as the interchain hopping $({t}_{\ensuremath{\perp}})$ increases. We analyze this quantum phase transition and obtain the phase diagram in the ${t}_{\ensuremath{\perp}}\ensuremath{-}U$ plane. We also consider the asymmetric case where the on-site interactions are different in the two chains and have shown that the system as a whole will not be in the Mott insulator phase unless both the chains have on-site interactions greater than the critical value.
By means of Monte Carlo techniques, we study the role of disorder on a system of hard-core bosons in a two-leg ladder with both intrachain (ttt) and interchain (${t}^{\ensuremath{'}}$) hoppings. We find that the phase diagram as a function of the boson density, disorder strength, and ${t}^{\ensuremath{'}}/t$ is far from being trivial. This contrasts with the case of spinless fermions where standard localization arguments apply and an Anderson-localized phase pervades the whole phase diagram. A compressible Bose-glass phase always intrudes between the Mott insulator with zero (or one) bosons per site and the superfluid that is stabilized for weak disorder. At half-filling, there is a direct transition between a (gapped) rung-Mott insulator and a Bose glass, which is driven by exponentially rare regions where disorder is suppressed. Finally, by doping the rung-Mott insulator, a direct transition to the superfluid is possible only in the clean system, whereas the Mott phase is always surrounded by the a Bose glass when disorder is present. The phase diagram based on our numerical evidence is finally reported.
We study the effects of disorder on a system of two coupled chains of strongly correlated fermions (the ladder system), using a renormalization-group technique. The stability of the phases of the pure system has been investigated as a function of interactions both for fermions with spin and spinless fermions. For spinless fermions the repulsive side is strongly localized whereas the system with attractive interactions is stable with respect to disorder, at variance with the single-chain case. For fermions with spins, the repulsive side is also localized, and in particular the ddd-wave superconducting phase found for the pure system is totally destroyed by an arbitrarily small amount of disorder. On the other hand, the attractive side is again remarkably stable with respect to localization. We have also computed the charge stiffness, the localization length, and the temperature dependence of the conductivity for the various phases. In the parameter range where ddd-wave superconductivity would occur for the pure system the conductivity is found to decrease monotonically with temperature, even at high temperature, and we discuss this surprising result. For a model with one-site repulsion and nearest-neighbor attraction, the most stable phase is an orbital antiferromagnet. Although this phase has no divergent superconducting fluctuation it can have a divergent conductivity at low temperature. Finally, to make a comparison of our results with experimental ladder systems, we treated the interladder coupling in a mean-field approximation. We argue based on our results that the superconductivity observed in some of these compounds cannot be a simple stabilization of the ddd-wave phase found for a pure single ladder. The application of our results to systems such as quantum wires is also discussed. In particular, the corrections to conductance in a two-channel quantum wire have been obtained as a function of system length, temperature, and interactions.
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{d}_{c}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^{4}\mathrm{He}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.