A. Fabricio Albuquerque

Federal University of Rio de Janeiro, Rio de Janeiro, Rio de Janeiro, Brazil

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Publications (14)

  • A Fabricio Albuquerque · Fabien Alet · Roderich Moessner
    [Show abstract] [Hide abstract] ABSTRACT: We investigate nearest-neighbor valence-bond wave functions on bipartite three-dimensional lattices. By performing large-scale Monte Carlo simulations, we find that long-range magnetic order coexists with dipolar four-spin correlations on the cubic lattice, this latter feature being reminiscent of the Coulomb phase for classical dimers on the same geometry. Similar properties are found for the lower-coordination diamond lattice. While this suggests that the coexistence of magnetic order and dipolar four-spin correlations is generic for such states on bipartite three-dimensional lattices, we show that simple generalizations of these wave functions can encode different ordering behaviors.
    Article · Oct 2012 · Physical Review Letters
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    H-Y. Yang · A Fabricio Albuquerque · Sylvain Capponi · [...] · Kai Phillip Schmidt
    [Show abstract] [Hide abstract] ABSTRACT: Motivated by the recent discovery of a spin-liquid phase for the Hubbard model on the honeycomb lattice at half-filling (Meng et al 2010 Nature 88 487), we apply both perturbative and non-perturbative techniques to derive effective spin Hamiltonians describing the low-energy physics of the Mott-insulating phase of the system. Exact diagonalizations of the so-derived models on small clusters are performed, in order to assess the quality of the effective low-energy theory in the spin-liquid regime. We show that six-spin interactions on the elementary loop of the honeycomb lattice are the dominant sub-leading effective couplings. A minimal spin model is shown to reproduce most of the energetic properties of the Hubbard model on the honeycomb lattice in its spin-liquid phase. Surprisingly, a more elaborate effective low-energy spin model obtained by a systematic graph expansion rather disagrees beyond a certain point with the numerical results for the Hubbard model at intermediate couplings.
    Full-text Article · Jul 2012 · New Journal of Physics
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    A. F. Albuquerque · David Schwandt · B. Hetényi · [...] · A. M. Läuchli
    [Show abstract] [Hide abstract] ABSTRACT: We present a comprehensive computational study of the phase diagram of the frustrated S=1/2 Heisenberg antiferromagnet on the honeycomb lattice, with second-nearest (J2) and third-neighbor (J3) couplings. Using a combination of exact diagonalizations of the original spin model, of the Hamiltonian projected into the nearest neighbor short range valence bond basis, and of an effective quantum dimer model, as well as a self-consistent cluster mean-field theory, we determine the boundaries of several magnetically ordered phases in the region J2,J3\in [0,1], and find a sizable magnetically disordered region in between. We characterize part of this magnetically disordered phase as a plaquette valence bond crystal phase. At larger J2, we locate a sizable region in which staggered valence bond crystal correlations are found to be important, either due to genuine valence bond crystal ordering or as a consequence of magnetically ordered phases which break lattice rotational symmetry. Furthermore we find that a particular parameter-free Gutzwiller projected tight-binding wave function has remarkably accurate energies compared to finite-size extrapolated ED energies along the transition line from conventional N\'eel to plaquette VBC phases, a fact that points to possibly interesting critical behavior - such as a deconfined critical point - across this transition. We also comment on the relevance of this spin model to model the spin liquid region found in the half-filled Hubbard model on the honeycomb lattice.
    Full-text Article · Feb 2011 · Physical review. B, Condensed matter
  • A. Fabricio Albuquerque · Fabien Alet
    [Show abstract] [Hide abstract] ABSTRACT: We investigate the arguably simplest $SU(2)$-invariant wave functions capable of accounting for spin-liquid behavior, expressed in terms of nearest-neighbor valence-bond states on the square lattice and characterized by different topological invariants. While such wave-functions are known to exhibit short-range spin correlations, we perform Monte Carlo simulations and show that four-point correlations decay algebraically with an exponent $1.16(4)$. This is reminiscent of the {\it classical} dimer problem, albeit with a slower decay. Furthermore, these correlators are found to be spatially modulated according to a wave-vector related to the topological invariants. We conclude that a recently proposed spin Hamiltonian that stabilizes the here considered wave-function(s) as its (degenerate) ground-state(s) should exhibit gapped spin and gapless non-magnetic excitations.
