Related papers: Machine learning phase transitions of the three-di…
Critical transitions are the abrupt shifts between qualitatively different states of a system, and they are crucial to understanding tipping points in complex dynamical systems across ecology, climate science, and biology. Detecting these…
Geometry and dimensionality have played crucial roles in our understanding of the fundamental laws of nature, with examples ranging from curved space-time in general relativity to modern theories of quantum gravity. In quantum many-body…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
Whether Quantum Chromodynamics (QCD) exhibits a phase transition at finite temperature and density is an open question. It is important for hydrodynamic modeling of heavy ion collisions and neutron star mergers. Lattice QCD simulations have…
We apply unsupervised learning techniques to classify the different phases of the $J_1-J_2$ antiferromagnetic Ising model on the honeycomb lattice. We construct the phase diagram of the system using convolutional autoencoders. These neural…
Applications of neural networks to condensed matter physics are becoming popular and beginning to be well accepted. Obtaining and representing the ground and excited state wave functions are examples of such applications. Another…
Three solvable models are set out in some detail in reviewing different types of phase transitions. Two of these relate directly to emergent critical phenomena, viz. melting and magnetic transitions in heavy rare-earth metals, and secondly,…
Contemporary deep neural networks offer state-of-the-art results when applied to visual reasoning, e.g., in the context of 3D point cloud data. Point clouds are important datatype for precise modeling of three-dimensional environments, but…
Neural networks possess formidable representational power, rendering them invaluable in solving complex quantum many-body systems. While they excel at analyzing static solutions, nonequilibrium processes, including critical dynamics during…
For the first time, we investigate susceptibilities of dense quark matter up to $8$th order using an effective model. Generally higher order susceptibilities will have more sign changes and larger magnitude, thus should give more…
We quantify the emergent complexity of quantum states near quantum critical points on regular 1D lattices, via complex network measures based on quantum mutual information as the adjacency matrix, in direct analogy to quantifying the…
In the presented study we investigated the second order endpoints of the lines of first order phase transitions which emerge for the QCD in the heavy and light quark mass regime and for the three-dimensional three state Potts model with an…
In this paper with study phase transitions of the $q$-state Potts model, through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA), $k$-means clustering, Uniform Manifold Approximation and…
In this paper we consider the quantum phase transition in the Ising model in the presence of a transverse field in one, two and three dimensions from a multi-partite entanglement point of view. Using \emph{exact} numerical solutions, we are…
The continuous ferromagnetic-paramagnetic phase transition in the two-dimensional Ising model has already been excessively studied by conventional canonical statistical analysis in the past. We use the recently developed generalized…
Normalizing flows are generative machine learning models which can efficiently approximate probability distributions, using only given samples of a distribution. This architecture is used to interpolate the chiral condensate obtained from…
Machine learning is capable of discriminating phases of matter, and finding associated phase transitions, directly from large data sets of raw state configurations. In the context of condensed matter physics, most progress in the field of…
We study transitions between phases of matter with topological order. By studying these transitions in exactly solvable lattice models we show how universality classes may be identified and critical properties described. As a familiar…
We study two-dimensional Ising spins, evolving through reinforcement learning using their state, action, and reward. The state of a spin is defined as whether it is in the majority or minority with its nearest neighbours. The spin updates…
We study the one-dimensional (1D) quantum compass model with two independent parameters by means of an exact mapping to the quantum Ising model. This allows us to uncover hidden features of the quantum phase transition in the ordinary…