Roger G. Melko

University of Waterloo, Waterloo, Ontario, Canada

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Publications (84)293.18 Total impact

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    ABSTRACT: We study resonating-valence-bond (RVB) states on the square lattice of spins and of dimers, as well as SU(N)-invariant states that interpolate between the two. These states are ground states of gapless models, although the SU(2)-invariant spin RVB state is also believed to be a gapped liquid in its spinful sector. We show that the gapless behavior in spin and dimer RVB states is qualitatively similar by studying the R\'enyi entropy for splitting a torus into two cylinders, We compute this exactly for dimers, showing it behaves similarly to the familiar one-dimensional log term, although not identically. We extend the exact computation to an effective theory believed to interpolate among these states. By numerical calculations for the SU(2) RVB state and its SU(N)-invariant generalizations, we provide further support for this belief. We also show how the entanglement entropy behaves qualitatively differently for different values of the R\'enyi index $n$, with large values of $n$ proving a more sensitive probe here, by virtue of exhibiting a striking even/odd effect.
    New Journal of Physics 07/2012; 15(1). · 4.06 Impact Factor
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    ABSTRACT: At low temperatures, a spin ice enters a Coulomb phase - a state with algebraic correlations and topologically constrained spin configurations. In Ho2Ti2O7, we have observed experimentally that this process is accompanied by a non-standard temperature evolution of the wave vector dependent magnetic susceptibility, as measured by neutron scattering. Analytical and numerical approaches reveal signatures of a crossover between two Curie laws, one characterizing the high temperature paramagnetic regime, and the other the low temperature topologically constrained regime, which we call the spin liquid Curie law. The theory is shown to be in excellent agreement with neutron scattering experiments. On a more general footing, i) the existence of two Curie laws appears to be a general property of the emergent gauge field for a classical spin liquid, and ii) sheds light on the experimental difficulty of measuring a precise Curie-Weiss temperature in frustrated materials; iii) the mapping between gauge and spin degrees of freedom means that the susceptibility at finite wave vector can be used as a local probe of fluctuations among topological sectors.
    Physical Review X. 04/2012; 3(1).
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    Ribhu K. Kaul, Roger G. Melko, Anders W. Sandvik
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    ABSTRACT: We discuss designer Hamiltonians---lattice models tailored to be free from sign problems ("de-signed") when simulated with quantum Monte Carlo methods but which still host complex many-body states and quantum phase transitions of interest in condensed matter physics. We focus on quantum spin systems in which competing interactions lead to non-magnetic ground states. These states and the associated quantum phase transitions can be studied in great detail, enabling direct access to universal properties and connections with low-energy effective quantum field theories. As specific examples, we discuss the transition from a Neel antiferromagnet to either a uniform quantum paramagnet or a spontaneously symmetry-broken valence-bond solid in SU(2) and SU(N) invariant spin models. We also discuss anisotropic (XXZ) systems harboring topological Z2 spin liquids and the XY* transition. We briefly review recent progress on quantum Monte Carlo algorithms, including ground state projection in the valence-bond basis and direct computation of the Renyi variants of the entanglement entropy.
    Annual Review of Condensed Matter Physics. 04/2012;
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    Rajiv R. P. Singh, Roger G. Melko, Jaan Oitmaa
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    ABSTRACT: We study the bipartite entanglement entropy of the two-dimensional (2D) transverse-field Ising model in the thermodynamic limit using series expansion methods. Expansions are developed for the Renyi entropy around both the small-field and large-field limits, allowing the separate calculation of the entanglement associated with lines and corners at the boundary between sub-systems. Series extrapolations are used to extract subleading power laws and logarithmic singularities as the quantum critical point is approached. In 1D, we find excellent agreement with exact results as well as quantum Monte Carlo simulations. In 2D, we find compelling evidence that the entanglement at a corner is significantly different from a free boson field theory. These results demonstrate the power of the series expansion method for calculating entanglement entropy in interacting systems, a fact that will be particularly useful in future searches for exotic quantum criticality in models with and without the sign problem.
    Physical review. B, Condensed matter 04/2012; 86(7). · 3.77 Impact Factor
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    Yuan Wang, Hans De Sterck, Roger G Melko
