Papers by Matthias Troyer
Physical Review Letters, 2008
More than half a century ago Penrose asked : are the superfluid and solid state of matter mutuall... more More than half a century ago Penrose asked : are the superfluid and solid state of matter mutually exclusive or do there exist "supersolid" materials where the atoms form a regular lattice and simultaneously flow without friction? Recent experiments provide evidence that supersolid behavior indeed exists in 4 He -the most quantum material known in Nature. In this paper we show that large local strain in the vicinity of crystalline defects is the origin of supersolidity in 4 He. Although ideal crystals of 4 He are not supersolid, the gap for vacancy creation closes when applying a moderate stress. While a homogeneous system simply becomes unstable at this point, the stressed core of crystalline defects (dislocations and grain boundaries) undergoes a radical transformation and can become superfluid.
Physical Review Letters, 2007
On the basis of first-principle Monte Carlo simulations we find that the screw dislocation along ... more On the basis of first-principle Monte Carlo simulations we find that the screw dislocation along the hexagonal axis of an hcp 4 He crystal features a superfluid (at T → 0) core. This is the first example of a regular quasi-one-dimensional supersolid -the phase featuring both translational and superfluid orders, and one of the cleanest cases of a Luttinger-liquid system. In contrast, the same type of screw dislocation in solid H2 is insulating.
Physical Review Letters, 2007
By large-scale quantum Monte Carlo simulations we show that grain boundaries in 4 He crystals are... more By large-scale quantum Monte Carlo simulations we show that grain boundaries in 4 He crystals are generically superfluid at low temperature, with a transition temperature of the order of ∼ 0.5K at the melting pressure; non-superfluid grain boundaries are found only for special orientations of the grains. We also find that close vicinity to the melting line is not a necessary condition for superfluid grain boundaries , and a grain boundary in direct contact with the superfluid liquid at the melting curve is found to be mechanically stable and the grain boundary superfluidity observed by Sasaki et al. [Science 313, 1098] is not just a crack filled with superfluid.
Physical Review Letters, 2006
The unitarity regime of the BCS-BEC crossover can be realized by diluting a system of twocomponen... more The unitarity regime of the BCS-BEC crossover can be realized by diluting a system of twocomponent lattice fermions with an on-site attractive interaction. We perform a systematic-errorfree finite-temperature simulations of this system by diagrammatic determinant Monte Carlo. The critical temperature in units of Fermi energy is found to be Tc/εF = 0.152(7). We also report the behavior of the thermodynamic functions, and discuss the issues of thermometry of ultracold Fermi gases.
A comprehensive theoretical and experimental study is presented of the magnetic susceptibility ve... more A comprehensive theoretical and experimental study is presented of the magnetic susceptibility versus temperature \chi(T) of spin S = 1/2 two- and three-leg Heisenberg ladders and ladder oxide compounds. Extensive quantum Monte Carlo simulations of \chi(T) were carried out for both isolated and coupled two-leg ladders with spatially anisotropic intraladder exchange. Accurate fits to these and related literature QMC data were obtained. We have also calculated the one- and two-magnon dispersion relations and the dynamical spin structure factor for anisotropic isolated 2 x 12 ladders. The exchange constants in the two-leg ladder compound SrCu2O3 are estimated from LDA+U calculations. We report the detailed crystal structure of SrCu2O3 and of the three-leg ladder compound Sr2Cu3O5. New experimental \chi(T) data are reported for the two-leg ladder cuprates SrCu2O3 and LaCuO_{2.5}, and for the (nominally) two-leg ladder vanadates CaV2O5 and MgV2O5. The new and literature \chi(T) data for these compounds and for Sr2Cu3O5 are modeled using our QMC \chi(T) simulation fits, and the exchange coupling constants between the spins-1/2 are thereby estimated for each material. The surpisingly strong spatial anisotropy of the bilinear intraladder exchange constants in the cuprate compounds is discussed together with the results of other experiments sensitive to this anisotropy. Recent theoretical predictions are discussed including those which indicate that a four-spin cyclic exchange interaction within a Cu4 plaquette is important to determining the magnetic properties and which can significantly influence the exchange interactions estimated from \chi(T) data assuming the presence of only bilinear exchange.
