F. Mila

École Polytechnique Fédérale de Lausanne, Lausanne, Vaud, Switzerland

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Publications (263)904.31 Total impact

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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.
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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}.
    Physical Review Letters 02/2015; 114(5):056402. · 7.51 Impact Factor
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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.
    Physical Review B 02/2015; 91(17). DOI:10.1103/PhysRevB.91.174427 · 3.74 Impact Factor
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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.
    Physical Review Letters 10/2014; 113(18):187001. DOI:10.1103/PhysRevLett.113.187001 · 7.51 Impact Factor
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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).
    Physical Review Letters 08/2014; 113(12). DOI:10.1103/PhysRevLett.113.127204 · 7.51 Impact Factor
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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.
    Physical Review B 07/2014; 90(13). DOI:10.1103/PhysRevB.90.134413 · 3.74 Impact Factor
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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.
    Physical Review Letters 07/2014; 114(5). DOI:10.1103/PhysRevLett.114.056402 · 7.51 Impact Factor
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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.
    Physical Review B 06/2014; 90(9). DOI:10.1103/PhysRevB.90.094422 · 3.74 Impact Factor
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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.
    Physical Review Letters 04/2014; 112(14):147203. DOI:10.1103/PhysRevLett.112.147203 · 7.51 Impact Factor
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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.
    Physical Review Letters 03/2014; 113(20). DOI:10.1103/PhysRevLett.113.200402 · 7.51 Impact Factor
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    ABSTRACT: The magnetization process of the orthogonal-dimer antiferromagnet SrCu_{2}(BO_{3})_{2} is investigated in high magnetic fields of up to 118 T. A 1/2 plateau is clearly observed in the field range 84 to 108 T in addition to 1/8, 1/4, and 1/3 plateaus at lower fields. Using a combination of state-of-the-art numerical simulations, the main features of the high-field magnetization, a 1/2 plateau of width 24 T, a 1/3 plateau of width 34 T, and no 2/5 plateau, are shown to agree quantitatively with the Shastry-Sutherland model if the ratio of inter- to intradimer exchange interactions J^{'}/J=0.63. It is further predicted that the intermediate phase between the 1/3 and 1/2 plateaus is not uniform but consists of a 1/3 supersolid followed by a 2/5 supersolid and possibly a domain-wall phase, with a reentrance into the 1/3 supersolid above the 1/2 plateau.
    Physical Review Letters 09/2013; 111(13):137204. DOI:10.1103/PhysRevLett.111.137204 · 7.51 Impact Factor
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    ABSTRACT: We revisit the old problem of the spin-1/2 Heisenberg antiferromagnet on kagome, a major candidate for a quantum spin liquid, focusing on the renormalization of nearest-neighbor valence-bond (NNVB) tunneling amplitudes by long-range singlet fluctuations outside the NNVB basis. We find that such virtual singlets have a dramatic influence on the dominant quantum dimer model (QDM) parameters, leading to qualitatively different physics within the NNVB framework. Based on recent numerical studies on the unconstrained QDM, the renormalized parameters favor a Z2 spin liquid, thus providing a plausible way to reconcile the NNVB description with density matrix renormalization group (DMRG) studies.
    Physical Review B 08/2013; 90(10). DOI:10.1103/PhysRevB.90.100406 · 3.74 Impact Factor
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    F. Michaud · F. Mila
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    ABSTRACT: We study the spin S=1 antiferromagnetic Heisenberg model on the square lattice with, in addition to the nearest-neighbor interaction, a three-site interaction of the form (S_i S_j)*(S_j S_k) + h.c.. This interaction appears naturally in a strong coupling exansion of the two-orbital, half-filled Hubbard model. For spin 1/2, this model reduces to a Heisenberg model with bilinear interactions up to third neighbors, with a second-neighbor interaction twice as large the third-neighbor one, a very frustrated model with an infinite family of helical classical ground states in a large parameter range. Using a variety of analytical and numerical methods, we show that the spin-1 case is also very frustrated, and that its phase diagram is even richer, with possibly the succession of seven different phases as a function of the ratio of the three-site interaction to the bilinear one. The phases are either purely magnetic phases with collinear order, or of mixed magnetic and quadrupolar character with helical order.