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    ABSTRACT: We introduce a generalized loop move (GLM) update for Monte Carlo simulations of frustrated Ising models on two-dimensional lattices with bond-sharing plaquettes. The GLM updates are designed to enhance Monte Carlo sampling efficiency when the system's low-energy states consist of an extensive number of degenerate or near-degenerate spin configurations, separated by large energy barriers to single spin flips. Through implementation on several frustrated Ising models, we demonstrate the effectiveness of the GLM updates in cases where both degenerate and near-degenerate sets of configurations are favored at low temperatures. The GLM update's potential to be straightforwardly extended to different lattices and spin interactions allows it to be readily adopted on many other frustrated Ising models of physical relevance.
    Physical Review E 03/2012; 85(3-2):036704. · 2.31 Impact Factor
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    ABSTRACT: Spin ice materials Dy2Ti2O7 and Ho2Ti2O7 have been the subject of ongoing interest for over ten years. The cooperative magnetic ground state can be mapped onto the proton disordered ground state in water ice, and its residual entropy follows the same Pauling's estimate. Interestingly it was found in a previous study that, upon dilution of the magnetic rare earth ions Dy^3+ and Ho^3+ by non-magnetic substitutes Y^3+, the residual entropy depends non-monotonically on the dilution level. In this work we investigate through Monte Carlo simulations microscopic models to account quantitatively for the calorimetric experimental measurements, and thus also the residual entropies as a function of dilution. Features of the dilution physics in the specific heat are captured quantitatively by the microscopic models and the interplay between dilution and frustration is understood on the basis of a Bethe lattice calculation. The effect of the dipolar interactions between magnetic spins are exposed numerically for various dilution concentrations. Our work explains the previous discrepancy of the residual entropy between different species of rare earth ions and the generalized Pauling's estimate.
    02/2012;
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    ABSTRACT: Entanglement entropy is a quantity that is desirable to examine at quantum critical points in condensed matter systems, because it is expected that sub-leading scaling terms should contain universal coefficients. In dimensions higher than one, these universal coefficients (that are sub-leading to the area law) may possibly be used to identify the universality class of the quantum critical point, much like the central charge in 1D systems. The recent development of zero temperature projector methods for the transverse field Ising model in combination with replica methods for stochastic series expansion quantum Monte Carlo (QMC) allows us to examine this idea, using measurements of Renyi entanglement entropies. We compare zero- and finite- temperature QMC results with series expansion, and discuss the scaling of the Renyi entropies at the 2D critical point in the transverse field Ising model.
    02/2012;
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    ABSTRACT: The resonating valence bond (RVB) state on a two-dimensional lattice is a superposition of all permutations of singlet spin pairs. This wavefunction was first proposed by Anderson as a simple spin liquid ground state, showing no long range order at T=0. Using a loop-algorithm Monte Carlo method that samples all nearest-neighbor singlet pairs, we examine the entanglement entropy of the nearest neighbor SU(2) RVB wavefunction on the square lattice. In addition to the area law, we show that the entanglement entropy splits into two branches, due to the different topological sectors of the RVB wavefunction. These branches individually scale with a logarithmic dependence on the size of the entangled region, the functional form of which appears to be similar to the conformal distance observed in scaling at conformal critical points in 1D. We comment on the implication for the search for topological order, and on generalizations of this wavefunction, including models involving SU(N) spins.
    02/2012;
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    ABSTRACT: Motivated by recent experiments on the organic materials κ-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, we numerically investigate the Mott metal-insulator transition in a system of interacting, itinerant electrons at half-filling on the two-leg triangular strip (i.e., zigzag chain). Previous work [1] has revealed that an exotic ``spin Bose-metal'' (SBM) phase with three gapless modes is stabilized on the zigzag strip in a pure spin model of Heisenberg exchange supplemented with four-site cyclic ring exchange, a model appropriate for describing weak Mott insulators near the Mott transition. Indeed, a physically appealing picture of the realized SBM phase is to view it as a particular Mott insulating instability out of a two-band metal of interacting electrons. Guided by this idea, we perform large-scale DMRG calculations across the Mott transition in various Hubbard-type models (e.g., with on-site repulsion, longer-ranged repulsion, and/or explicit spin exchange terms). We focus on the successes and failures of describing the insulating phase near the transition within the SBM framework. Finally, the implications of our findings to the full 2D triangular lattice will be discussed.[4pt] [1] D. N. Sheng et al., PRB 79, 250112 (2009).
    02/2012;
