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Reaching the Continuum Limit in Finite-Temperature Ab Initio Field-Theory Computations in Many-Fermion Systems

Physical Review Letters 2019年第13期123卷 136402-136402页

作者： Yuan-Yao He Hao Shi Shiwei Zhang Center for Computational Quantum Physics Flatiron Institute New York New York 10010 USA Department of Physics College of William and Mary Williamsburg Virginia 23187 USA

Finite-temperature grand-canonical computations based on field theory are widely applied in areas including condensed matter physics, ultracold atomic gas systems, and the lattice gauge theory. However, these calculations have computational costs scaling as Ns3 with the size of the lattice or basis set, Ns. We report a new approach based on systematically controllable low-rank factorization that reduces the scaling of such computations to NsNe2, where Ne is the average number of fermions in the system. In any realistic calculations aiming to describe the continuum limit, Ns/Ne is large and needs to be extrapolated effectively to infinity for convergence. The method thus fundamentally changes the prospect for finite-temperature many-body computations in correlated fermion systems. Its application, in combination with frameworks to control the sign or phase problem as needed, will provide a powerful tool in ab initio quantum chemistry and correlated electron materials. We demonstrate the method by computing exact properties of the two-dimensional Fermi gas with zero-range attractive interaction as a function of temperature in both the normal and superfluid states.

关键词： Fermi gases Superfluidity Two-dimensional electron gas Computational complexity Finite-size scaling Hubbard model Lattice models in condensed matter metropolis algorithm Path-integral Monte Carlo

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Homophily-Based Social Group Formation in a Spin Glass Self-Assembly Framework

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Physical Review Letters 2023年第5期130卷 057401-057401页

作者： Jan Korbel Simon D. Lindner Tuan Minh Pham Rudolf Hanel Stefan Thurner Section for the Science of Complex Systems CeMSIIS Medical University of Vienna Spitalgasse 23 A-1090 Vienna Austria Complexity Science Hub Vienna Josefstädterstrasse 39 A-1080 Vienna Austria Niels Bohr Institute Blegdamsvej 17 2100 Copenhagen Denmark Santa Fe Institute 1399 Hyde Park Road Santa Fe New Mexico 87501 USA

Homophily, the tendency of humans to attract each other when sharing similar features, traits, or opinions, has been identified as one of the main driving forces behind the formation of structured societies. Here we ask to what extent homophily can explain the formation of social groups, particularly their size distribution. We propose a spin-glass-inspired framework of self-assembly, where opinions are represented as multidimensional spins that dynamically self-assemble into groups; individuals within a group tend to share similar opinions (intragroup homophily), and opinions between individuals belonging to different groups tend to be different (intergroup heterophily). We compute the associated nontrivial phase diagram by solving a self-consistency equation for “magnetization” (combined average opinion). Below a critical temperature, there exist two stable phases: one ordered with nonzero magnetization and large clusters, the other disordered with zero magnetization and no clusters. The system exhibits a first-order transition to the disordered phase. We analytically derive the group-size distribution that successfully matches empirical group-size distributions from online communities.

关键词： Classical statistical mechanics Network formation & growth Network phase transitions Phase diagrams Phase transitions Self-assembly Social systems Networks & random structures Social dynamics Social networks Spin glasses Data analysis Ising model Markovian processes Mean field theory metropolis algorithm Simulated annealing

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Formation and morphological evolution of self-similar 3D nanostructures on weakly interacting substrates

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Physical Review Materials 2018年第6期2卷 063401-063401页

作者： B. Lü G. A. Almyras V. Gervilla J. E. Greene K. Sarakinos Nanoscale Engineering Division Department of Physics Chemistry and Biology Linköping University SE 581 83 Linköping Sweden Thin Film Physics Division Department of Physics Chemistry and Biology Linköping University SE-581 83 Linköping Sweden Materials Science and Physics Departments University of Illinois Urbana Illinois 61801 USA

