F. Mila

École Polytechnique Fédérale de Lausanne, Lausanne, Vaud, Switzerland

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Publications (278)930.85 Total impact

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    ABSTRACT: We revisit the SU(6) Heisenberg model on the honeycomb lattice, which has been predicted to be a chiral spin liquid by mean-field theory [G. Szirmai et al., Phys. Rev. A 84, 011611 (2011)]. Using exact diagonalizations of finite clusters, infinite projected entangled pair states simulations, and variational Monte Carlo simulations based on Gutzwiller projected wave functions, we provide strong evidence in favour of the competing plaquette state, which was reported to be higher but close by in energy according to mean-field theory. This is further confirmed by the investigation of the model with a ring exchange term, which shows that there is a transition between the plaquette state and the chiral state at a finite value of the ring exchange term.
    Preview · Article · Jan 2016
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    ABSTRACT: We show that, in the presence of a $\pi/2$ artificial gauge field per plaquette, Mott insulating phases of ultra-cold fermions with $SU(N)$ symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by a multiplet of $N$ low-lying singlet excitations for periodic boundary conditions, and by chiral edge states described by the $SU(N)_1$ Wess-Zumino-Novikov-Witten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for $N$ between $3$ and $9$, and by a parton construction based on a set of $N$ Gutzwiller projected fermionic wave-functions with flux $\pi/N$ per triangular plaquette. Experimental implications are briefly discussed.
    Preview · Article · Jan 2016
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    Pierre Nataf · Frederic Mila
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    ABSTRACT: Motivated by recent experimental progress in the context of ultra-cold multi-color fermionic atoms in optical lattices, we have developed a method to exactly diagonalize the Heisenberg $SU(N)$ Hamiltonian with several particles per site living in a fully symmetric or antisymmetric representation of $SU(N)$. The method, based on the use of standard Young tableaux, takes advantage of the full $SU(N)$ symmetry, allowing one to work directly in each irreducible representations of the global $SU(N)$ group. Since the $SU(N)$ singlet sector is often much smaller than the full Hilbert space, this enables one to reach much larger system sizes than with conventional exact diagonalizations. The method is applied to the study of Heisenberg chains in the symmetric representation with two and three particles per site up to $N=10$ and up to 20 sites. For the length scales accessible to this approach, all systems except the Haldane chain ($SU(2)$ with two particles per site) appear to be gapless, and the central charge and scaling dimensions extracted from the results are consistent with a critical behaviour in the $SU(N)$ level $k$ Wess-Zumino-Witten universality class, where $k$ is the number of particles per site. These results point to the existence of a cross-over between this universality class and the asymptotic low-energy behavior with a gapped spectrum or a critical behavior in the $SU(N)$ level $1$ WZW universality class.
    Preview · Article · Jan 2016
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    ABSTRACT: We show that the critical fields of the magnetization plateaus of the Shastry-Sutherland model decrease significantly upon increasing the ratio of inter- to intra-dimer coupling, and accordingly that the magnetization plateaus of SrCu_2(BO_3)_2 shift to lower field under pressure, making the first two plateaus at 1/8 and 2/15 potentially accessible to neutron scattering experiments. These conclusions are based on the derivation of an effective classical model of interacting pinwheel-shaped spin-2 bound states using a combination of perturbative and graph-based continuous unitary transformations, showing that pinwheel crystals are indeed the lowest-energy plateau structures at low magnetization, and that a simple model of intermediate-range two-body repulsion between pinwheels is able to account quantitatively for the plateau sequence.