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    ABSTRACT: We use a Loop-Ratio Valence Bond quantum Monte Carlo algorithm to study the scaling of the bipartite Renyi entanglement entropy in the 2D Heisenberg ground state. We uncover the surprising result that finite-size scaling supports a logarithmic correction to the entropic area law even with the absence of corners in the entangled region. In addition, examining the scaling within a single system, we observe an aspect-ratio dependent scaling term resembling the ``conformal distance'' term that appears in one-dimensional systems with conformal symmetry.
    02/2012;
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    ABSTRACT: Ground states of certain materials can support exotic excitations with a charge equal to a fraction of the fundamental electron charge. The condensation of these fractionalized particles has been predicted to drive unusual quantum phase transitions. Through numerical and theoretical analysis of a physical model of interacting lattice bosons, we establish the existence of such an exotic critical point, called XY*. We measure a highly nonclassical critical exponent η = 1.493 and construct a universal scaling function of winding number distributions that directly demonstrates the distinct topological sectors of an emergent Z(2) gauge field. The universal quantities used to establish this exotic transition can be used to detect other fractionalized quantum critical points in future model and material systems.
    Science 01/2012; 335(6065):193-5. · 31.20 Impact Factor
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    ABSTRACT: We numerically determine subleading scaling terms in the ground-state entanglement entropy of several two-dimensional (2D) gapless systems, including a Heisenberg model with N\'eel order, a free Dirac fermion in the {\pi}-flux phase, and the nearest-neighbor resonating-valence-bond wavefunction. For these models, we show that the entanglement entropy between cylindrical regions of length x and L - x, extending around a torus of length L, depends upon the dimensionless ratio x/L. This can be well-approximated on finite-size lattices by a function ln(sin({\pi}x/L)), akin to the familiar chord-length dependence in one dimension. We provide evidence, however, that the precise form of this bulk-dependent contribution is a more general function in the 2D thermodynamic limit.
    Physical review. B, Condensed matter 12/2011; 85(16). · 3.77 Impact Factor
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    Long Dang, Stephen Inglis, Roger G. Melko
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    ABSTRACT: We study the ground-state phase diagram of a two-dimensional kagome-lattice spin-1/2 XY model (J) with a four-site ring-exchange interaction (K) using quantum Monte Carlo simulations. We find that the superfluid phase, existing in the regime of small ring exchange, undergoes a direct transition to a Z2 quantum spin liquid phase at (K/J)c≈22, which is related to the phase proposed by L. Balents, M. P. A. Fisher, and S. M. Girvin [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.65.224412 65, 224412 (2002)]. The quantum phase transition between the superfluid and the spin liquid phase has exponents z and nu falling in the three-dimensional XY universality class, making it a candidate for an exotic XY* quantum critical point, mediated by the condensation of bosonic spinons.
    Physical review. B, Condensed matter 10/2011; 84. · 3.77 Impact Factor
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    ABSTRACT: We compute the bipartite entanglement properties of the spin-half square-lattice Heisenberg model by a variety of numerical techniques that include valence bond quantum Monte Carlo (QMC), stochastic series expansion QMC, high temperature series expansions and zero temperature coupling constant expansions around the Ising limit. We find that the area law is always satisfied, but in addition to the entanglement entropy per unit boundary length, there are other terms that depend logarithmically on the subregion size, arising from broken symmetry in the bulk and from the existence of corners at the boundary. We find that the numerical results are anomalous in several ways. First, the bulk term arising from broken symmetry deviates from an exact calculation that can be done for a mean-field Neel state. Second, the corner logs do not agree with the known results for non-interacting Boson modes. And, third, even the finite temperature mutual information shows an anomalous behavior as T goes to zero, suggesting that T->0 and L->infinity limits do not commute. These calculations show that entanglement entropy demonstrates a very rich behavior in d>1, which deserves further attention.
    Physical review. B, Condensed matter 07/2011; 84. · 3.77 Impact Factor
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    ABSTRACT: We examine the onset of classical topological order in a nearest neighbour kagome ice model. Using Monte Carlo simulations, we characterize the topological sectors of the ground state using a nonlocal cut measure which circumscribes the toroidal geometry of the simulation cell. We demonstrate that simulations which employ global loop updates that are allowed to wind around the periodic boundaries cause the topological sector to fluctuate, while restricted local loop updates freeze the simulation into one topological sector. The freezing into one topological sector can also be observed in the susceptibility of the real magnetic spin vectors projected onto the kagome plane. The ability of the susceptibility to distinguish between fluctuating and non-fluctuating topological sectors should motivate its use as a local probe of topological order in a variety of related systems.
    Journal of Physics Condensed Matter 04/2011; 23(16):164208. · 2.22 Impact Factor