Vapor condensation on weakly interacting substrates leads to the formation of three-dimensional (3D) nanoscale islands (i.e., nanostructures). While it is widely accepted that this process is driven by minimization of the total film/substrate surface and interface energy, current film-growth theory cannot fully explain the atomic-scale mechanisms and pathways by which 3D island formation and morphological evolution occurs. Here, we use kinetic Monte Carlo simulations to describe the dynamic evolution of single-island shapes during deposition of Ag on weakly interacting substrates. The results show that 3D island shapes evolve in a self-similar manner, exhibiting a constant height-to-radius aspect ratio, which is a function of the growth temperature. Furthermore, our results reveal the following chain of atomic-scale events that lead to compact 3D island shapes: 3D nuclei are first formed due to facile adatom ascent at single-layer island steps, followed by the development of sidewall facets bounding the islands, which in turn facilitates upward diffusion from the base to the top of the islands. The limiting atomic process which determines the island height, for a given number of deposited atoms, is the temperature-dependent rate at which adatoms cross from sidewall facets to the island top. The overall findings of this study provide insights into the directed growth of metal nanostructures with controlled shapes on weakly interacting substrates, including two-dimensional crystals, for use in catalytic and nanoelectronic applications.

关键词： Growth Island Nucleation on surfaces Surface diffusion Nanoparticles Thin films metropolis algorithm Molecular dynamics

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Liquid-hexatic transition for soft disks

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Physical Review E 2023年第2期108卷 024103-024103页

作者： Yoshihiko Nishikawa Werner Krauth A. C. Maggs Graduate School of Information Sciences Tohoku University Sendai 980-8579 Japan Laboratoire de Physique de l'Ecole normale supérieure ENS Université PSL CNRS Sorbonne Université Université de Paris Cité 75005 Paris France CNRS UMR7083 ESPCI Paris Université PSL 10 rue Vauquelin 75005 Paris France

We study the liquid-hexatic transition of soft disks with massively parallel simulations and determine the equation of state as a function of system size. For systems with interactions decaying as the inverse mth power of the separation, the liquid-hexatic phase transition is continuous for m=12 and m=8, while it is of first order for m=24. The critical power m for the transition between continuous and first-order behavior is larger than previously reported. The continuous transition for m=12 implies that the two-dimensional Lennard-Jones model has a continuous liquid-hexatic transition at high temperatures. We also study the Weeks-Chandler-Andersen model and find a continuous transition at high temperatures that is consistent with the soft-disk case for m=12. Pressure data as well as our implementation are available from an open-source repository.

关键词： BKT transition Equations of state Phase transitions 2-dimensional systems metropolis algorithm

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Subphase transitions in first-order aggregation processes

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Physical Review E 2017年第3期95卷 032502-032502页

作者： Tomas Koci Michael Bachmann Soft Matter Systems Research Group Center for Simulational Physics The University of Georgia Athens Georgia 30602 USA Instituto de Física Universidade Federal de Mato Grosso Cuiabá (MT) Brazil Departamento de Física Universidade Federal de Minas Gerais Belo Horizonte (MG) Brazil

In this paper, we investigate the properties of aggregation transitions in the context of generic coarse-grained homopolymer systems. By means of parallel replica-exchange Monte Carlo methods, we perform extensive simulations of systems consisting of up to 20 individual oligomer chains with five monomers each. Using the tools of the versatile microcanonical inflection-point analysis, we show that the aggregation transition is a first-order process consisting of a sequence of subtransitions between intermediate structural phases. We unravel the properties of these intermediate phases by collecting and analyzing their individual contributions towards the density of states of the system. The central theme of this systematic study revolves around translational entropy and its role in the striking phenomena of missing intermediate phases. We conclude with a brief discussion of the scaling properties of the transition temperature and the latent heat.