    Preview · Article · Jan 2016
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    ABSTRACT: Quantum antiferromagnets have proven to be some of the cleanest realizations available for theoretical, numerical, and experimental studies of quantum fluctuation effects. At finite temperatures, however, the additional effects of thermal fluctuations in the restricted phase space of a low-dimensional system have received much less attention, particularly the situation in frustrated quantum magnets, where the excitations may be complex collective (bound or even fractionalized) modes. We investigate this problem by studying the thermodynamic properties of the frustrated two-leg S=1/2 spin ladder, with particular emphasis on the fully frustrated case. We present numerical results for the magnetic specific heat and susceptibility, obtained from exact diagonalization and quantum Monte Carlo studies, which we show can be rendered free of the sign problem even in a strongly frustrated system and which allow us to reach unprecedented sizes of L=200 ladder rungs. We find that frustration effects cause an unconventional evolution of the thermodynamic response across the full parameter regime of the model. However, close to the first-order transition they cause a highly anomalous reduction in temperature scales with no concomitant changes in the gap; the specific heat shows a very narrow peak at very low energies and the susceptibility rises abruptly at extremely low temperatures. Unusually, the two quantities have different gaps over an extended region of the parameter space. We demonstrate that these results reflect the presence of large numbers of multi-particle bound-state excitations, whose energies fall below the one-triplon gap in the transition region.
    Full-text · Article · Nov 2015
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    ABSTRACT: We investigate by resonant inelastic x-ray scattering the magnetic excitations in thin films of tetragonal CuO. We identify a spin wave excitation, dispersing on two cupratelike antiferromagnetic sublattices. Its energy at the boundary of the Brillouin zone (220 meV), is significantly lower than typical values (E∼300 meV) found in two-dimensional cuprates. A spin wave expansion starting from an extended Hubbard model suggests two possible scenarios for this energy lowering. © 2015 American Physical Society.
    No preview · Article · Oct 2015 · Physical Review B
  • Andrew Smerald · Frédéric Mila
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    ABSTRACT: Recent experiments on the Ba3XSb2O9 family have revealed materials that potentially realize spin- and spin-orbital liquid physics. However, the lattice structure of these materials is complicated due to the presence of charged X2+-Sb5+ dumbbells, with two possible orientations. To model the lattice structure, we consider a frustrated model of charged dumbbells on the triangular lattice, with long-range Coulomb interactions. We study this model using Monte Carlo simulation, and find a freezing temperature, Tfrz, at which the simulated structure factor matches well to low-temperature x-ray diffraction data for Ba3CuSb2O9. At T=Tfrz we find a complicated "branching" structure of superexchange-linked X2+ clusters, which form a fractal pattern with fractal dimension df=1.90. We show that this gives a natural explanation for the presence of orphan spins. Finally we provide a plausible mechanism by which such dumbbell disorder can promote a spin-orbital resonant state with delocalized orphan spins.
    No preview · Article · Oct 2015 · Physical Review Letters
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    ABSTRACT: Using quantum Monte Carlo simulations along with higher-order spin-wave theory, bond-operator and strong-coupling expansions, we analyse the dynamical spin structure factor of the spin-half Heisenberg model on the square-lattice bilayer. We identify distinct contributions from the low-energy Goldstone modes in the magnetically ordered phase and the gapped triplon modes in the quantum disordered phase. In the antisymmetric (with respect to layer inversion) channel, the dynamical spin structure factor exhibits a continuous evolution of spectral features across the quantum phase transition, connecting the two types of modes. Instead, in the symmetric channel we find a depletion of the spectral weight when moving from the ordered to the disordered phase. While the dynamical spin structure factor does not exhibit a well-defined distinct contribution from the amplitude (or Higgs) mode in the ordered phase, we identify an only marginally-damped amplitude mode in the dynamical singlet structure factor, obtained from interlayer bond correlations, in the vicinity of the quantum critical point. These findings provide quantitative information in direct relation to possible neutron or light scattering experiments in a fundamental two-dimensional quantum-critical spin system.
