arXiv subjects

Simon Trebst

Publications and source records attributed to Simon Trebst.

At least 127 records · Page 7Linked to original sources

arXiv2009

A short introduction to Fibonacci anyon models

We discuss how to construct models of interacting anyons by generalizing quantum spin Hamiltonians to anyonic degrees of freedom. The simplest interactions energetically favor pairs of anyons to fuse into the trivial ("identity") channel, similar to the quantum Heisenberg model favoring pairs of spins to form spin singlets. We present an introduction to the theory of anyons and discuss in detail how basis sets and matrix representations of the interaction terms can be obtained, using non-Abelian Fibonacci anyons as example. Besides discussing the "golden chain", a one-dimensional system of anyons with nearest neighbor interactions, we also present the derivation of more complicated interaction terms, such as three-anyon interactions in the spirit of the Majumdar-Ghosh spin chain, longer range interactions and two-leg ladders. We also discuss generalizations to anyons with general non-Abelian su(2)_k statistics. The k to infinity limit of the latter yields ordinary SU(2) spin chains.

cond-mat.stat-mech↗

arXiv2008

Local interactions and non-Abelian quantum loop gases

Two-dimensional quantum loop gases are elementary examples of topological ground states with Abelian or non-Abelian anyonic excitations. While Abelian loop gases appear as ground states of local, gapped Hamiltonians such as the toric code, we show that gapped non-Abelian loop gases require non-local interactions (or non-trivial inner products). Perturbing a local, gapless Hamiltonian with an anticipated ``non-Abelian'' ground-state wavefunction immediately drives the system into the Abelian phase, as can be seen by measuring the Hausdorff dimension of loops. Local quantum critical behavior is found in a loop gas in which all equal-time correlations of local operators decay exponentially.

cond-mat.stat-mech↗

arXiv2008

Strong-Coupling Phases of Frustrated Bosons on a 2-leg Ladder with Ring Exchange

Developing a theoretical framework to access quantum phases of itinerant bosons or fermions in two dimensions (2D) that exhibit singular structure along surfaces in momentum space but have no quasi-particle description remains as a central challenge in the field of strongly correlated physics. In this paper we propose that distinctive signatures of such 2D strongly correlated phases will be manifest in quasi-one-dimensional "N-leg ladder" systems. Characteristic of each parent 2D quantum liquid would be a precise pattern of 1D gapless modes on the N-leg ladder. These signatures could be potentially exploited to approach the 2D phases from controlled numerical and analytical studies in quasi-1D. As a first step we explore itinerant boson models with a frustrating ring exchange interaction on the 2-leg ladder, searching for signatures of the recently proposed two-dimensional d-wave correlated Bose liquid (DBL) phase. A combination of exact diagonalization, density matrix renormalization group, variational Monte Carlo, and bosonization analysis of a quasi-1D gauge theory, all provide compelling evidence for the existence of a new strong-coupling phase of bosons on the 2-leg ladder which can be understood as a descendant of the two-dimensional DBL. We suggest several generalizations to quantum spin and electron Hamiltonians on ladders which could likewise reveal fingerprints of such 2D non-Fermi liquid phases.

cond-mat.str-el↗

arXiv2008

Collective states of interacting Fibonacci anyons

We show that chains of interacting Fibonacci anyons can support a wide variety of collective ground states ranging from extended critical, gapless phases to gapped phases with ground-state degeneracy and quasiparticle excitations. In particular, we generalize the Majumdar-Ghosh Hamiltonian to anyonic degrees of freedom by extending recently studied pairwise anyonic interactions to three-anyon exchanges. The energetic competition between two- and three-anyon interactions leads to a rich phase diagram that harbors multiple critical and gapped phases. For the critical phases and their higher symmetry endpoints we numerically establish descriptions in terms of two-dimensional conformal field theories. A topological symmetry protects the critical phases and determines the nature of gapped phases.

cond-mat.stat-mech↗

arXiv2007

Optimized Broad-Histogram Ensembles for the Simulation of Quantum Systems

The efficiency of statistical sampling in broad-histogram Monte Carlo simulations can be considerably improved by optimizing the simulated extended ensemble for fastest equilibration. Here we describe how a recently developed feedback algorithm can be generalized to find optimized sampling distributions for the simulation of quantum systems in the context of the stochastic series expansion (SSE) when defining an extended ensemble in the expansion order. If the chosen update method is efficient, such as non-local updates for systems undergoing a second-order phase transition, the optimized ensemble is characterized by a flat histogram in the expansion order if a variable-length formulation of the SSE is used. Whenever the update method suffers from slowdown, such as at a first-order phase transition, the feedback algorithm shifts weight towards the expansion orders in the transition region, resulting in a non-uniform histogram.

cond-mat.stat-mech↗

arXiv2006

Interacting anyons in topological quantum liquids: The golden chain

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 conformal field theory with central charge c=7/10. An exact mapping of the anyonic chain onto the two-dimensional tricritical Ising model is given using the restricted-solid-on-solid (RSOS) representation of the Temperley-Lieb algebra. The gaplessness of the chain is shown to have topological origin.

cond-mat.str-el↗

arXiv2006

Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets

Frustration refers to competition between different interactions that cannot be simultaneously satisfied, a familiar feature in many magnetic solids. Strong frustration results in highly degenerate ground states, and a large suppression of ordering by fluctuations. Key challenges in frustrated magnetism are characterizing the fluctuating spin-liquid regime and determining the mechanism of eventual order at lower temperature. Here, we study a model of a diamond lattice antiferromagnet appropriate for numerous spinel materials. With sufficiently strong frustration a massive ground state degeneracy develops amongst spirals whose propagation wavevectors reside on a continuous two-dimensional ``spiral surface'' in momentum space. We argue that an important ordering mechanism is entropic splitting of the degenerate ground states, an elusive phenomena called order-by-disorder. A broad ``spiral spin-liquid'' regime emerges at higher temperatures, where the underlying spiral surface can be directly revealed via spin correlations. We discuss the agreement between these predictions and the well characterized spinel MnSc2S4.