关键词： Aggregation Polymer folding Specific phase transitions Coarse graining metropolis algorithm

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Three-dimensional Heisenberg model with Dzyaloshinskii-Moriya interaction: A Monte Carlo study

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Physical Review E 2024年第6期109卷 064113-064113页

作者： G. Albuquerque Silva A. R. Bergeron J. A. Plascak D. P. Landau Departamento de Física Instituto de Ciências Exatas Center for Simulational Physics The Centro de Ciências Exatas e da Natureza–Campus I Departamento de Física–CCEN Cidade Universitária 58051-970 João Pessoa PB Brazil

The three-dimensional classical Heisenberg model on a simple cubic lattice with Dzyaloshinskii-Moriya (DM) interactions between nearest-neighbors in all directions has been studied using Monte Carlo simulations. The metropolis algorithm, combined with single histogram reweighting techniques and finite-size scaling analyses, has been used to obtain the thermodynamic behavior of the system in the thermodynamic limit. Simulations were performed with the same set of interaction parameters for both shifted boundary conditions (SBC) and fluctuating boundary conditions (FBC). Because of an incommensurability caused by the DM interaction, the SBC incorporated a fixed shift angle at the boundary which varies as a function of the DM interaction and lattice size. This SBC method decreases the simulation time significantly, but the distribution of states is somewhat different than that obtained with FBC. The ground state for nonzero DM interaction is a spiral configuration where the spins are restricted to lie in planes perpendicular to the DM vector. We found that this spiral configuration undergoes a conventional second-order phase transition into a disordered, paramagnetic state with the transition temperature being a function of the magnitude of the DM interaction. The limiting case with only DM interaction in the model has also been considered. The critical exponent ν, the critical exponent ratios α/ν, β/ν, γ/ν, as well as the critical temperature Tc and fourth-order cumulant of the order parameter U4* at Tc have been estimated for different magnitudes of DM interaction. The critical exponents and cumulants at the transition are different from those for the three-dimensional Heisenberg model, but the ratios α/ν, β/ν, γ/ν, U4*/ν are the same, implying that weak universality is valid for all values of DM interaction. Structure factor calculations for particular cases have been performed considering SBC and FBC in the simulations with different lattice sizes at the critical t

关键词： Classical statistical mechanics Critical phenomena Phase transitions Classical spin models Lattice models in statistical physics metropolis algorithm Monte Carlo methods

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Simulated annealing for tensor network states

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NEW JOURNAL OF PHYSICS 2014年第10期16卷 103022-103022页

作者： Iblisdir, S. Univ Barcelona Dept Estruct & Constituents Mat Barcelona 08028 Spain

Markov chains for probability distributions related to matrix product states and one-dimensional Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a simulated annealing scheme for ground states of such Hamiltonians. Numerical experiments suggest that a linear, i.e., fast, schedule is possible in non-trivial cases. A natural extension of these chains to two-dimensional settings is next presented and tested. The obtained results compare well with Euclidean evolution. The proposed Markov chains are easy to implement and are inherently sign problem free (even for fermionic degrees of freedom).

关键词： matrix product states projected entangled pair states metropolis algorithm strongly correlated systems

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Spirit: Multifunctional framework for atomistic spin simulations

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Physical Review B 2019年第22期99卷 224414-224414页

作者： Gideon P. Müller Markus Hoffmann Constantin Dißelkamp Daniel Schürhoff Stefanos Mavros Moritz Sallermann Nikolai S. Kiselev Hannes Jónsson Stefan Blügel Peter Grünberg Institut and Institute for Advanced Simulation Forschungszentrum Jülich and JARA 52425 Jülich Germany Science Institute and Faculty of Physical Sciences University of Iceland VR-III 107 Reykjavík Iceland Department of Physics RWTH Aachen University 52056 Aachen Germany