    Full-text · Article · Aug 2015 · Physical Review B
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    ABSTRACT: The magnetic excitation spectrum in the bilayer iridate Sr$_3$Ir$_2$O$_7$ has been investigated using high-resolution resonant inelastic x-ray scattering (RIXS) performed at the iridium L$_3$ edge and theoretical techniques. A study of the systematic dependence of the RIXS spectrum on the orientation of the wavevector transfer, $\mathbf{Q}$, with respect to the iridium-oxide bilayer has revealed that the magnon dispersion is comprised of two branches well separated in energy and gapped across the entire Brillouin zone. Our results contrast with those of an earlier study which reported the existence of a single dominant branch. While these earlier results were interpreted as two overlapping modes within a spin-wave model of weakly coupled iridium-oxide planes, our results are more reminiscent of those expected for a system of weakly coupled dimers. In this latter approach the lower and higher energy modes find a natural explanation as those corresponding to transverse and longitudinal fluctuations, respectively. We have therefore developed a bond-operator theory which describes the magnetic dispersion in Sr$_3$Ir$_2$O$_7$ in terms of quantum dimer excitations. In our model dimerisation is produced by the leading Heisenberg exchange, $J_c$, which couples iridium ions in adjacent planes of the bilayer. The Hamiltonian also includes in plane exchange, $J$, as well as further neighbour couplings and relevant anisotropies. The bond-operator theory provides an excellent account of the dispersion of both modes, while the measured $\mathbf{Q}$ dependence of the RIXS intensities is in reasonable qualitative accord with the spin-spin correlation function calculated from the theory. We discuss our results in the context of the quantum criticality of bilayer dimer systems in the presence of anisotropic interactions derived from strong spin-orbit coupling.
    Full-text · Article · Jul 2015 · Physical Review B
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    Andrew Smerald · Frederic Mila
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    ABSTRACT: Recent experiments on the Ba$_3$XSb$_2$O$_9$ family have revealed materials that potentially realise spin- and spin-orbital liquid physics. However, the lattice structure of these materials is complicated due to the presence of charged X$^{2+}$-Sb$^{5+}$ dumbbells, with two possible orientations. To model the lattice structure, we consider a frustrated model of charged dumbbells on the triangular lattice, with long-range Coulomb interactions. We study this model using Monte Carlo simulation, and find a freezing temperature, $T_{\sf frz}$, at which the simulated structure factor matches well to low-temperature x-ray diffraction data for Ba$_3$CuSb$_2$O$_9$. At $T=T_{\sf frz}$ we find a complicated "branching" structure of superexchange-linked X$^{2+}$ clusters, and show that this gives a natural explanation for the presence of orphan spins. Finally we provide a plausible mechanism by which such dumbbell disorder can promote a spin-orbital resonant state with delocalised orphan spins.
    Preview · Article · Jun 2015
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    ABSTRACT: We report on the real space profile of spin polarons in the quasi-two-dimensional frustrated dimer spin system SrCu_{2}(BO_{3})_{2} doped with 0.16% of Zn. The ^{11}B nuclear magnetic resonance spectrum exhibits 15 additional boron sites near nonmagnetic Zn impurities. With the help of exact diagonalizations of finite clusters, we have deduced from the boron spectrum, the distribution of local magnetizations at the Cu sites with fine spatial resolution, providing direct evidence for an extended spin polaron. The results are confronted with those of other experiments performed on doped and undoped samples of SrCu_{2}(BO_{3})_{2}.
    No preview · Article · Feb 2015 · Physical Review Letters
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    Jérôme Dufour · Pierre Nataf · Frédéric Mila
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    ABSTRACT: Motivated by recent experimental progress in the context of ultra-cold multi-color fermionic atoms in optical lattices, we have investigated the properties of the SU($N$) Heisenberg chain with totally antisymmetric irreducible representations, the effective model of Mott phases with $m < N$ particles per site. These models have been studied for arbitrary $N$ and $m$ with non-abelian bosonization [I. Affleck, Nuclear Physics B 265, 409 (1986); 305, 582 (1988)], leading to predictions about the nature of the ground state (gapped or critical) in most but not all cases. Using exact diagonalization and variational Monte-Carlo based on Gutzwiller projected fermionic wave functions, we have been able to verify these predictions for a representative number of cases with $N \leq 10$ and $m \leq N/2$, and we have shown that the opening of a gap is associated to a spontaneous dimerization or trimerization depending on the value of m and N. We have also investigated the marginal cases where abelian bosonization did not lead to any prediction. In these cases, variational Monte-Carlo predicts that the ground state is critical with exponents consistent with conformal field theory.