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    ABSTRACT: We study mutual information for Renyi entropy of arbitrary index n, in interacting quantum systems at finite-temperature critical points, using high-temperature expansion, quantum Monte Carlo simulations and scaling theory. We find that, for n>1, the critical behavior is manifest at two temperatures T(c) and nT(c). For the XXZ model with Ising anisotropy, the coefficient of the area law has a t lnt singularity, whereas the subleading correction from corners has a logarithmic divergence, with a coefficient related to the exact results of Cardy and Peschel. For T<nT(c) there is a constant term associated with broken symmetries that jumps at both T(c) and nT(c), which can be understood in terms of a scaling function analogous to the boundary entropy of Affleck and Ludwig.
    Physical Review Letters 04/2011; 106(13):135701. · 7.73 Impact Factor
  • Long Dang, Roger Melko
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    ABSTRACT: We have studied the 2D Kagome lattice spin-1/2 XY model with 4-site exchange. The ground state properties are investigated within the framework of the Stochastic Series Expansion quantum Monte Carlo (QMC) technique. We have found a featureless insulating phase in the regime of large 4-site exchange interaction. This novel phase is a potential candidate for a the Z2 quantum spin liquid phase proposed by Balents, Girvin and Fisher [Phys. Rev. B, 65, 224412 (2002)] in a related model. Our efforts to characterize this phase using large-scale QMC simulations are also discussed.
    03/2011;
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    ABSTRACT: We develop a quantum Monte Carlo procedure to compute the Renyi entanglement entropy of interacting quantum many-body systems at nonzero temperature. We illustrate the method by calculating the topological entanglement entropy in a featureless Mott Insulating phase of a Bose-Hubbard model on the kagome lattice. The topological entanglement entropy displays a characteristic finite-temperature crossover behavior discussed previously in the context of the toric code. At zero-temperature it becomes the log of the quantum dimension of the topological order, confirming the existence of a Z2 spin liquid phase in the groundstate of this model.
    03/2011;
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    ABSTRACT: The Landau paradigm of classifying phases by broken symmetries was demonstrated to be incomplete when it was realized that different quantum Hall states could only be distinguished by more subtle, topological properties. Today, the role of topology as an underlying description of order has branched out to include topological band insulators, and certain featureless gapped Mott insulators with a topological degeneracy in the groundstate wavefunction. Despite intense focus, very few candidates for these topologically ordered "spin liquids" exist. The main difficulty in finding systems that harbour spin liquid states is the very fact that they violate the Landau paradigm, making conventional order parameters non-existent. Here, we uncover a spin liquid phase in a Bose-Hubbard model on the kagome lattice, and measure its topological order directly via the topological entanglement entropy. This is the first smoking-gun demonstration of a non-trivial spin liquid, identified through its entanglement entropy as a gapped groundstate with emergent Z2 gauge symmetry.
    Nature Physics 02/2011; 7. · 19.35 Impact Factor
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    Stephen Inglis, Roger G. Melko
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    ABSTRACT: We examine the effects of quantum fluctuations on a classical spin liquid state in the fully-frustrated honeycomb lattice Bose Hubbard model using quantum Monte Carlo simulations. Frustration is induced explicitly in the model by modulating the sign of the interaction spatially around each lattice hexagon. A superfluid to Mott insulating quantum phase transition can be induced by varying the relative strength of the classical interaction and quantum hopping. In the cases where the interaction has a regular spatial modulation, hopping promotes a phase transition to a symmetry-broken valence-bond solid state. When the interaction is forced to have no regular pattern, the Mott insulating phase is found to be featureless and gapped, making it an interesting candidate state for a quantum spin liquid arising in a Hamiltonian with only nearest-neighbor interactions.
    New Journal of Physics 12/2010; 13(5). · 4.06 Impact Factor

Publication Stats

1k Citations
293.18 Total Impact Points

Institutions

  • 2001–2014
    • University of Waterloo
      • • Department of Physics and Astronomy
      • • Department of Applied Mathematics
      Waterloo, Ontario, Canada
  • 2012
    • ETH Zurich
      • Institute for Theoretical Physics
      Zürich, ZH, Switzerland
  • 2011
    • University of California, Davis
      • Department of Physics
      Davis, CA, United States
  • 2003–2010
    • University of California, Santa Barbara
      • Department of Physics
      Santa Barbara, California, United States
  • 2008
    • National Taiwan University
      • Department of Physics
      T’ai-pei, Taipei, Taiwan
    • Harvard University
      • Department of Physics
      Cambridge, MA, United States
  • 2006
    • Oak Ridge National Laboratory
      • Materials Science and Technology Division
      Oak Ridge, FL, United States
    • Boston University
      • Department of Physics
      Boston, Massachusetts, United States