Related papers: Global Optimization by Adiabatic Switching
Generalized Ising models, also known as cluster expansions, are an important tool in many areas of condensed-matter physics and materials science, as they are often used in the study of lattice thermodynamics, solid-solid phase transitions,…
We present a general technique to compute how the energy of a configuration varies as a function of its overlap with the ground state in the case of optimization problems. Our approach is based on a generalization of the cavity method to a…
Most of the novel energy materials contain multiple elements occupying a single site in their lattice. The exceedingly large configurational space of these materials imposes challenges in determining their ground-state structures. Coulomb…
An energy functional for orbital based $O(N)$ calculations is proposed, which depends on a number of non orthogonal, localized orbitals larger than the number of occupied states in the system, and on a parameter, the electronic chemical…
In order to efficiently explore the chemical space of all possible small molecules, a common approach is to compress the dimension of the system to facilitate downstream machine learning tasks. Towards this end, we present a data driven…
We apply inverse statistical-mechanical methods to find a simple family of optimized isotropic, monotonic pair potentials, under certain constraints, whose ground states for a wide range of pressures is the diamond crystal. These…
In the current work we revisit the pair-potential recently proposed by Wang et al. (Phys. Chem. Chem. Phys. 10624, 22, 2020) as a well defined finite-range alternative to the widely used Lennard-Jones interaction model. The advantage of…
The Lennard-Jones (LJ) Potential Energy Problem is to construct the most stable form of $N$ atoms of a molecule with the minimal LJ potential energy. This problem has a simple mathematical form $f(x) = 4\sum_{i=1}^N \sum_{j=1,j<i}^N…
In this chapter the physical aspects of the global optimization of the geometry of atomic clusters are elucidated. In particular, I examine the structural principles that determine the nature of the lowest-energy structure, the physical…
We present an operational method to determine the 'locally preferred structure'' of model liquids, a notion often put forward to explain supercooling of a liquid and glass formation. The method relies on finding the global minimum in the…
We present a new theoretical framework for modelling the cluster growing process. Starting from the initial tetrahedral cluster configuration, adding new atoms to the system and absorbing its energy at each step, we find cluster growing…
Discrete combinatorial optimization consists in finding the optimal configuration that minimizes a given discrete objective function. An interpretation of such a function as the energy of a classical system allows us to reduce the…
This note establishes, first of all, the monotonic increase with $N$ of the average $K$-body energy of classical $N$-body ground state configurations with $N\geq K$ monomers that interact solely through a permutation-symmetric $K$-body…
We propose a method to determine the locally preferred structure of model liquids. This latter is obtained numerically as the global minimum of the effective energy surface of clusters formed by small numbers of particles embedded in a…
We use local adiabatic evolution to experimentally create and determine the ground state spin ordering of a fully-connected Ising model with up to 14 spins. Local adiabatic evolution -- in which the system evolution rate is a function of…
Quantum state preparation is vital to quantum computation and quantum information processing tasks. In adiabatic state preparation, the target state is theoretically obtained with nearly perfect fidelity if the control parameter is tuned…
We introduce a method for global optimization of the structure of atomic systems that uses additional atoms with fractional existence. The method allows for movement of atoms over long distances bypassing energy barriers encountered in the…
The characterization of nanostructued materials under reactive environments is challenging due to the complexity of the structural motifs involved and their chemical transformations. Global optimization approaches allow predicting stable…
This work explores the global optimization problem of finding lowest-energy configurations (ground states) in disordered continuous spins models from statistical physics, with a particular focus on the random field XY model. Due to an…
We consider pairwise interaction energies and we investigate their minimizers among lattices with prescribed minimal vectors (length and coordination number), i.e. the one corresponding to the crystal's bonds. In particular, we show the…