The Spirit framework is designed for atomic-scale spin simulations of magnetic systems with arbitrary geometry and magnetic structure, providing a graphical user interface with powerful visualizations and an easy-to-use scripting interface. An extended Heisenberg-type spin-lattice Hamiltonian including competing exchange interactions between neighbors at arbitrary distances, higher-order exchange, Dzyaloshinskii-Moriya and dipole-dipole interactions is used to describe the energetics of a system of classical spins localized at atom positions. A variety of common simulation methods are implemented including Monte Carlo and various time evolution algorithms based on the Landau-Lifshitz-Gilbert (LLG) equation of motion. These methods can be used to determine static ground-state and metastable spin configurations, sample equilibrium and finite-temperature thermodynamical properties of magnetic materials and nanostructures, or calculate dynamical trajectories including spin torques induced by stochastic temperature or electric current. Methods for finding the mechanism and rate of thermally assisted transitions include the geodesic nudged elastic band method, which can be applied when both initial and final states are specified, and the minimum mode-following method when only the initial state is given. The lifetimes of magnetic states and rates of transitions can be evaluated within the harmonic approximation of transition-state theory. The framework offers performant central processing unit (CPU) and graphics processing unit (GPU) parallelizations. All methods are verified and applications to several systems, such as vortices, domain walls, skyrmions, and bobbers are described.

关键词： Dipolar interaction Exchange interaction Frustrated magnetism Magnetic anisotropy Magnetic order Magnetic texture Magnetization dynamics Skyrmions Spintronics Ferrimagnets Magnetic systems Nanostructures Noncollinear magnets Heisenberg model Landau-Lifschitz-Gilbert equation Langevin algorithm metropolis algorithm Monte Carlo methods Spin lattice models

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Structural properties of the Jagla fluid

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Physical Review E 2018年第1期98卷 012138-012138页

作者： Mariano López de Haro Álvaro Rodríguez-Rivas Santos B. Yuste Andrés Santos Instituto de Energías Renovables Universidad Nacional Autónoma de México (U.N.A.M.) Temixco Morelos 62580 Mexico Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx) Universidad de Extremadura Badajoz E-06006 Spain

The structural properties of the Jagla fluid are studied by Monte Carlo (MC) simulations, numerical solutions of integral equation theories, and the (semi-analytical) rational-function approximation (RFA) method. In the latter case, the results are obtained from the assumption (supported by our MC simulations) that the Jagla potential and a potential with a hard core plus an appropriate piecewise constant function lead to practically the same cavity function. The predictions obtained for the radial distribution function, g(r), from this approach are compared against MC simulations and integral equations for the Jagla model, and also for the limiting cases of the triangle-well potential and the ramp potential, with a general good agreement. The analytical form of the RFA in Laplace space allows us to describe the asymptotic behavior of g(r) in a clean way and compare it with MC simulations for representative states with oscillatory or monotonic decay. The RFA predictions for the Fisher-Widom and Widom lines of the Jagla fluid are obtained.

关键词： Classical statistical mechanics Colloids Soft colloids metropolis algorithm Monte Carlo methods

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Enhanced Sampling of Configuration and Path Space in a Generalized Ensemble by Shooting Point Exchange

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Physical Review Letters 2024年第12期132卷 128001-128001页

作者： Sebastian Falkner Alessandro Coretti Christoph Dellago University of Vienna Faculty of Physics 1090 Vienna Austria.

The computer simulation of many molecular processes is complicated by long timescales caused by rare transitions between long-lived states. Here, we propose a new approach to simulate such rare events, which combines transition path sampling with enhanced exploration of configuration space. The method relies on exchange moves between configuration and trajectory space, carried out based on a generalized ensemble. This scheme substantially enhances the efficiency of the transition path sampling simulations, particularly for systems with multiple transition channels, and yields information on thermodynamics, kinetics and reaction coordinates of molecular processes without distorting their dynamics. The method is illustrated using the isomerization of proline in the KPTP tetrapeptide.

关键词： Biomolecular dynamics Stochastic processes Thermodynamics Biomolecules Peptides Langevin algorithm metropolis algorithm Molecular dynamics Monte Carlo methods

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