    Preview · Article · Feb 2015 · Physical Review B
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    ABSTRACT: The magnetic excitation spectrum in the bilayer iridate Sr3Ir2O7 has been investigated using high-resolution resonant inelastic x-ray scattering (RIXS) performed at the iridium L-3 edge and theoretical techniques. A study of the systematic dependence of the RIXS spectrum on the orientation of the wave-vector transfer Q, with respect to the iridium-oxide bilayer, has revealed that the magnon dispersion is comprised of two branches well separated in energy and gapped across the entire Brillouin zone. Our results contrast with those of an earlier study which reported the existence of a single dominant branch. While these earlier results were interpreted as two overlapping modes within a spin-wave model of weakly coupled iridium-oxide planes, our results are more reminiscent of those expected for a system of weakly coupled dimers. In this latter approach, the lower-and higher-energy modes find a natural explanation as those corresponding to transverse and longitudinal fluctuations, respectively. We have therefore developed a bond-operator theory which describes the magnetic dispersion in Sr3Ir2O7 in terms of quantum dimer excitations. In our model, dimerization is produced by the leading Heisenberg exchange J(c), which couples iridium ions in adjacent planes of the bilayer. The Hamiltonian also includes in-plane exchange J, as well as further neighbor couplings and relevant anisotropies. The bond-operator theory provides an excellent account of the dispersion of both modes, while the measured Q dependence of the RIXS intensities is in reasonable qualitative accord with the spin-spin correlation function calculated from the theory. We discuss our results in the context of the quantum criticality of bilayer dimer systems in the presence of anisotropic interactions derived from strong spin-orbit coupling.
    No preview · Article · Jan 2015
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    ABSTRACT: We investigate by angle-resolved photoemission the electronic structure of in situ grown tetragonal CuO, a synthetic quasi-two-dimensional edge-sharing cuprate. We show that, in spite of the very different nature of the copper oxide layers, with twice as many Cu in the CuO layers of tetragonal CuO as compared to the CuO_{2} layers of the high-T_{c} cuprates, the low-energy electronic excitations are surprisingly similar, with a Zhang-Rice singlet dispersing on weakly coupled cupratelike sublattices. This system should thus be considered as a member of the high-T_{c} cuprate family, with, however, interesting differences due to the intralayer coupling between the cupratelike sublattices.
    Full-text · Article · Oct 2014 · Physical Review Letters
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    Pierre Nataf · Frederic Mila
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    ABSTRACT: Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labelled by the set of {\it standard Young tableaux} in which the matrix of the Heisenberg SU(N) model (the quantum permutation of N-color objects) takes an explicit and extremely simple form. Since the relative dimension of the full Hilbert space to that of the singlet space on $n$ sites increases very fast with N, this formulation allows to extend exact diagonalizations of finite clusters to much larger values of N than accessible so far. Using this method, we show that, on the square lattice, there is long-range color order for SU(5), spontaneous dimerization for SU(8), and evidence in favor of a quantum liquid for SU(10).
    Full-text · Article · Aug 2014 · Physical Review Letters
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    ABSTRACT: Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice with Heisenberg intra-dimer and Ising inter-dimer couplings are found by two independent rigorous procedures. The first method uses a unitary transformation to establish a mapping correspondence with an effective classical spin model, while the second method relies on the derivation of an effective hard-core boson model by continuous unitary transformations. Both methods lead to equivalent effective Hamiltonians providing a convincing proof that the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice exhibits a zero-temperature magnetization curve with just two intermediate plateaus at one-third and one-half of the saturation magnetization, which correspond to stripe and checkerboard orderings of singlets and polarized triplets, respectively. The nature of the remarkable stripe order relevant to the one-third plateau is thoroughly investigated with the help of the corresponding exact eigenvector. The rigorous results for the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice are compared with the analogous results for the purely classical Ising and fully quantum Heisenberg models. Finally, we discuss to what extent the critical fields of SrCu2(BO3)2 and (CuCl)Ca2Nb3O10 can be described within the suggested Ising-Heisenberg model.