cond-mat.str-el↗

arXiv2006

Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension

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.

cond-mat.stat-mech↗

arXiv2006

d-wave resonating valence bond states of fermionic atoms in optical lattices

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 time-dependent numerical studies for ladders systems are presented, suggesting generation of RVB states on timescale smaller than typical experimental decoherence times.

cond-mat.str-el↗

arXiv2006

Feedback-optimized parallel tempering Monte Carlo

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.

cond-mat.other↗

arXiv2006

Optimized parallel tempering simulations of proteins

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. Feedback iterations allow us to identify an optimal set of temperatures/replicas which are found to concentrate at the bottlenecks of the simulations. A measure of convergence for the equilibration of the parallel tempering algorithm is discussed. We test our algorithm by simulating the 36-residue villin headpiece sub-domain HP-36 wherewe find a lowest-energy configuration with a root-mean-square-deviation of less than 4 Angstroem to the experimentally determined structure.

q-bio.QM↗

arXiv2005

Quasiparticle Dynamics in the Kondo Lattice Model at Half Filling

We study spectral properties of quasiparticles in the Kondo lattice model in one and two dimensions including the coherent quasiparticle dispersions, their spectral weights and the full two-quasiparticle spectrum using a cluster expansion scheme. We investigate the evolution of the quasiparticle band as antiferromagnetic correlations are enhanced towards the RKKY limit of the model. In both the 1D and the 2D model we find that a repulsive interaction between quasiparticles results in a distinct antibound state above the two-quasiparticle continuum. The repulsive interaction is correlated with the emerging antiferromagnetic correlations and can therefore be associated with spin fluctuations. On the square lattice, the antibound state has an extended s-wave symmetry.

cond-mat.str-el↗

arXiv2005

Optimized ensemble Monte Carlo simulations of dense Lennard-Jones fluids

We apply the recently developed adaptive ensemble optimization technique to simulate dense Lennard-Jones fluids and a particle-solvent model by broad-histogram Monte Carlo techniques. Equilibration of the simulated fluid is improved by sampling an optimized histogram in radial coordinates that shifts statistical weight towards the entropic barriers between the shells of the liquid. Interstitial states in the vicinity of these barriers are identified with unprecedented accuracy by sharp signatures in the quickly converging histogram and measurements of the local diffusivity. The radial distribution function and potential of mean force are calculated to high precision.

cond-mat.stat-mech↗

arXiv2004

Overcoming the critical slowing down of flat-histogram Monte Carlo simulations: Cluster updates and optimized broad-histogram ensembles

We study the performance of Monte Carlo simulations that sample a broad histogram in energy by determining the mean first-passage time to span the entire energy space of d-dimensional ferromagnetic Ising/Potts models. We first show that flat-histogram Monte Carlo methods with single-spin flip updates such as the Wang-Landau algorithm or the multicanonical method perform sub-optimally in comparison to an unbiased Markovian random walk in energy space. For the d=1,2,3 Ising model, the mean first-passage time τscales with the number of spins N=L^d as τ\propto N^2L^z. The critical exponent z is found to decrease as the dimensionality d is increased. In the mean-field limit of infinite dimensions we find that z vanishes up to logarithmic corrections. We then demonstrate how the slowdown characterized by z>0 for finite d can be overcome by two complementary approaches - cluster dynamics in connection with Wang-Landau sampling and the recently developed ensemble optimization technique. Both approaches are found to improve the random walk in energy space so that τ\propto N^2 up to logarithmic corrections for the d=1 and d=2 Ising model.

cond-mat.stat-mech↗

arXiv2004

Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations

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.

cond-mat.stat-mech↗

arXiv2004

Computational complexity and simulation of rare events of Ising spin glasses

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 Frechet 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 Frechet 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.

cs.NE↗

arXiv2003

Spin nematics in the bilinear-biquadratic S=1 spin chain

We report the existence of an extended critical, nondimerized region in the phase diagram of the bilinear-biquadratic spin-one chain. The dominant power law correlations are ferroquadrupolar, i.e. spin nematic in character. Another known critical region is also characterized by dominant quadrupolar correlations, although with a different wave vector. Our results show that spin nematic correlations play an important role in quantum magnets with spin S >= 1 in regions between antiferromagnetic and ferromagnetic phases.

cond-mat.str-el↗

arXiv2000

Linked Cluster Series Expansions for Two-Particle Bound States

We develop strong-coupling series expansion methods to study two-particle spectra of quantum lattice models. At the heart of the method lies the calculation of an effective Hamiltonian in the two-particle subspace. We explicitly consider an orthogonality transformation to generate this block diagonalization, and find that maintaining orthogonality is crucial for systems where the ground state and the two-particle subspace are characterized by identical quantum numbers. We discuss the solution of the two-particle Schrödinger equation by using a finite lattice approach in coordinate space or by an integral equation in momentum space. These methods allow us to precisely determine the low-lying excitation spectra of the models at hand, including all two-particle bound/antibound states. Further, we discuss how to generate series expansions for the dispersions of the bound/antibound states. These allow us to employ series extrapolation techniques, whereby binding energies can be determined even when the expansion parameters are not small. We apply the method to the (1+1)D transverse Ising model and the two-leg spin-$\case 1/2$ Heisenberg ladder. For the latter model, we also calculate the coherence lengths and determine the critical properties where bound states merge with the two-particle continuum.

cond-mat.str-el↗