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Register a new userBridging the Gap between Deep Learning and Frustrated Quantum Spin System for Extreme-scale Simulations on New Generation of Sunway Supercomputer
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Efficient numerical methods are promising tools for delivering unique insights into the fascinating properties of physics, such as the highly frustrated quantum many-body systems. However, the computational complexity of obtaining the wave functions for accurately describing the quantum states increases exponentially with respect to particle number. Here we present a novel convolutional neural network (CNN) for simulating the two-dimensional highly frustrated spin-$1/2$ $J_1-J_2$ Heisenberg model, meanwhile the simulation is performed at an extreme scale system with low cost and high scalability. By ingenious employment of transfer learning and CNNs translational invariance, we successfully investigate the quantum system with the lattice size up to $24times24$, within 30 million cores of the new generation of Sunway supercomputer. The final achievement demonstrates the effectiveness of CNN-based representation of quantum-state and brings the state-of-the-art record up to a brand-new level from both aspects of remarkable accuracy and unprecedented scales.
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The study of strongly frustrated magnetic systems has drawn great attentions from both theoretical and experimental physics. Efficient simulations of these models are essential for understanding their exotic properties. Here we present PEPS++, a novel computational paradigm for simulating frustrated magnetic systems and other strongly correlated quantum many-body systems. PEPS++ can accurately solve these models at the extreme scale with low cost and high scalability on modern heterogeneous supercomputers. We implement PEPS++ on Sunway TaihuLight based on a carefully designed tensor computation library for manipulating high-rank tensors and optimize it by invoking various high-performance matrix and tensor operations. By solving a 2D strongly frustrated $J_1$-$J_2$ model with over ten million cores, PEPS++ demonstrates the capability of simulating strongly correlated quantum many-body problems at unprecedented scales with accuracy and time-to-solution far beyond the previous state of the art.
Despite the enormous interest in quantum spin liquids, their experimental existence still awaits broad consensus. In particular, quenched disorder may turn a specific system into a spin glass and possibly preclude the formation of a quantum spin liquid. Here, we demonstrate that the glass transition among geometrically frustrated magnets, a materials class in which spin liquids are expected, differs qualitatively from conventional spin glass. Whereas conventional systems have a glass temperature that increases with increasing disorder, geometrically frustrated systems have a glass temperature that increases with decreasing disorder, approaching, in the clean limit, a finite value. This behaviour implies the existence of a hidden energy scale (far smaller than the Weiss constant) which is independent of disorder and drives the glass transition in the presence of disorder. Motivated by these observations, we propose a scenario in which the interplay of interactions and entropy in the disorder-free system yields a temperature-dependent magnetic permeability with a crossover temperature that determines the hidden energy scale. The relevance of this scale for quantum spin liquids is discussed.
This paper describes the architecture, the development and the implementation of Janus II, a new generation application-driven number cruncher optimized for Monte Carlo simulations of spin systems (mainly spin glasses). This domain of computational physics is a recognized grand challenge of high-performance computing: the resources necessary to study in detail theoretical models that can make contact with experimental data are by far beyond those available using commodity computer systems. On the other hand, several specific features of the associated algorithms suggest that unconventional computer architectures, which can be implemented with available electronics technologies, may lead to order of magnitude increases in performance, reducing to acceptable values on human scales the time needed to carry out simulation campaigns that would take centuries on commercially available machines. Janus II is one such machine, recently developed and commissioned, that builds upon and improves on the successful JANUS machine, which has been used for physics since 2008 and is still in operation today. This paper describes in detail the motivations behind the project, the computational requirements, the architecture and the implementation of this new machine and compares its expected performances with those of currently available commercial systems.
When an electronic system is subjected to a sufficiently strong magnetic field that the cyclotron energy is much larger than the Fermi energy, the system enters the extreme quantum limit (EQL) and becomes susceptible to a number of instabilities. Bringing a three-dimensional electronic system deeply into the EQL can be difficult, however, since it requires a small Fermi energy, large magnetic field, and low disorder. Here we present an experimental study of the EQL in lightly-doped single crystals of strontium titanate, which remain good bulk conductors down to very low temperatures and high magnetic fields. Our experiments probe deeply into the regime where theory has long predicted electron-electron interactions to drive the system into a charge density wave or Wigner crystal state. A number of interesting features arise in the transport in this regime, including a striking re-entrant nonlinearity in the current-voltage characteristics and a saturation of the quantum-limiting field at low carrier density. We discuss these features in the context of possible correlated electron states, and present an alternative picture based on magnetic-field induced puddling of electrons.
Recently measurements on various spin-1/2 quantum magnets such as H$_3$LiIr$_2$O$_6$, LiZn$_2$Mo$_3$O$_8$, ZnCu$_3$(OH)$_6$Cl$_2$ and 1T-TaS$_2$ -- all described by magnetic frustration and quenched disorder but with no other common relation -- nevertheless showed apparently universal scaling features at low temperature. In particular the heat capacity C[H,T] in temperature T and magnetic field H exhibits T/H data collapse reminiscent of scaling near a critical point. Here we propose a theory for this scaling collapse based on an emergent random-singlet regime extended to include spin-orbit coupling and antisymmetric Dzyaloshinskii-Moriya (DM) interactions. We derive the scaling $C[H,T]/T sim H^{-gamma} F_q[T/H]$ with $F_q[x] = x^{q}$ at small $x$, with $q in$ (0,1,2) an integer exponent whose value depends on spatial symmetries. The agreement with experiments indicates that a fraction of spins form random valence bonds and that these are surrounded by a quantum paramagnetic phase. We also discuss distinct scaling for magnetization with a $q$-dependent subdominant term enforced by Maxwells relations.
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