Physical Review B, 2000
The magnetic susceptibility chi and specific heat C versus temperature T of the spin-1/2 antiferr... more The magnetic susceptibility chi and specific heat C versus temperature T of the spin-1/2 antiferromagnetic alternating-exchange (J1 and J2) Heisenberg chain are studied for the entire range 0 \leq alpha \leq 1 of the alternation parameter alpha = J2/J1. For the uniform chain (alpha = 1), detailed comparisons of the high-accuracy chi(T) and C(T) Bethe ansatz data of Kluemper and Johnston are made with the asymptotically exact low-T field theory predictions of Lukyanov. QMC simulations and TMRG calculations of chi(alpha,T) are presented. From the low-T TMRG data, the spin gap Delta(alpha)/J1 is extracted for 0.8 \leq alpha \leq 0.995. High accuracy fits to all of the above numerical data are obtained. We examine in detail the theoretical predictions of Bulaevskii for chi(alpha,T) and compare them with our results. Our experimental chi(T) and C(T) data for NaV2O5 single crystals are modeled in detail. The chi(T) data above the spin dimerization temperature Tc = 34 K are not in agreement with the prediction for the uniform Heisenberg chain, but can be explained if there is a moderate ferromagnetic interchain coupling and/or if J changes with T. By fitting the chi(T) data, we obtain Delta(T = 0) = 103(2) K, alternation parameter delta(0) = (1 - alpha)/(1 + alpha) = 0.034(6) and average exchange constant J(0) = 640(80) K. The delta(T) and Delta(T) are derived from the data. A spin pseudogap with a large magnitude \approx 0.4 Delta(0) is consistently found just above Tc, which decreases with increasing T. Analysis of our C(T) data indicates that at Tc, at least 77% of the entropy change due to the transition at Tc and associated order parameter fluctuations arise from the lattice and/or charge degrees of freedom and less than 23% from the spin degrees of freedom.
Physical Review Letters, 2005
Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign... more Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem'' when applied to fermions - causing an exponential increase of the computing time with the number of particles. A polynomial time solution to the sign problem is highly desired since it would provide an unbiased and numerically exact method to simulate correlated quantum systems. Here we show, that such a solution is almost certainly unattainable by proving that the sign problem is NP-hard, implying that a generic solution of the sign problem would also solve all problems in the complexity class NP (nondeterministic polynomial) in polynomial time.
Physical Review Letters, 2004
We determine the optimal scaling of local-update flat-histogram methods with system size by using... more We determine the optimal scaling of local-update flat-histogram methods with system size by using a perfect flat-histogram scheme based on the exact density of states of 2D Ising models. The typical tunneling time needed to sample the entire bandwidth does not scale with the number of spins N as the minimal N 2 of an unbiased random walk in energy space. While the scaling is power law for the ferromagnetic and fully frustrated Ising model, for the ±J nearest-neighbor spin glass the distribution of tunneling times is governed by a fat-tailed Fréchet extremal value distribution that obeys exponential scaling. We find that the Wang-Landau algorithm shows the same scaling as the perfect scheme and is thus optimal.
We present the ALPS (Algorithms and Libraries for Physics Simulations) project, an international ... more We present the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. Development is centered on common XML and binary data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs. The programs enable non-experts to start carrying out numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), as well as the density matrix renormalization group (DMRG). The software is available from our web server at http://alps.comp-phys.org/.
Physical Review E, 2004
We present an adaptive algorithm which optimizes the statistical-mechanical ensemble in a general... more We present an adaptive algorithm which optimizes the statistical-mechanical ensemble in a generalized broad-histogram Monte Carlo simulation to maximize the system's rate of round trips in total energy. The scaling of the mean round-trip time from the ground state to the maximum entropy state for this local-update method is found to be O([N log N]^2) for both the ferromagnetic and the fully frustrated 2D Ising model with N spins. Our new algorithm thereby substantially outperforms flat-histogram methods such as the Wang-Landau algorithm.
Physical Review Letters, 2005
We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction... more We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D.S. Rokhsar and S.A. Kivelson, Phys. Rev. Lett.{\bf 61}, 2376 (1988)]. By means of Monte Carlo and Transfer Matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding Coulomb gas, whose coupling constant is computed numerically. We also discuss doped models and implications on the finite-temperature phase diagram of quantum dimer models.
Physical Review Letters, 2007
We study the stability of topological order against local perturbations by considering the effect... more We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model -- the toric code -- which is in a topological phase. The model can be mapped onto a quantum loop gas where the perturbation introduces a bare loop tension. When the loop tension is small, the topological order survives. When it is large, it drives a continuous quantum phase transition into a magnetic state. The transition can be understood as the condensation of `magnetic' vortices, leading to confinement of the elementary `charge' excitations. We also show how the topological order breaks down when the system is coupled to an Ohmic heat bath and discuss our results in the context of quantum computation applications.
Physical Review Letters, 2006
We study controlled generation and measurement of superfluid d-wave resonating valence bond (RVB)... more We study controlled generation and measurement of superfluid d-wave resonating valence bond (RVB) states of fermionic atoms in 2D optical lattices. Starting from loading spatial and spin patterns of atoms in optical superlattices as pure quantum states from a Fermi gas, we adiabatically transform this state to an RVB state by change of the lattice parameters. Results of exact timedependent numerical studies for ladders systems are presented, suggesting generation of RVB states on timescale smaller than typical experimental decoherence times.
