Publications (93)311.61 Total impact
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ABSTRACT: We develop a method to calculate the bipartite entanglement entropy of quantum lattice models in the thermodynamic limit, using a Numerical Linked Cluster Expansion (NLCE) involving only rectangular clusters. The NLCE is based on exact diagonalization of all N x M rectangular clusters at the interface between entangled subsystems A and B. We show that the method can be used to obtain the Renyi entanglement entropy of the twodimensional transverse field Ising model, for arbitrary real Renyi index. Furthermore, extrapolating these results as a function of the order of the calculation, one can obtain subleading universal pieces of the entanglement entropy at a quantum critical point. These results are compared with series expansions, quantum Monte Carlo simulations and field theories, where available, and they demonstrate the utility of the NLCE in obtaining accurate results for the universal properties of this critical point for von Neumann and noninteger Renyi entropies.  [Show abstract] [Hide abstract]
ABSTRACT: Spin ice materials, such as Dy2Ti2O7 and Ho2Ti2O7, have been the subject of much interest for over the past fifteen years. Their low temperature strongly correlated state can be mapped onto the proton disordered state of common water ice and, consequently, spin ices display the same low temperature residual Pauling entropy as water ice. Interestingly, it was found in a previous study [X. Ke {\it et. al.} Phys. Rev. Lett. {\bf 99}, 137203 (2007)] that, upon dilution of the magnetic rareearth ions (Dy^{3+} and Ho^{3+}) by nonmagnetic Yttrium (Y^{3+}) ions, the residual entropy depends {\it nonmonotonically} on the concentration of Y^{3+} ions. In the present work, we report results from Monte Carlo simulations of sitediluted microscopic dipolar spin ice models (DSIM) that account quantitatively for the experimental specific heat measurements, and thus also for the residual entropy, as a function of dilution, for both Dy2Ti2O7 and Ho2Ti2O7. The main features of the dilution physics displayed by the magnetic specific heat data are quantitatively captured by the diluted DSIM up to, and including, 85% of the magnetic ions diluted (x=1.7). The previously reported departures in the residual entropy between Dy2Ti2O7 versus Ho2Ti2O7, as well as with a sitedilution variant of Pauling's approximation, are thus rationalized through the sitediluted DSIM. For 90% (x=1.8) and 95% (x=1.9) of the magnetic ions diluted, we find a significant discrepancy between the experimental and Monte Carlo specific heat results. We discuss some possible reasons for this disagreement.Physical Review B 03/2013; 90(21). DOI:10.1103/PhysRevB.90.214433 · 3.74 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: By extending the calculation of the Renyi entropy from quantum models [Phys. Rev. B 82, 100409(R) (2010)] to classical modes, we introduce a general procedure to calculate the Renyi mutual information in Monte Carlo simulations. Examining an array of quantum and classical models we show that the mutual information is able to detect general finite temperature phase transitions from different universality classes without knowledge of the specific order parameter or any special thermodynamic estimators. We demonstrate this technique on a standard symmetry breaking phase transition, the classical Ising model and anisotropic Heisenberg model, and a vortexunbinding transition without a local order parameter, the classical and quantum XY model, and present the details necessary to implement this procedure on other models [arXiv:1210.2403].  [Show abstract] [Hide abstract]
ABSTRACT: We implement a WangLandau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on twodimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a threedimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finitetemperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.Physical Review E 01/2013; 87(11):013306. DOI:10.1103/PhysRevE.87.013306 · 2.29 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: This Chapter outlines the fundamental construction of the Stochastic Series Expansion, a highly efficient and easily implementable quantum Monte Carlo method for quantum lattice models. Originally devised as a finitetemperature simulation based on a Taylor expansion of the partition function, the method has recently been recast in the formalism of a zerotemperature projector method, where a large power of the Hamiltonian is applied to a trial wavefunction to project out the groundstate. Although these two methods appear formally quite different, their implementation via nonlocal loop or cluster algorithms reveals their underlying fundamental similarity. Here, we briefly review the finiteand zerotemperature formalisms, and discuss concrete manifestations of the algorithm for the spin 1/2 Heisenberg and transverse field Ising models.  [Show abstract] [Hide abstract]
ABSTRACT: By developing a method to represent the Renyi entropies via a replicatrick on classical statistical mechanical systems, we introduce a procedure to calculate the Renyi Mutual Information in any Monte Carlo simulation. Through simulations on several classical models, we demonstrate that the Renyi Mutual Information can detect finitetemperature critical points, and even identify their universality class, without knowledge of an order parameter or other thermodynamic estimators. Remarkably, in addition to critical points mediated by symmetry breaking, the Renyi Mutual Information is able to detect topological vortexunbinding transitions, as we explicitly demonstrate on simulations of the XY model.Physical review. B, Condensed matter 10/2012; 87(19). DOI:10.1103/PhysRevB.87.195134 · 3.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study resonatingvalencebond (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 onedimensional 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). DOI:10.1088/13672630/15/1/015004 · 3.56 Impact Factor  [Show abstract] [Hide abstract]
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 nonstandard 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 CurieWeiss 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). DOI:10.1103/PhysRevX.3.011014 · 9.04 Impact Factor 