    Article · Sep 2010 · Physical review. B, Condensed matter
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    A. Fabricio Albuquerque · Nicolas Laflorencie · Jean-David Picon · Frédéric Mila
    [Show abstract] [Hide abstract] ABSTRACT: We investigate the competition between spin-supersolidity and phase separation in a frustrated spin-half model of weakly coupled dimers. We start by considering systems of hard-core bosons on the square lattice, onto which the low-energy physics of the herein investigated spin model can be mapped, and devise a criterion for gauging the interplay between supersolid order and domain wall formation based on strong coupling arguments. Effective bosonic models for the spin model are derived via the contractor renormalization (CORE) algorithm and we propose to combine a self-consistent cluster mean-field solution with our criterion for the occurrence of phase separation to derive the phase diagram as a function of frustration and magnetic field. In the limit of strong frustration, the model is shown to be unstable toward phase separation, in contradiction with recently published results. However, a region of stable supersolidity is identified for intermediate frustration, in a parameter range not investigated so far and of possible experimental relevance.
    Full-text Article · May 2010 · Physical review. B, Condensed matter
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    A. Fabricio Albuquerque · Fabien Alet · Clément Sire · Sylvain Capponi
    [Show abstract] [Hide abstract] ABSTRACT: The behavior of the ground-state fidelity susceptibility in the vicinity of a quantum critical point is investigated. We derive scaling relations describing its singular behavior in the quantum critical regime. Unlike it has been found in previous studies, these relations are solely expressed in terms of conventional critical exponents. We also describe in detail a quantum Monte Carlo scheme that allows for the evaluation of the fidelity susceptibility for a large class of many-body systems and apply it in the study of the quantum phase transition for the transverse-field Ising model on the square lattice. Finite size analysis applied to the so obtained numerical results confirm the validity of our scaling relations. Furthermore, we analyze the properties of a closely related quantity, the ground-state energy's second derivative, that can be numerically evaluated in a particularly efficient way. The usefulness of both quantities as alternative indicators of quantum criticality is examined. Comment: 13 pages, 7 figures. Published version
    Full-text Article · Dec 2009 · Physical Review B
  • A Fabricio Albuquerque · Helmut G Katzgraber · Matthias Troyer
    [Show abstract] [Hide abstract] ABSTRACT: Contractor renormalization (CORE) is a real-space renormalization-group method to derive effective Hamiltionians for microscopic models. The original CORE method is based on a real-space decomposition of the lattice into small blocks and the effective degrees of freedom on the lattice are tensor products of those on the small blocks. We present an extension of the CORE method that overcomes this restriction. Our generalization allows the application of CORE to derive arbitrary effective models whose Hilbert space is not just a tensor product of local degrees of freedom. The method is especially well suited to search for microscopic models to emulate low-energy exotic models and can guide the design of quantum devices.
    Article · May 2009 · Physical Review E
  • A. Fabricio Albuquerque · Chris J. Hamer · Jaan Oitmaa
    [Show abstract] [Hide abstract] ABSTRACT: We investigate the zero-temperature phase diagram of the one-dimensional S=1 Heisenberg antiferromagnet with single-ion anisotropy. By employing high-order series expansions and quantum Monte Carlo simulations we obtain accurate estimates for the critical points separating different phases in the quantum phase diagram. Additionally, excitation spectra and gaps in the large-D and N\'{e}el phases are obtained.
    Article · Dec 2008 · Physical review. B, Condensed matter
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    J.-D. Picon · A. F. Albuquerque · K. P. Schmidt · [...] · F. Mila
    [Show abstract] [Hide abstract] ABSTRACT: Using perturbative expansions and the contractor renormalization (CORE) algorithm, we obtain effective hard-core bosonic Hamiltonians describing the low-energy physics of S=1/2 spin-dimer antiferromagnets known to display supersolid phases under an applied magnetic field. The resulting effective models are investigated by means of mean-field analysis and quantum Monte Carlo simulations. A ``leapfrog mechanism,'' through means of which extra singlets delocalize in a checkerboard-solid environment via correlated hoppings, is unveiled that accounts for the supersolid behavior.