Physical Review Letters, 2007
We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The sim... more We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial (''identity'') channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical with a dynamical critical exponent z 1, and described by a two-dimensional (2D) conformal field theory with central charge c 7
We determine the optimal scaling of local-update flat-histogram methods with system size by using... more We determine the optimal scaling of local-update flat-histogram methods with system size by using a perfect flat-histogram scheme based on the exact density of states of 2D Ising models. The typical tunneling time needed to sample the entire bandwidth does not scale with the number of spins N as the minimal N 2 of an unbiased random walk in energy space. While the scaling is power law for the ferromagnetic and fully frustrated Ising model, for the ±J nearest-neighbor spin glass the distribution of tunneling times is governed by a fat-tailed Fréchet extremal value distribution that obeys exponential scaling. We find that the Wang-Landau algorithm shows the same scaling as the perfect scheme and is thus optimal.
Physical Review Letters, 2002
In the absence of a confining potential, the boson Hubbard model in its ground state is known to ... more In the absence of a confining potential, the boson Hubbard model in its ground state is known to exhibit a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong on-site repulsion. In this paper, we use quantum Monte Carlo simulations to study the ground state of the one dimensional bosonic Hubbard model in a trap. We show that some, but not all, aspects of the Mott insulating phase persist when a confining potential is present. The Mott behavior is present for a continuous range of incommensurate fillings, a very different situation from the unconfined case. Furthermore the establishment of the Mott phase does not proceed via a quantum phase transition in the traditional sense. These observations have important implications for the interpretation of experimental results for atoms trapped on optical lattices. Initial results show that, qualitatively, the same results persist in higher dimensions.
Physical Review A, 2004
We study properties of ultra-cold bosonic atoms in one, two and three dimensional optical lattice... more We study properties of ultra-cold bosonic atoms in one, two and three dimensional optical lattices by large scale quantum Monte Carlo simulations of the Bose Hubbard model in parabolic confinement potentials. Local phase structures of the atoms are shown to be accessible via a well defined local compressibility, quantifying a global response of the system to a local perturbation. An indicator for the presence of extended Mott plateaux is shown to stem from the shape of the coherent component of the momentum distribution function, amenable to experimental detection. Additional fine structures in the momentum distribution are found to appear unrelated to the local phase structure, disproving previous claims. We discuss limitations of local potential approximations for confined Bose gases, and the absence of quantum criticality and critical slowing down in parabolic confinement potentials, thus accounting for the fast dynamics in establishing phase coherence in current experiments. In contrast, we find that flat confinement potentials allow quantum critical behavior to be observed already on moderately sized optical lattices. Our results furthermore demonstrate, that the experimental detection of the Mott transition would be significantly eased in flat confinement potentials.
Journal of Statistical Mechanics-theory and Experiment, 2006
We introduce an algorithm to systematically improve the efficiency of parallel tempering Monte Ca... more We introduce an algorithm to systematically improve the efficiency of parallel tempering Monte Carlo simulations by optimizing the simulated temperature set. Our approach is closely related to a recently introduced adaptive algorithm that optimizes the simulated statistical ensemble in generalized broad-histogram Monte Carlo simulations. Conventionally, a temperature set is chosen in such a way that the acceptance rates for replica swaps between adjacent temperatures are independent of the temperature and large enough to ensure frequent swaps. In this paper, we show that by choosing the temperatures with a modified version of the optimized ensemble feedback method we can minimize the round-trip times between the lowest and highest temperatures which effectively increases the efficiency of the parallel tempering algorithm. In particular, the density of temperatures in the optimized temperature set increases at the "bottlenecks'' of the simulation, such as phase transitions. In turn, the acceptance rates are now temperature dependent in the optimized temperature ensemble. We illustrate the feedback-optimized parallel tempering algorithm by studying the two-dimensional Ising ferromagnet and the two-dimensional fully-frustrated Ising model, and briefly discuss possible feedback schemes for systems that require configurational averages, such as spin glasses.
Computing Research Repository, 2004
We discuss the computational complexity of random 2D Ising spin glasses, which represent an inter... more We discuss the computational complexity of random 2D Ising spin glasses, which represent an interesting class of constraint satisfaction problems for black box optimization. Two extremal cases are considered: (1) the ± J spin glass, and (2) the Gaussian spin glass. We also study a smooth transition between these two extremal cases. The computational complexity of all studied spin glass systems is found to be dominated by rare events of extremely hard spin glass samples. We show that complexity of all studied spin glass systems is closely related to Fréchet extremal value distribution. In a hybrid algorithm that combines the hierarchical Bayesian optimization algorithm (hBOA) with a deterministic bit-flip hill climber, the number of steps performed by both the global searcher (hBOA) and the local searcher follow Fréchet distributions. Nonetheless, unlike in methods based purely on local search, the parameters of these distributions confirm good scalability of hBOA with local search. We further argue that standard performance measures for optimization algorithms—such as the average number of evaluations until convergence—can be misleading. Finally, our results indicate that for highly multimodal constraint satisfaction problems, such as Ising spin glasses, recombination-based search can provide qualitatively better results than mutation-based search.
We apply a recently developed adaptive algorithm that systematically improves the efficiency of p... more We apply a recently developed adaptive algorithm that systematically improves the efficiency of parallel tempering or replica exchange methods in the numerical simulation of small proteins.
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Papers by Matthias Troyer