Article: Bridging LatticeScale Physics and Continuum Field Theory with Quantum Monte Carlo Simulations
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ABSTRACT: We discuss designer Hamiltonianslattice models tailored to be free from sign problems ("designed") when simulated with quantum Monte Carlo methods but which still host complex manybody states and quantum phase transitions of interest in condensed matter physics. We focus on quantum spin systems in which competing interactions lead to nonmagnetic 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 lowenergy effective quantum field theories. As specific examples, we discuss the transition from a Neel antiferromagnet to either a uniform quantum paramagnet or a spontaneously symmetrybroken valencebond 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 valencebond basis and direct computation of the Renyi variants of the entanglement entropy.Annual Review of Condensed Matter Physics 04/2012; 4(1). DOI:10.1146/annurevconmatphys030212184215 · 14.79 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the bipartite entanglement entropy of the twodimensional (2D) transversefield Ising model in the thermodynamic limit using series expansion methods. Expansions are developed for the Renyi entropy around both the smallfield and largefield limits, allowing the separate calculation of the entanglement associated with lines and corners at the boundary between subsystems. 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). DOI:10.1103/PhysRevB.86.075106 · 3.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We introduce a generalized loop move (GLM) update for Monte Carlo simulations of frustrated Ising models on twodimensional lattices with bondsharing plaquettes. The GLM updates are designed to enhance Monte Carlo sampling efficiency when the system's lowenergy states consist of an extensive number of degenerate or neardegenerate 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 neardegenerate 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(32):036704. DOI:10.1103/PhysRevE.85.036704 · 2.29 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We use a LoopRatio 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 finitesize 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 aspectratio dependent scaling term resembling the ``conformal distance'' term that appears in onedimensional systems with conformal symmetry.  [Show abstract] [Hide abstract]
ABSTRACT: The resonating valence bond (RVB) state on a twodimensional 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 loopalgorithm Monte Carlo method that samples all nearestneighbor 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.  [Show abstract] [Hide abstract]
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 metalinsulator transition in a system of interacting, itinerant electrons at halffilling on the twoleg triangular strip (i.e., zigzag chain). Previous work [1] has revealed that an exotic ``spin Bosemetal'' (SBM) phase with three gapless modes is stabilized on the zigzag strip in a pure spin model of Heisenberg exchange supplemented with foursite 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 twoband metal of interacting electrons. Guided by this idea, we perform largescale DMRG calculations across the Mott transition in various Hubbardtype models (e.g., with onsite repulsion, longerranged 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).  [Show abstract] [Hide abstract]
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 nonmagnetic substitutes Y^3+, the residual entropy depends nonmonotonically 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.  [Show abstract] [Hide abstract]
ABSTRACT: Entanglement entropy is a quantity that is desirable to examine at quantum critical points in condensed matter systems, because it is expected that subleading scaling terms should contain universal coefficients. In dimensions higher than one, these universal coefficients (that are subleading 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.  [Show abstract] [Hide abstract]
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):1935. DOI:10.1126/science.1212207 · 33.61 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We numerically determine subleading scaling terms in the groundstate entanglement entropy of several twodimensional (2D) gapless systems, including a Heisenberg model with N\'eel order, a free Dirac fermion in the {\pi}flux phase, and the nearestneighbor resonatingvalencebond 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 wellapproximated on finitesize lattices by a function ln(sin({\pi}x/L)), akin to the familiar chordlength dependence in one dimension. We provide evidence, however, that the precise form of this bulkdependent contribution is a more general function in the 2D thermodynamic limit.Physical review. B, Condensed matter 12/2011; 85(16). DOI:10.1103/PhysRevB.85.165121 · 3.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the ground state phase diagram of a twodimensional kagome lattice spin1/2 XY model (J) with a foursite 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 Z_2 quantum spin liquid phase at (K/J)_c ~ 22, which is related to the phase proposed by Balents, Girvin and Fisher [Phys. Rev. B, 65 224412 (2002)]. The quantum phase transition between the superfluid and the spin liquid phase has exponents z and \nu falling in the 3D 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(13). DOI:10.1103/PhysRevB.84.132409 · 3.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We compute the bipartite entanglement properties of the spinhalf squarelattice 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 meanfield Neel state. Second, the corner logs do not agree with the known results for noninteracting 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(16). DOI:10.1103/PhysRevB.84.165134 · 3.66 Impact Factor
Publication Stats
2k  Citations  
311.61  Total Impact Points  
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Institutions

20012015

University of Waterloo
 Department of Physics and Astronomy
Ватерлоо, Ontario, Canada


2006

Oak Ridge National Laboratory
 Materials Science and Technology Division
Oak Ridge, FL, United States


20032005

University of California, Santa Barbara
 Department of Physics
Santa Barbara, CA, United States