    Full-text Article · Nov 2008 · Physical review. B, Condensed matter
  • A. Fabricio Albuquerque · Matthias Troyer · Jaan Oitmaa
    [Show abstract] [Hide abstract] ABSTRACT: We present numerical results for an $S=1/2$ Heisenberg antiferromagnet on a inhomogeneous square lattice with tunable interaction between spins belonging to different plaquettes. Employing Quantum Monte Carlo, we significantly improve on previous results for the the critical point separating singlet-disordered and N\'{e}el-ordered phases, and obtain an estimate for the critical exponent $\nu$ consistent with the three-dimensional classical Heisenberg universality class. Additionally, we show that a fairly accurate result for the critical point can be obtained from a Contractor Renormalization (CORE) expansion by applying a surprisingly simple analysis to the effective Hamiltonian.
    Article · Aug 2008 · Physical review. B, Condensed matter
  • A. Fabricio Albuquerque · Helmut G. Katzgraber · Matthias Troyer · Gianni Blatter
    [Show abstract] [Hide abstract] ABSTRACT: We use a nonperturbative extended contractor renormalization (ENCORE) method for engineering quantum devices for the implementation of topologically protected quantum bits described by an effective quantum dimer model on the triangular lattice. By tuning the couplings of the device, topological protection might be achieved if the ratio between effective two-dimer interactions and flip amplitudes lies in the liquid phase of the phase diagram of the quantum dimer model. For a proposal based on a quantum Josephson junction array [L. B. Ioffe {\it et al.}, Nature (London) {\bf 415}, 503 (2002)] our results show that optimal operational temperatures below 1 mK can only be obtained if extra interactions and dimer flips, which are not present in the standard quantum dimer model and involve three or four dimers, are included. It is unclear if these extra terms in the quantum dimer Hamiltonian destroy the liquid phase needed for quantum computation. Minimizing the effects of multi-dimer terms would require energy scales in the nano-Kelvin regime. An alternative implementation based on cold atomic or molecular gases loaded into optical lattices is also discussed, and it is shown that the small energy scales involved--implying long operational times--make such a device impractical. Given the many orders of magnitude between bare couplings in devices, and the topological gap, the realization of topological phases in quantum devices requires careful engineering and large bare interaction scales.
    Article · Sep 2007 · Physical review. B, Condensed matter
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    A. F. Albuquerque · Fabien Alet · P. Corboz · [...] · S. Wessel
    [Show abstract] [Hide abstract] ABSTRACT: We present release 1.3 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. Development is centered on common XML and binary data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs. The programs enable non-experts to start carrying out numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), as well as the density matrix renormalization group (DMRG). Changes in the new release include a DMRG program for interacting models, support for translation symmetries in the diagonalization programs, the ability to define custom measurement operators, and support for inhomogeneous systems, such as lattice models with traps. The software is available from our web server at http://alps.comp-phys.org/ .
    Full-text Article · Mar 2007 · Journal of Magnetism and Magnetic Materials
  • A. Fabricio Albuquerque · Chris J. Hamer · Jaan Oitmaa
    Article ·
  • Jaan Oitmaa · A. Fabricio Albuquerque
    [Show abstract] [Hide abstract] ABSTRACT: We investigate finite temperature properties of a one-dimensional S=1/2 spin model expected to describe a family of recently synthesised copper based materials. We obtain results for the specific heat and magnetic susceptibility which may be used to fit experimental data. Additionally, we analyse the static magnetic structure factor and confirm the existence of incommensurate correlations in the strongly frustrated regime.
    Article ·

Publication Stats

638 Citations


  • 2012
    • Federal University of Rio de Janeiro
      • Instituto de Física (IF)
      Rio de Janeiro, Rio de Janeiro, Brazil
  • 2010-2011
    • University of Toulouse
      Tolosa de Llenguadoc, Midi-Pyrénées, France
  • 2009-2010
    • French National Centre for Scientific Research
      • Institut Néel
      Lutetia Parisorum, Île-de-France, France
  • 2008
    • University of New South Wales
      • School of Physics
      Kensington, New South Wales, Australia