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The classification of phase transitions is a central and challenging task in condensed matter physics. Typically, it relies on the identification of order parameters and the analysis of singularities in the free energy and its derivatives. Here, we propose an alternative framework to identify quantum phase transitions, employing both unsupervised and supervised machine learning techniques. Using the axial next-nearest neighbor Ising (ANNNI) model as a benchmark, we show how unsupervised learning can detect three phases (ferromagnetic, paramagnetic, and a cluster of the antiphase with the floating phase) as well as two distinct regions within the paramagnetic phase. Employing supervised learning we show that transfer learning becomes possible: a machine trained only with nearest-neighbour interactions can learn to identify a new type of phase occurring when next-nearest-neighbour interactions are introduced. All our results rely on few and low dimensional input data (up to twelve lattice sites), thus providing a computational friendly and general framework for the study of phase transitions in many-body systems.
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Theories of photoinduced phase transitions have developed along with the progress in experimental studies, especially concerning their nonlinear characters and transition dynamics. At an early stage, paths from photoinduced local structural distortions to global ones are explained in classical statistical models. Their dynamics are governed by transition probabilities and inevitably stochastic, but they were sufficient to describe coarse-grained time evolutions. Recently, however, a variety of dynamics including ultrafast ones are observed in different electronic states. They are explained in relevant electronic models. In particular, a coherent lattice oscillation and coherent motion of a macroscopic domain boundary need appropriate interactions among electrons and lattice displacements. Furthermore, some transitions proceed almost in one direction, which can be explained by considering relevant electronic processes. We describe the history of theories of photoinduced phase transitions and discuss a future perspective.
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 networks can detect phase transitions in the system via `anomaly detection, without the need for any label or a priori knowledge of the phases. We present different ways of training these autoencoders and we evaluate them to discriminate between distinct magnetic phases. In this process, we highlight the case of high temperature or even random training data. Finally, we analyze the capability of the autoencoder to detect the ground state degeneracy through the reconstruction error.
We present an analytical strong-disorder renormalization group theory of the quantum phase transition in the dissipative random transverse-field Ising chain. For Ohmic dissipation, we solve the renormalization flow equations analytically, yielding asymptotically exact results for the low-temperature properties of the system. We find that the interplay between quantum fluctuations and Ohmic dissipation destroys the quantum critical point by smearing. We also determine the phase diagram and the behavior of observables in the vicinity of the smeared quantum phase transition.
We investigate the thermal-driven charge density wave (CDW) transition of two cubic superconducting intermetallic systems Lu(Pt1-xPdx)2In and (Sr1-xCax)3Ir4Sn13 by means of x-ray diffraction technique. A detailed analysis of the CDW modulation superlattice peaks as function of temperature is performed for both systems as the CDW transition temperature T_CDW is suppressed to zero by an non-thermal control parameter. Our results indicate an interesting crossover of the classical thermal-driven CDW order parameter critical exponent from a three-dimensional universality class to a mean-field tendency, as T_CDW vanishes. Such behavior might be associated with presence of quantum fluctuations which influences the classical second-order phase transition, strongly suggesting the presence of a quantum critical point (QCP) at T_CDW = 0. This also provides experimental evidence that the effective dimensionality exceeds its upper critical dimension due to a quantum phase transition.
We study the relation between Chern numbers and Quantum Phase Transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian. These invariants contain global information, in addition to the usual one (obtained by integrating the Berry connection around a closed loop). We compute these invariants (Chern numbers) and discuss their relation to QPT. In particular we show that Chern numbers can be used to label regions corresponding to different phases.
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