Classifying phases of matter is key to our understanding of many problems in physics. For quantum-mechanical systems in particular, the task can be daunting due to the exponentially large Hilbert space. With modern computing power and access to ever-larger data sets, classification problems are now routinely solved using machine-learning techniques 1 . Here, we propose a neural-network approach to finding phase transitions, based on the performance of a neural network after it is trained with data that are deliberately labelled incorrectly. We demonstrate the success of this method on the topological phase transition in the Kitaev chain 2 , the thermal phase transition in the classical Ising model 3 , and the many-body-localization transition in a disordered quantum spin chain 4 . Our method does not depend on order parameters, knowledge of the topological content of the phases, or any other specifics of the transition at hand. It therefore paves the way to the development of a generic tool for identifying unexplored phase transitions.Machine learning as a tool for analysing data is becoming more and more prevalent in an increasing number of fields. This is due to a combination of availability of large amounts of data and the advances in hardware and computational power, the latter most notably through the use of graphical processing units.Two typical methods of machine learning can be distinguished, namely the unsupervised and supervised methods. In the former the machine receives no input other than the data and is asked, for example, to extract features or to cluster the samples. Such an unsupervised approach was applied to identify phase transitions and order parameters from images of classical configurations of Ising models 5 . In the supervised learning methods, the data have to be supplemented by a set of labels. A typical example is classification of data, where each sample is assigned a class label. The machine is trained to recognize samples and predict their associated label, demonstrating that it has learned by generalizing to samples it has not encountered before. This approach, too, has been demonstrated on Ising models Motivated by previous studies, we apply machine-learning techniques to the detection of phase transitions. In contrast to the earlier works, however, we focus on a combination of supervised and unsupervised techniques. In most cases, namely, it is exactly the labelling that one would like to find out (that is, classification of phases). That implies that a labelling is not known beforehand, and hence supervised techniques are not directly applicable. In this Letter we demonstrate that it is possible to find the correct labels, by purposefully mislabelling the data and evaluating the performance of the machine learner. We will base our method on NNs, which are capable of fitting arbitrary nonlinear functions 11 . Indeed, if a linear feature extraction method worked, there would have been no need to explicitly find labels in the first place.We emphasize the main result in this work is...

We propose a mechanism to pin skyrmions in chiral magnetic thin films by introducing local maxima of magnetic exchange strength as pinning centers. The local maxima can be realized by engineering the local density of itinerant electrons. The stationary properties and the dynamical pinning and depinning processes of an isolated skyrmion around a pinning center are studied. We carry out numerical simulations of the Landau-Lifshitz-Gilbert (LLG) equation and find a way to control the position of an isolated skyrmion in a pinning center lattice using electric current pulses. The results are verified by a Thiele equation analysis. We also find that the critical current to depin a skyrmion, which is estimated to have order of magnitude 10(7)-10(8) A m(-2), has linear dependence on the pinning strength.

We present a guiding principle for designing fermionic Hamiltonians and quantum Monte Carlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the Monte Carlo weight of fermionic QMC simulations. Specifically, rigorous mathematical constraints on the determinants involving matrices that lie in the split orthogonal group provide a guideline for sign-free simulations of fermionic models on bipartite lattices. This guiding principle not only unifies the recent solutions of the sign problem based on the continuous-time quantum Monte Carlo methods and the Majorana representation, but also suggests new efficient algorithms to simulate physical systems that were previously prohibitive because of the sign problem.PACS numbers: 02.70. Ss, 71.10.Fd, 02.20.Tw One of the biggest challenges to classical simulation of quantum systems is the infamous fermion sign problem of quantum Monte Carlo (QMC) simulations. It appears when the weights of configurations in a QMC simulation may become negative and therefore cannot be directly interpreted as probabilities [1]. In the presence of a sign problem, the simulation effort typically grows exponentially with system size and inverse temperature.While the sign problem is nondeterministic polynomial (NP) hard [2], implying that there is little hope of finding a generic solution, this does not exclude ad hoc solutions to the sign problem for specific models. For example, one can sometimes exploit symmetries to design appropriate sign-problem-free QMC algorithms for a restricted class of models [3]. However, it is unclear how broad these classes are and it is in general hard to foresee whether a given physical model would have a sign problem in any QMC simulations. The situation is not dissimilar to the study of many intriguing problems in the NP complexity class, where a seemingly infeasible problem might turn out to have a polynomial-time solution surprisingly [4].A fruitful approach in pursuing such specific solutions is to design Hamiltonians that capture the right low energy physics and allow sign-problem-free QMC simulations at the same time, called "designer" Hamiltonians [5]. This naturally calls for design principles. For bosonic and quantum spin systems a valuable guiding principle is the Marshall sign rule [6,7] which ensures nonnegative weight for all configurations. The design of the sign-problem-free fermionic Hamiltonians is harder. The method of choice for fermionic QMC simulations are the determinantal QMC approaches, including traditional discrete-time [8] and new continuous-time approaches [9][10][11][12][13]. Both approaches map the original interacting system to free fermions with an imaginary-time dependent Hamiltonian. The partition function is then written as a weighted sum of matrix determinants after tracing out the fermions [8,9,12]:where f C is a c-number and H C (τ ) is an imaginary-time dependent single-particle Hamiltonian matrix (whose matrix elements denote hopping amplitude...

The fidelity susceptibility is a general purpose probe of phase transitions. With its origin in quantum information and in the differential geometry perspective of quantum states, the fidelity susceptibility can indicate the presence of a phase transition without prior knowledge of the local order parameter, as well as reveal the universal properties of a critical point. The wide applicability of the fidelity susceptibility to quantum many-body systems is, however, hindered by the limited computational tools to evaluate it. We present a generic, efficient, and elegant approach to compute the fidelity susceptibility of correlated fermions, bosons, and quantum spin systems in a broad range of quantum Monte Carlo methods. It can be applied both to the ground-state and nonzero temperature cases. The Monte Carlo estimator has a simple yet universal form, which can be efficiently evaluated in simulations. We demonstrate the power of this approach with applications to the Bose-Hubbard model, the spin-1/2 XXZ model, and use it to examine the hypothetical intermediate spin-liquid phase in the Hubbard model on the honeycomb lattice. CONTENTS