    Full-text · Article · Jul 2014 · Physical Review B
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    ABSTRACT: We report on the real space profile of spin polarons in the quasi two-dimensional frustrated dimer spin system SrCu2(BO3)2 doped with 0.16% of Zn. The 11B nuclear magnetic resonance spectrum exhibits 15 additional boron sites near non-magnetic Zn impurities. With the help of exact diagonalizations of finite clusters, we have deduced from the boron spectrum the distribution of local magnetizations at the Cu sites with fine spatial resolution, providing direct evidence for an extended spin polaron. The results are confronted with those of other experiments performed on doped and undoped samples of SrCu2(BO3)2.
    Full-text · Article · Jul 2014 · Physical Review Letters
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    Andrew Smerald · Frederic Mila
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    ABSTRACT: Motivated by the absence of both spin freezing and a cooperative Jahn-Teller effect at the lowest measured temperatures, we study the ground state of Ba3CuSb2O9. We solve a general spin-orbital model on both the honeycomb and the decorated honeycomb lattice, revealing rich phase diagrams. The spin-orbital model on the honeycomb lattice contains an SU(4) point, where previous studies have shown the existence of a spin-orbital liquid with algebraically decaying correlations. For realistic parameters on the decorated honeycomb lattice, we find a phase that consists of clusters of nearest-neighbour spin singlets, which can be understood in terms of dimer coverings of an emergent square lattice. While the experimental situation is complicated by structural disorder, we show qualitative agreement between our theory and a range of experiments.
    Preview · Article · Jun 2014 · Physical Review B
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    Philippe Corboz · Frédéric Mila
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    ABSTRACT: Using infinite projected entangled-pair states (iPEPS), we show that the Shastry-Sutherland model in an external magnetic field has low-magnetization plateaus which, in contrast to previous predictions, correspond to crystals of bound states of triplets, and {\it not} to crystals of triplets. The first sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with experiments on the orthogonal-dimer antiferromagnet SrCu$_2$(BO$_3$)$_2$, and they can be naturally understood as regular patterns of bound states, including the intriguing 2/15 one. We also show that, even in a confined geometry, two triplets bind into a {\it localized} bound state with $S_z=2$. Finally, we discuss the role of competing domain-wall and supersolid phases as well as that of additional anisotropic interactions.
    Preview · Article · Apr 2014 · Physical Review Letters
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    Laurent de Forges de Parny · H-Y. Yang · Frédéric Mila
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    ABSTRACT: We investigate the structure of the spectrum of antiferromagnetically coupled spin-1 bosons on a square lattice using degenerate perturbation theory and exact diagonalizations of finite clusters. We show that the superfluid phase develops an Anderson tower of states typical of nematic long-range order with broken SU(2) symmetry, by contrast to the case of spin-1 bosons in a trap where a genuine polar superfluid ground state only appears in the presence of an external perturbation that breaks the SU(2) symmetry. We further show that this order persists into the Mott insulating phase down to zero hopping for one boson per site, and down to a critical hopping for two bosons per site, in agreement with mean-field and Quantum Monte Carlo results.
    Full-text · Article · Mar 2014 · Physical Review Letters

Publication Stats

6k Citations
930.85 Total Impact Points

Institutions

  • 2004-2015
    • École Polytechnique Fédérale de Lausanne
      • Institute of Theoretical Physics
      Lausanne, Vaud, Switzerland
  • 2000-2012
    • University of Lausanne
      • Institut de géophysique
      Lausanne, Vaud, Switzerland
  • 2007
    • Université de Neuchâtel
      • Institut de physique (IPH)
      Neuchâtel, NE, Switzerland
  • 1993-2007
    • Paul Sabatier University - Toulouse III
      • Laboratoire de Physique Théorique - UMR 5152 - LPT
      Tolosa de Llenguadoc, Midi-Pyrénées, France
  • 1990-2007
    • Rutgers, The State University of New Jersey
      • Department of Physics
      Нью-Брансуик, New Jersey, United States
  • 2006
    • Aoyama Gakuin University
      Edo, Tōkyō, Japan
  • 2001
    • French National Centre for Scientific Research
      • Institut Néel
      Lutetia Parisorum, Île-de-France, France