Related papers: A Short Introduction to Numerical Linked-Cluster E…
We demonstrate that a numerical linked cluster expansion method is a powerful tool to calculate quantum dynamics. We calculate the dynamics of the magnetization and spin correlations in the two-dimensional transverse field Ising and XXZ…
Density functional theory (DFT)-based simulations of materials have first-principles accuracy, but are very computationally expensive. For simulating various properties of multi-component alloys, the cluster expansion (CE) technique has…
We propose a generalization of the linked-cluster expansions to study driven-dissipative quantum lattice models, directly accessing the thermodynamic limit of the system. Our method leads to the evaluation of the desired extensive property…
We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum -- and, in particular, classical -- interactions. Our approach is based on the use of ``decoupling parameters", advocated by Park [34], which…
We introduce a numerical linked cluster expansion for square-lattice models whose building block is an L-shape cluster. For the spin-1/2 models studied in this work, we find that this expansion exhibits a similar or better convergence of…
The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…
A novel and intuitive nearest neighbours based clustering algorithm is introduced, in which a cluster is defined in terms of an equilibrium condition which balances its size and cohesiveness. The formulation of the equilibrium condition…
We propose a nearest neighbor based clustering algorithm that results in a naturally defined hierarchy of clusters. In contrast to the agglomerative and divisive hierarchical clustering algorithms, our approach is not dependent on the…
We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into…
Exponential random graph theory is the complex network analog of the canonical ensemble theory from statistical physics. While it has been particularly successful in modeling networks with specified degree distributions, a naive model of a…
In this paper we develop a cluster-variant of the Stochastic Series expansion method (SCSE). For certain systems with longer-range interactions the SCSE is considerably more efficient than the standard implementation of the Stochastic…
Imperfections in correlated materials can alter their ground state as well as finite-temperature properties in significant ways. Here, we develop a method based on numerical linked-cluster expansions for calculating exact finite-temperature…
When electron correlations are important it is often necessary to use numerical methods to solve the Hamiltonian for a finite system (cluster) "exactly". Unfortunately, such methods are restricted to small systems. We propose to combine the…
Cluster expansions for the exponential of local operators are constructed using tensor networks. In contrast to other approaches, the cluster expansion does not break any spatial or internal symmetries and exhibits a very favourable…
Crowdsourced, or human computation based clustering algorithms usually rely on relative distance comparisons, as these are easier to elicit from human workers than absolute distance information. A relative distance comparison is a statement…
We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster…
Graph clustering is a fundamental task in network analysis where the goal is to detect sets of nodes that are well-connected to each other but sparsely connected to the rest of the graph. We present faster approximation algorithms for an…
We develop a simple and unified approach to investigate several aspects of the cluster statistics of random expansive (multi-)sets. In particular, we determine the limiting distribution of the size of the smallest and largest clusters, we…
Especially in lattice structured populations, homogeneous mixing represents an inadequate assumption. Various improvements upon the ordinary pair approximation based on a number of assumptions concerning the higher-order correlations have…
Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their…