Related papers: Spin models from nonlinear cellular automata
The emergent dynamics in spacetime diagrams of cellular automata (CAs) is often organised by means of a number of behavioural classes. Whilst classification of elementary CAs is feasible and well-studied, non-elementary CAs are generally…
General conditions are formulated that allow to determine which quantum phase transitions in itinerant electron systems can be described by a local Landau-Ginzburg-Wilson or LGW theory solely in terms of the order parameter. A crucial…
Elementary cellular automata (ECA) present iconic examples of complex systems. Though described only by one-dimensional strings of binary cells evolving according to nearest-neighbour update rules, certain ECA rules manifest complex…
The quantum cellular automata (QCA) effect is a transition in which multiple electron move coordinately by Coulomb interactions and observed in multiple quantum dots. This effect will be useful for realizing and improving quantum cellular…
Cellular automata (CA) are dynamical systems on symbolic configurations on the lattice. They are also used as models of massively parallel computers. As dynamical systems, one would like to understand the effect of small random…
Motivated by recent experiments on the frustrated quantum magnetic compound YbMgGaO4, we study an effective spin model on triangular lattice taking into account the effects of the spin-orbit coupling. We determine the classical ground-state…
A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the…
Let $G$ be a group and $A$ a set. A cellular automaton (CA) $\tau$ over $A^G$ is von Neumann regular (vN-regular) if there exists a CA $\sigma$ over $A^G$ such that $\tau \sigma\tau = \tau$, and in such case, $\sigma$ is called a…
Taking the excess electron spin in a unit cell of semiconductor multiple quantum-dot structure as a qubit, we can implement scalable quantum computation without resorting to spin-spin interactions. The technique of single electron…
We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
We study the classical 120-degree and related orbital models. These are the classical limits of quantum models which describe the interactions among orbitals of transition-metal compounds. We demonstrate that at low temperatures these…
This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended…
Neural Cellular Automata (NCA) represent a powerful framework for modeling biological self-organization, extending classical rule-based systems with trainable, differentiable (or evolvable) update rules that capture the adaptive…
Very much as its classical counterpart, quantum cellular automata are expected to be a great tool for simulating complex quantum systems. Here we introduce a partitioned model of quantum cellular automata and show how it can simulate, with…
We present a new method to study the ground state of quantum spin systems using the Monte Carlo techniques together with restructured intermediate states which we proposed previously. Our basic idea is to obtain coefficients in the…
Stochastic processes with absorbing states feature remarkable examples of non-equilibrium universal phenomena. While a broad understanding has been progressively established in the classical regime, relatively little is known about the…
We study a frustrated spin-$S$ staggered-dimer Heisenberg model on square lattice by using the bond-operator representation for quantum spins, and investigate the emergence of classical magnetic order from the quantum mechanical…
We formalize a notion of discrete Lorentz transforms for Quantum Walks (QW) and Quantum Cellular Automata (QCA), in (1 + 1)-dimensional discrete spacetime. The theory admits a diagrammatic representation in terms of a few local, circuit…
We study the time evolution of spin squeezing in the one-dimensional spin-1/2 XY model subject to a sudden quantum quench of a transverse magnetic field. The initial state is selected from the ground state phase diagram of the model,…