Related papers: Comparison of two quantum-cluster approximations
Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…
We propose novel first-order stochastic approximation algorithms for canonical correlation analysis (CCA). Algorithms presented are instances of inexact matrix stochastic gradient (MSG) and inexact matrix exponentiated gradient (MEG), and…
Clustering is one of the most fundamental problem in Machine Learning. Researchers in the field often require a lower bound on the size of the clusters to maintain anonymity and upper bound for the ease of analysis. Specifying an optimal…
The promise of quantum computing lies in harnessing programmable quantum devices for practical applications such as efficient simulation of quantum materials and condensed matter systems. One important task is the simulation of…
In this paper, we study the convergence rate of the DCA (Difference-of-Convex Algorithm), also known as the convex-concave procedure, with two different termination criteria that are suitable for smooth and nonsmooth decompositions…
This paper discusses a deterministic clustering approach to capacitated resource allocation problems. In particular, the Deterministic Annealing (DA) algorithm from the data-compression literature, which bears a distinct analogy to the…
Quantum periodic cluster methods for strongly correlated electron systems are reformulated and developed. The reformulation and development are based on a canonical transformation which periodizes the fermions in the cluster space. The…
The performance of the Quantum Approximate Optimization Algorithm (QAOA) is closely tied to the structure of the dynamical Lie algebra (DLA) generated by its Hamiltonians, which determines both its expressivity and trainability. In this…
We consider a system of interacting particles with random initial conditions. Continuum approximations of the system, based on truncations of the BBGKY hierarchy, are described and simulated for various initial distributions and types of…
Diffusion-Limited Aggregation (DLA), the canonical model for non-equilibrium fractal growth, emerges from the simple rule of irreversible attachment by random walkers. Despite four decades of study, a unified computational framework…
The relationship linking a galaxy cluster's total mass with the concentration of its mass profile and its redshift is a fundamental prediction of the Cold Dark Matter (CDM) paradigm of cosmic structure formation. However, confronting those…
Non-unitary theories are commonly seen in the classical simulations of quantum systems. Among these theories, the method of moments of coupled-cluster equations (MMCCs) and the ensuing classes of the renormalized coupled-cluster (CC)…
The unitary coupled cluster (UCC) approximation is one of the more promising wave-function ans\"atze for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems…
Extensions of dynamical-mean-field-theory (DMFT) make use of quantum impurity models as non-perturbative and exactly solvable reference systems which are essential to treat the strong electronic correlations. Through the introduction of…
Based on the results of a previous paper (Paper I), by performing the geometrical mapping via coherent states, phase transitions are investigated and compared within two algebraic cluster models. The difference between the Semimicroscopic…
We present experimental evidence that the effective medium approximation (EMA), developed by D.C. Morse [Phys. Rev. E {\bf 63}, 031502, (2001)], provides the correct scaling law of the macroscopic plateau modulus…
Most quark actions in lattice QCD encounter difficulties with chiral symmetry and its spontaneous breakdown. Minimally doubled fermions (MDF) are a category of strictly local chiral lattice fermions, whose continuum limit reproduces two…
These lecture notes provide an introduction to quantum cluster methods for strongly correlated systems. Cluster Perturbation Theory (CPT), the Variational Cluster Approximation (VCA) and Cellular Dynamical Mean Field Theory (CDMFT) are…
We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with…
Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and…