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Helmut G. Katzgraber

Publications and source records attributed to Helmut G. Katzgraber.

At least 145 records · Page 8Linked to original sources
arXiv2008

Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models

We use a nonperturbative extended contractor renormalization (ENCORE) method for engineering quantum devices for the implementation of topologically protected quantum bits described by an effective quantum dimer model on the triangular lattice. By tuning the couplings of the device, topological protection might be achieved if the ratio between effective two-dimer interactions and flip amplitudes lies in the liquid phase of the phase diagram of the quantum dimer model. For a proposal based on a quantum Josephson junction array [L. B. Ioffe {\it et al.}, Nature (London) {\bf 415}, 503 (2002)] our results show that optimal operational temperatures below 1 mK can only be obtained if extra interactions and dimer flips, which are not present in the standard quantum dimer model and involve three or four dimers, are included. It is unclear if these extra terms in the quantum dimer Hamiltonian destroy the liquid phase needed for quantum computation. Minimizing the effects of multi-dimer terms would require energy scales in the nano-Kelvin regime. An alternative implementation based on cold atomic or molecular gases loaded into optical lattices is also discussed, and it is shown that the small energy scales involved--implying long operational times--make such a device impractical. Given the many orders of magnitude between bare couplings in devices, and the topological gap, the realization of topological phases in quantum devices requires careful engineering and large bare interaction scales.

cond-mat.other↗
arXiv2008

Behavior of Ising Spin Glasses in a Magnetic Field

We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field--temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first tested on the Ising spin glass on a Bethe lattice where the instability line separating the spin glass from the paramagnetic state is also computed analytically. While the instability line is reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model.

cond-mat.dis-nn↗
arXiv2008

New Insights from One-Dimensional Spin Glasses

The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial analysis. Thus it is of paramount importance to understand which predictions of the mean-field solution apply to non-mean-field systems, such as realistic short-range spin-glass models. The one-dimensional spin glass with random power-law interactions promises to be an ideal test-bed to answer this question: Not only can large system sizes-which are usually a shortcoming in simulations of high-dimensional short-range system-be studied, by tuning the power-law exponent of the interactions the universality class of the model can be continuously tuned from the mean-field to the short-range universality class. We present details of the model, as well as recent applications to some questions of the physics of spin glasses. First, we study the existence of a spin-glass state in an external field. In addition, we discuss the existence of ultrametricity in short-range spin glasses. Finally, because the range of interactions can be changed, the model is a formidable test-bed for optimization algorithms.

cond-mat.dis-nn↗
arXiv2008

Local field distributions in spin glasses

Numerical results for the local field distributions of a family of Ising spin-glass models are presented. In particular, the Edwards-Anderson model in dimensions two, three, and four is considered, as well as spin glasses with long-range power-law-modulated interactions that interpolate between a nearest-neighbour Edwards-Anderson system in one dimension and the infinite-range Sherrington-Kirkpatrick model. Remarkably, the local field distributions only depend weakly on the range of the interactions and the dimensionality, and show strong similarities except for near zero local field.

cond-mat.dis-nn↗
arXiv2008

Finding Ground States of Sherrington-Kirkpatrick Spin Glasses with Hierarchical BOA and Genetic Algorithms

This study focuses on the problem of finding ground states of random instances of the Sherrington-Kirkpatrick (SK) spin-glass model with Gaussian couplings. While the ground states of SK spin-glass instances can be obtained with branch and bound, the computational complexity of branch and bound yields instances of not more than about 90 spins. We describe several approaches based on the hierarchical Bayesian optimization algorithm (hBOA) to reliably identifying ground states of SK instances intractable with branch and bound, and present a broad range of empirical results on such problem instances. We argue that the proposed methodology holds a big promise for reliably solving large SK spin-glass instances to optimality with practical time complexity. The proposed approaches to identifying global optima reliably can also be applied to other problems and they can be used with many other evolutionary algorithms. Performance of hBOA is compared to that of the genetic algorithm with two common crossover operators.

cond-mat.dis-nn↗
arXiv2007

Spin glasses and algorithm benchmarks: A one-dimensional view

Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore large-scale numerical simulations are the tool of choice. Concepts and algorithms derived from the study of spin glasses have been applied to diverse fields in computer science and physics. In this work a one-dimensional long-range spin-glass model with power-law interactions is discussed. The model has the advantage over conventional systems in that by tuning the power-law exponent of the interactions the effective space dimension can be changed thus effectively allowing the study of large high-dimensional spin-glass systems to address questions as diverse as the existence of an Almeida-Thouless line, ultrametricity and chaos in short range spin glasses. Furthermore, because the range of interactions can be changed, the model is a formidable test-bed for optimization algorithms.

