NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems

We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural-network quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the implicit generation of gradients thanks to automatic differentiation. NetKet 3 also comes with support for GPU and TPU accelerators, advanced support for discrete symmetry groups, chunking to scale up to thousands of degrees of freedom, drivers for quantum dynamics applications, and improved modularity, allowing users to use only parts of the toolbox as a foundation for their own code

Low energy excitations in graphite: The role of dimensionality and lattice defects

In this paper, we present a high resolution angle resolved photoemission spectroscopy (ARPES) study of the electronic properties of graphite. We found that the nature of the low energy excitations in graphite is particularly sensitive to interlayer coupling as well as lattice disorder. As a consequence of the interlayer coupling, we observed for the first time the splitting of the $\pi$ bands by $\approx$ 0.7 eV near the Brillouin zone corner K. At low binding energy, we observed signatures of massless Dirac fermions with linear dispersion (as in the case of graphene), coexisting with quasiparticles characterized by parabolic dispersion and finite effective mass. We also report the first ARPES signatures of electron-phonon interaction in graphite: a kink in the dispersion and a sudden increase in the scattering rate. Moreover, the lattice disorder strongly affects the low energy excitations, giving rise to new localized states near the Fermi level. These results provide new insights on the unusual nature of the electronic and transport properties of graphite.Comment: 10 pages, 15 figure

Magnetic susceptibility of EuTe/PbTe Heisenberg superlattices: experimental and theoretical studies

We report results on the temperature dependence of the susceptibilities of a set of MBE-grown short-period EuTe/PbTe antiferromagnetic superlattices having different EuTe layer thicknesses. In-plane and orthogonal susceptibilities have been measured and display a strong anisotropy at low temperature, confirming the occurrence of a magnetic phase transition in the thicker samples, as seen also in neutron diffraction studies. We suggest that dipolar interactions stabilize antiferromagnetic long-range order in an otherwise isotropic system and we present numerical and analytical results for the low-temperature orthogonal susceptibility.Comment: 30 pages, 8 ps figures, RevTe

Electron spin-lattice relaxation of Yb3+ and Gd3+ ions in glasses

The electron spin-lattice relaxation rate (T1 -1) was measured in two glass samples: (i) a phosphate glass doped with 1 wt% Yb2O3 and (ii) a Li2Si4O9 glass sample doped with 0.2 wt% Gd2O3. In the Yb3+-doped glass sample, T1, was measured by an electron-spin-echo technique from 4.2 to 6 K, by the modulation method from 10 to 26 K and by the EPR linewidth from 30 to 100 K. It was found that (T1 -1) ∝ Tn with n = 9 in the range 4.2-6 K. n decreased gradually as the temperature was increased and tended towards 2 above 40 K. Over the entire temperature range 4.2-100 K, (T1 -1) was fitted to AT + BT9J8 (ΘD/T) (where A and B are two temperature-independent constants, J8 is the well-known Van Vleck integral and ΘD is the Debye temperature). The value of ΘD (= 46.3±0.9 K) so determined is in good agreement with that of Stevens and Stapleton from their T1, measurements in the range 1.5 to 7 K. In the Gd3+-doped glass, it was observed that (T1 -1) ∝ T over the range 50-150 K. The data for Ye3+-doped glass sample were accounted for by assuming that the phonon modulation of the ligand field is the dominant mechanism, associated with a low Debye temperature in accordance with the published data obtained by using other techniques to study lattice dynamics. On the other hand, the data on the Gd3+-doped glass sample were explained to be predominantly due to a mechanism involving Two-Level-Systems (TLS). © Springer-Verlag 1996 Printed in Austria

Scale invariance of a diodelike tunnel junction

We measure the current vs voltage (I-V) characteristics of a diodelike tunnel junction consisting of a sharp metallic tip placed at a variable distance d from a planar collector and emitting electrons via electric-field assisted emission. All curves collapse onto one single graph when I is plotted as a function of the single scaling variable Vd^{-\lambda}, d being varied from a few mm to a few nm, i.e., by about six orders of magnitude. We provide an argument that finds the exponent {\lambda} within the singular behavior inherent to the electrostatics of a sharp tip. A simulation of the tunneling barrier for a realistic tip reproduces both the scaling behavior and the small but significant deviations from scaling observed experimentally.Comment: 6 pages, 6 figures. Accepted for publication in Physical Review

Ferromagnetism and Temperature-Driven Reorientation Transition in Thin Itinerant-Electron Films

The temperature-driven reorientation transition which, up to now, has been studied by use of Heisenberg-type models only, is investigated within an itinerant-electron model. We consider the Hubbard model for a thin fcc(100) film together with the dipole interaction and a layer-dependent anisotropy field. The isotropic part of the model is treated by use of a generalization of the spectral-density approach to the film geometry. The magnetic properties of the film are investigated as a function of temperature and film thickness and are analyzed in detail with help of the spin- and layer-dependent quasiparticle density of states. By calculating the temperature dependence of the second-order anisotropy constants we find that both types of reorientation transitions, from out-of-plane to in-plane (``Fe-type'') and from in-plane to out-of-plane (``Ni-type'') magnetization are possible within our model. In the latter case the inclusion of a positive volume anisotropy is vital. The reorientation transition is mediated by a strong reduction of the surface magnetization with respect to the inner layers as a function of temperature and is found to depend significantly on the total band occupation.Comment: 10 pages, 8 figures included (eps), Phys Rev B in pres

A Scaling Hypothesis for Modulated Systems

We propose a scaling hypothesis for pattern-forming systems in which modulation of the order parameter results from the competition between a short-ranged interaction and a long-ranged interaction decaying with some power $\alpha$ of the inverse distance. With L being a spatial length characterizing the modulated phase, all thermodynamic quantities are predicted to scale like some power of L. The scaling dimensions with respect to L only depend on the dimensionality of the system d and the exponent \alpha. Scaling predictions are in agreement with experiments on ultra-thin ferromagnetic films and computational results. Finally, our scaling hypothesis implies that, for some range of values \alpha>d, Inverse-Symmetry-Breaking transitions may appear systematically in the considered class of frustrated systems.Comment: 13 pages, 6 figures, expanded versio