    Physical Review B 07/2013; 88(9). DOI:10.1103/PhysRevB.88.094435 · 3.74 Impact Factor
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    Jozef Strecka · Frederic Michaud · Frederic Mila
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    ABSTRACT: Ground states of the frustrated spin-1 Ising-Heisenberg two-leg ladder with Heisenberg intra-rung coupling and only Ising interaction along legs and diagonals are rigorously found by taking advantage of local conservation of the total spin on each rung. The constructed ground-state phase diagram of the frustrated spin-1 Ising-Heisenberg ladder is then compared with the analogous phase diagram of the fully quantum spin-1 Heisenberg two-leg ladder obtained by density matrix renormalization group (DMRG) calculations. It is demonstrated that both investigated spin models exhibit quite similar magnetization scenarios, which involve intermediate plateaux at one-quarter, one-half and three-quarters of the saturation magnetization.
    Acta Physica Polonica Series a 05/2013; DOI:10.12693/APhysPolA.126.24 · 0.60 Impact Factor
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    Sandro Wenzel · Sergey E. Korshunov · Karlo Penc · Frédéric Mila
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    ABSTRACT: We investigate the ground-state properties of the highly degenerate non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice with Monte Carlo simulations. For that purpose, we introduce an Ising pseudospin representation of the ground states, and we use a simple Metropolis algorithm with local updates, as well as a powerful cluster algorithm. At sizes that can be sampled with local updates, the presence of long-range order is surprisingly combined with an algebraic decay of correlations and the complete disordering of the chirality. It is only thanks to the investigation of unusually large systems (containing $\sim 10^8$ spins) with cluster updates that the true asymptotic regime can be reached and that the system can be proven to consist of equivalent (i.e., equally ordered) sublattices. These large-scale simulations also demonstrate that the scalar chirality exhibits long-range order at zero temperature, implying that the system has to undergo a finite-temperature phase transition. Finally, we show that the average distance in the order parameter space, which has the structure of an infinite Cayley tree, remains remarkably small between any pair of points, even in the limit when the real space distance between them tends to infinity.
    Physical review. B, Condensed matter 05/2013; 88(9). DOI:10.1103/PhysRevB.88.094404 · 3.66 Impact Factor
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    Laura Messio · Philippe Corboz · Frédéric Mila
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    ABSTRACT: We study a quantum version of the three-state Potts model that includes as special cases the effective models of bosons and fermions on the square lattice in the Mott insulating limit. It can be viewed as a model of quantum permutations with amplitudes J_parallel and J_perp for identical and different colors, respectively. For J_parallel=J_perp>0, it is equivalent to the SU(3) Heisenberg model, which describes the Mott insulating phase of 3-color fermions, while the parameter range J_perp<min(0,-J_parallel) can be realized in the Mott insulating phase of 3-color bosonic atoms. Using linear flavor wave theory, infinite projected entangled-pair states (iPEPS), and continuous-time quantum Monte-Carlo simulations, we construct the full T=0 phase diagram, and we explore the T>0 properties for J_perp<0. For dominant antiferromagnetic J_parallel interactions, a three-sublattice long-range ordered stripe state is selected out of the ground state manifold of the antiferromagnetic Potts model by quantum fluctuations. Upon increasing |J_perp|, this state is replaced by a uniform superfluid for J_perp<0, and by an exotic three-sublattice superfluid followed by a two-sublattice superfluid for J_perp>0. The transition out of the uniform superfluid (that can be realized with bosons) is shown to be a peculiar type of Kosterlitz-Thouless transition with three types of elementary vortices.