cond-mat.dis-nn↗
arXiv2007

Finite versus zero-temperature hysteretic behavior of spin glasses: Experiment and theory

We present experimental results attempting to fingerprint nonanalyticities in the magnetization curves of spin glasses found by Katzgraber et al. [Phys. Rev. Lett. 89, 257202 (2002)] via zero-temperature Monte Carlo simulations of the Edwards-Anderson Ising spin glass. Our results show that the singularities at zero temperature due to the reversal-field memory effect are washed out by the finite temperatures of the experiments. The data are analyzed via the first order reversal curve (FORC) magnetic fingerprinting method. The experimental results are supported by Monte Carlo simulations of the Edwards-Anderson Ising spin glass at finite temperatures which agree qualitatively very well with the experimental results. This suggests that the hysteretic behavior of real Ising spin-glass materials is well described by the Edwards-Anderson Ising spin glass. Furthermore, reversal-field memory is a purely zero-temperature effect.

cond-mat.dis-nn↗
arXiv2007

Absence of a structural glass phase in a monoatomic model liquid predicted to undergo an ideal glass transition

We study numerically a monodisperse model of interacting classical particles predicted to exhibit a static liquid-glass transition. Using a dynamical Monte Carlo method we show that the model does not freeze into a glassy phase at low temperatures. Instead, depending on the choice of the hard-core radius for the particles the system either collapses trivially or a polycrystalline hexagonal structure emerges.

cond-mat.dis-nn↗
arXiv2007

Typical versus average helicity modulus in the three-dimensional gauge glass: Understanding the vortex glass phase

We numerically compute the helicity modulus of the three-dimensional gauge glass by Monte Carlo simulations. Because the average free energy is independent of a twist angle, it is expected that the average helicity modulus, directly related to the superfluid density, vanishes when simulations are performed with periodic boundary conditions. This is not necessarily the case for the typical (median) value, which is nonzero, because the distribution of the helicity modulus among different disorder realizations is very asymmetric. We show that the data for the helicity modulus distribution are well described by a generalized extreme-value distribution with a nonzero location parameter (most probable value). A finite-size scaling analysis of the location parameter yields a critical temperature and critical exponents in agreement with previous results. This suggests that the location parameter is a good observable. There have been conflicting claims as to whether the superfluid density vanishes in the vortex glass phase, with Fisher et al. [Phys. Rev. B 43, 130 (1991)] arguing that it is finite and Korshunov [Phys. Rev. B 63, 174514 (2001)] predicting that it is zero. Because the gauge glass is commonly used to describe the vortex glass in high-temperature superconductors, we discuss this issue in light of our results on the gauge glass.

cond-mat.dis-nn↗
arXiv2007

Effective critical behavior of the two-dimensional Ising spin glass with bimodal interactions

Monte Carlo data of the two-dimensional Ising spin glass with bimodal interactions are presented with the aim of understanding the low-temperature physics of the model. An analysis of the specific heat, spin-glass susceptibility, finite-size correlation length, and the Binder ratio is performed to try to verify a recent proposal in which for large system sizes and finite but low temperatures the effective critical exponents are identical to the critical exponents of the two-dimensional Ising spin glass with Gaussian interactions. Our results show that with present system sizes the recently proposed scenario in which the two-dimensional Ising spin glass with bimodally distributed interactions is in the same universality class as the model with Gaussian-distributed disorder at low but finite temperatures cannot be reliably proven.

cond-mat.dis-nn↗
arXiv2007

Temperature and Disorder Chaos in Three-Dimensional Ising Spin Glasses

We study the effects of small temperature as well as disorder perturbations on the equilibrium state of three-dimensional Ising spin glasses via an alternate scaling ansatz. By using Monte Carlo simulations, we show that temperature and disorder perturbations yield chaotic changes in the equilibrium state and that temperature chaos is considerably harder to observe than disorder chaos.

