Although artificial neural networks have recently been proven to provide a promising new framework for constructing quantum many-body wave functions, the parameterization of a quantum wavefunction with nonabelian symmetries in terms of a Boltzmann machine inherently leads to biased results due to the basis dependence. We demonstrate that this problem can be overcome by sampling in the basis of irreducible representations instead of spins, for which the corresponding ansatz respects the nonabelian symmetries of the system. We apply our methodology to find the ground states of the one-dimensional antiferromagnetic Heisenberg (AFH) model with spin-1 ⁄2 and spin-1 degrees of freedom, and obtain a substantially higher accuracy than when using the sz-basis as input to the neural network. The proposed ansatz can target excited states, which is illustrated by calculating the energy gap of the AFH model. We also generalize the framework to the case of anyonic spin chains.

Still under debate is the question of whether machine learning is capable of going beyond blackbox modeling for complex physical systems. We investigate the generalizing and interpretability properties of learning algorithms. To this end, we use supervised and unsupervised learning to infer the phase boundaries of the active Ising model, starting from an ensemble of configurations of the system. We illustrate that unsupervised learning techniques are powerful at identifying the phase boundaries in the control parameter space, even in situations of phase coexistence. It is demonstrated that supervised learning with neural networks is capable of learning the characteristics of the phase diagram, such that the knowledge obtained at a limited set of control variables can be used to determine the phase boundaries across the phase diagram. In this way, we show that properly designed supervised learning provides predictive power to regions in the phase diagram that are not included in the training phase of the algorithm. We stress the importance of introducing interpretability methods in order to perform a physically relevant classification of the phases with deep learning.

We provide a systematic study of the isospin composition and neutron-to-proton N Z ratio dependence of nuclear short-range correlations (SRC) across the nuclear mass table. We use the low-order correlation operator approximation (LCA) to compute the SRC contribution to the single-nucleon momentum distributions for 14 different nuclei from A = 4 to A = 208. Ten asymmetric nuclei are included for which the neutrons outnumber the protons by a factor of up to 1.54. The computed momentum distributions are used to extract the pair composition of the SRC. We find that there is a comprehensive picture for the isospin composition of SRC and their evolution with nucleon momentum. We also compute the non-relativistic kinetic energy of neutrons and protons and its evolution with nuclear mass A and N Z . Confirming the conclusions from alternate studies it is shown that the minority species (protons) become increasingly more short-range correlated as the neutron-to-proton ratio increases. We forge connections between measured nucleon-knockout quantities sensitive to SRC and single-nucleon momentum distributions. It is shown that the LCA can account for the observed trends in the data, like the fact that in neutron-rich nuclei the protons are responsible for an unexpectedly large fraction of the high-momentum components.

Background: High-momentum nucleons in a nuclear environment can be associated with short-range correlations (SRC) that primarily occur between nucleon pairs. Observations and theoretical developments have indicated that the SRC properties can be captured by general quantitative principles that are subject to model-dependence upon quantification. The variations in the aggregated effect of SRC across nuclei, however, can be quantified in an approximately model-independent fashion in terms of the so-called SRC scaling factors that capture the aggregated effect of SRC for a specific nucleus A relative to the deuteron (A-to-d).Purpose: Provide predictions for the SRC scaling factors across the nuclear periodic table and determine the relative contribution of the different nucleon pair combinations to this quantity. Determine the SRC scaling factors for both bound protons and bound neutrons and study how these quantities evolve with the neutron-to-proton ( N Z ) ratio in asymmetric nuclei. Methods: We employ the low-order correlation operator approximation (LCA) to compute the SRC contribution to the single-nucleon momentum distribution and ratios of A-to-d momentum distributions. We do this for a sample of fifteen nuclei from He to Pb thereby gaining access to the evolution of the SRC scaling factor with the nuclear mass 4 ≤ A ≤ 208 and the neutron-to-proton ratio 1.0 ≤ N Z ≤ 1.54. Results: We provide evidence for approximate A-to-d scaling of the single-nucleon momentum distribution at nucleon momenta exceeding about 4 fm −1 . For the studied sample of fifteen nuclei, the total SRC scaling factor is in the range 4.05-5.14 of which roughly 3 can be attributed to proton-neutron (pn) correlations. The SRC scaling factors receive sizeable contributions from pp and nn correlations. They depend on the N Z ratio reflecting the fact that the minority species (protons) becomes increasingly more short-range correlated with increasing N Z . We compare the computed SRC scaling factors in the LCA with those of ab-initio calculations and with measured quantities from SRC-sensitive inclusive electron-scattering data.Conclusions: It is shown that the LCA provides predictions for the SRC scaling factors across the nuclear table that are in line with measured values. In asymmetric nuclei there are sizeable differences between the SRC scaling factors for protons and neutrons. It is suggested that this phenomenon may impact the variations of the magnitude of the European muon collaboration (EMC) effect across nuclei. Our results corroborate the finding that SRC physics can be qualitatively understood by universal principles that build on local modifications of mean-field wave functions of nucleon pairs.

Structural balance in social network theory starts from signed networks with active relationships (friendly or hostile) to establish a hierarchy between four different types of triadic relationships. The lack of an active link also provides information about the network. To exploit the information that remains uncovered by structural balance, we introduce the inactive relationship that accounts for both neutral and nonexistent ties between two agents. This addition results in ten types of triads, with the advantage that the network analysis can be done with complete networks. To each type of triadic relationship, we assign an energy that is a measure for its average occupation probability. Finite temperatures account for a persistent form of disorder in the formation of the triadic relationships. We propose a Hamiltonian with three interaction terms and a chemical potential (capturing the cost of edge activation) as an underlying model for the triadic energy levels. Our model is suitable for empirical analysis of political networks and allows to uncover generative mechanisms. It is tested on an extended data set for the standings between two classes of alliances in a massively multi-player on-line game (MMOG) and on real-world data for the relationships between countries during the Cold War era. We find emergent properties in the triadic relationships between the nodes in a political network. For example, we observe a persistent hierarchy between the ten triadic energy levels across time and networks. In addition, the analysis reveals consistency in the extracted model parameters and a universal data collapse of a derived combination of global properties of the networks. We illustrate that the model has predictive power for the transition probabilities between the different triadic states. arXiv:1807.09042v3 [physics.soc-ph] 17 Dec 2018Heider [1] and its extension to graphs by Cartwright [2] is based on active relationships that can be friendly ("+") or unfriendly ("−"). The four types of emerging triadic relationships are categorized in two stable (= balanced) and two unstable (= unbalanced) ones, whereby one anticipates an overall tendency to create more balanced triads. Balanced triads [+ + +] and [+ − −] have an even number of "−" edges. Unbalanced [+ + −] and [− − −] triads, however, are a key ingredient in real-life political networks. Balance theory has found applications in many branches of sciences including psychology [1], studies of international networks [3,4,5,6,7], sociology [8,9,10,11,12] and ecology [13].As balance theory introduces correlations between the edge attributes in triads, in a physics framework [14,15,16,17] it maps onto a system with predominant three-edge interactions. Associating the existence of unbalanced triads to the occurrence of a non-vanishing excitation energy, the principles of social balance can be mapped onto a model with variations in an energy landscape. Marvel et al. [14] investigated the energy landscape of a social-balance inspired system and stressed the occurrence ...