    Physical Review B 04/2013; 88(15). DOI:10.1103/PhysRevB.88.155106 · 3.74 Impact Factor
  • Natalia Chepiga · Frédéric Michaud · Frédéric Mila
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    ABSTRACT: We show that spin-S ladders undergo, for antiferromagnetic rung coupling, a series of 4S topological phase transitions when the ratio of the leg to rung coupling changes from strongly antiferromagnetic to strongly ferromagnetic. These phase transitions are characterized by a change of Berry phase on the rungs, and, with appropriate boundary conditions, by the appearance and disappearance of edge states without the bulk gap ever closing. The various phases can be distinguished by the number of valence bond singlets on the rungs, which decreases from 2S for strong rung coupling to 0 for dominant leg coupling. In particular, the isotropic spin-3/2 ladder with equal leg and rung coupling is explicitly shown to be in the valence bond solid phase with one singlet per bond.
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    Natalia Chepiga · Frédéric Michaud · Frédéric Mila
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    ABSTRACT: We investigate the properties of antiferromagnetic spin-S ladders with the help of local Berry phases defined by imposing a twist on one or a few local bonds. In gapped systems with time reversal symmetry, these Berry phases are quantized, hence able in principle to characterize different phases. In the case of a fully frustrated ladder where the total spin on a rung is a conserved quantity that changes abruptly upon increasing the rung coupling, we show that two Berry phases are relevant to detect such phase transitions: the rung Berry phase defined by imposing a twist on one rung coupling, and the twist Berry phase defined by twisting the boundary conditions along the legs. In the case of non-frustrated ladders, we have followed the fate of both Berry phases when interpolating between standard ladders and dimerized spin chains. A careful investigation of the spin gap and of edge states shows that a change of twist Berry phase is associated to a quantum phase transition at which the bulk gap closes, and at which, with appropriate boundary conditions, edge states appear or disappear, while a change of rung Berry phase is not necessarily associated to a quantum phase transition. The difference is particularly acute for regular ladders, in which the twist Berry phase does not change at all upon increasing the rung coupling from zero to infinity while the rung Berry phase changes 2S times. By analogy with the fully frustrated ladder, these changes are interpreted as cross-overs between domains in which the rungs are in different states of total spin from 0 in the strong rung limit to 2S in the weak rung limit. This interpretation is further supported by the observation that these cross-overs turn into real phase transitions as a function of rung coupling if one rung is strongly ferromagnetic, or equivalently if one rung is replaced by a spin 2S impurity.
    Physical Review B 04/2013; 88(18). DOI:10.1103/PhysRevB.88.184418 · 3.74 Impact Factor
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    ABSTRACT: We have investigated the ground-state and finite-temperature phase diagram of quantum square ice - realized by the transverse-field Ising model on a checkerboard lattice - using both linear spin-wave (LSW) theory and quantum Monte Carlo (QMC). We generalize the model with different couplings between nearest (J1) and next-to-nearest (J2) neighbors on the checkerboard lattice. Our QMC approach generalizes the loop algorithm - very efficient in the study of constrained classical systems - to a ``brane algorithm'' for quantum systems. At the LSW level the vast degeneracy of the ground-state for J1=J2 and J2>J1 remains intact; moreover LSW theory breaks down in extended regions of the phase diagram, pointing at non-classical states [1]. Our QMC study goes beyond perturbative schemes and addresses directly the nature of the low-temperature phases. We have critically examined the possibility of a resonating-plaquette state for J1=J2, suggested by degenerate perturbation theory on the ice-rule manifold for weak fields. Our QMC results for finite fields confirm the absence of Néel or collinear order, but they do not confirm the presence of resonating-plaquette order, pointing at a possibly more complex non-classical state.[4pt] [1] L.-P. Henry et al., PRB 85, 134427 (2012).

Publication Stats

5k Citations
904.31 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
  • 2001
    • French National Centre for Scientific Research
      • Institut Néel
      Lutetia Parisorum, Île-de-France, France