cond-mat.dis-nn↗
arXiv2006

Ramping fermions in optical lattices across a Feshbach resonance

We study the properties of ultracold Fermi gases in a three-dimensional optical lattice when crossing a Feshbach resonance. By using a zero-temperature formalism, we show that three-body processes are enhanced in a lattice system in comparison to the continuum case. This poses one possible explanation for the short molecule lifetimes found when decreasing the magnetic field across a Feshbach resonance. Effects of finite temperatures on the molecule formation rates are also discussed by computing the fraction of double-occupied sites. Our results show that current experiments are performed at temperatures considerably higher than expected: lower temperatures are required for fermionic systems to be used to simulate quantum Hamiltonians. In addition, by relating the double occupancy of the lattice to the temperature, we provide a means for thermometry in fermionic lattice systems, previously not accessible experimentally. The effects of ramping a filled lowest band across a Feshbach resonance when increasing the magnetic field are also discussed: fermions are lifted into higher bands due to entanglement of Bloch states, in good agreement with recent experiments.

cond-mat.other↗
arXiv2006

Critical behavior of the three- and ten-state short-range Potts glass: A Monte Carlo study

We study the critical behavior of the short-range p-state Potts spin glass in three and four dimensions using Monte Carlo simulations. In three dimensions, for p = 3, a finite-size scaling analysis of the correlation length shows clear evidence of a transition to a spin-glass phase at T_c = 0.273(5) for a Gaussian distribution of interactions and T_c = 0.377(5) for a bimodal distribution. These results indicate that the lower critical dimension of the 3-state Potts glass is below three. By contrast, the correlation length of the ten-state (p = 10) Potts glass in three dimensions remains small even at very low temperatures and thus shows no sign of a transition. In four dimensions we find that the p = 3 Potts glass with Gaussian interactions has a spin-glass transition at T_c =0.536(3).

cond-mat.dis-nn↗
arXiv2006

Hysteretic memory effects in disordered magnets

We study the return point as well as the complementary point memory effects numerically with paradigmatic models for random magnets and show that already simple systems with Ising spin symmetry can reproduce the experimental results of Pierce et al. where both memory effects become more pronounced for increasing disorder and return point memory is always better than complementary point memory.

cond-mat.dis-nn↗
arXiv2006

Universality in three-dimensional Ising spin glasses: A Monte Carlo study

We study universality in three-dimensional Ising spin glasses by large-scale Monte Carlo simulations of the Edwards-Anderson Ising spin glass for several choices of bond distributions, with particular emphasis on Gaussian and bimodal interactions. A finite-size scaling analysis suggests that three-dimensional spin glasses obey universality.

cond-mat.dis-nn↗
arXiv2006

Simulations of ultracold bosonic atoms in optical lattices with anharmonic traps

We report results of quantum Monte Carlo simulations in the canonical and the grand-canonical ensemble of the two- and three-dimensional Bose-Hubbard model with quadratic and quartic confining potentials. The quantum criticality of the superfluid-Mott insulator transition is investigated both on the boundary layer separating the two coexisting phases and at the center of the traps where the Mott-insulating phase is first established. Recent simulations of systems in quadratic traps have shown that the transition is not in the critical regime due to the finite gradient of the confining potential and that critical fluctuations are suppressed. In addition, it has been shown that quantum critical behavior is recovered in flat confining potentials as they approach the uniform regime. Our results show that quartic traps display a behavior similar to quadratic ones, yet locally at the center of the traps the bulk transition has enhanced critical fluctuations in comparison to the quadratic case. Therefore quartic traps provide a better prerequisite for the experimental observation of true quantum criticality of ultracold bosonic atoms in optical lattices.

cond-mat.other↗
arXiv2006

Probing tails of energy distributions using importance-sampling in the disorder with a guiding function

We propose a simple and general procedure based on a recently introduced approach that uses an importance-sampling Monte Carlo algorithm in the disorder to probe to high precision the tails of ground-state energy distributions of disordered systems. Our approach requires an estimate of the ground-state energy distribution as a guiding function which can be obtained from simple-sampling simulations. In order to illustrate the algorithm, we compute the ground-state energy distribution of the Sherrington-Kirkpatrick mean-field Ising spin glass to eighteen orders of magnitude. We find that the ground-state energy distribution in the thermodynamic limit is well fitted by a modified Gumbel distribution as previously predicted, but with a value of the slope parameter m which is clearly larger than 6 and of the order 11.

cond-mat.dis-nn↗