Revealing Nonperturbative Effects in the SYK Model

Non-nearest-neighbor interactions in nonlinear dynamical lattices

In addition to spin angular momentum, light can carry orbital angular momentum. The orbital angular momentum degree of freedom in the extreme ultraviolet and x-ray regimes enables fundamental studies of light–matter interactions and new methods to study materials. Advances in x-ray optics, as well as undulator radiation and high harmonic generation techniques, lead to the creation of beams with non-trivial phase structure, such as a helical phase structure, creating new possibilities for the use of extreme ultraviolet and x-ray photons with orbital angular momentum in probing complex electronic structures in matter. In this article, we review the generation and applications of orbital angular momentum beams in the x-ray and extreme ultraviolet regime. We discuss several recent works that exploit the orbital angular momentum degree of freedom and showcase the potential advantages of using these beams.

Non-trivial phase structure of N f = 3 QCD with O( a)-improved Wilson fermion at zero temperature

We investigate the nonperturbative effects in the Sadchev–Ye–Kitaev (SYK) model at large $$N$$ . The replica-nondiagonal solutions are considered in the SYK model with an integer number of replicas $$M > 1$$ . An important property of such solutions is the fact that they realize spontaneous breaking of the time translation group on $$M$$ replicas of the thermal circle. It is demonstrated in this study that this spontaneous symmetry breaking can be described in terms of the Bogolyubov quasi-averages, if we consider the system of nonlocally interacting replicas of the SYK model. The inclusion of the interaction of the replicas in this system transforms the subleading replica-nondiagonal saddle points from a pure SYK to thermodynamic phases, thereby generating a nontrivial phase structure. We investigate this phase structure exactly analytically in the SYK2 model and numerically in the SYK4 model.

The accuracy of predicting protein local and global structural properties such as secondary structure and solvent accessible surface area has been stagnant for many years because of the challenge of accounting for non-local interactions between amino acid residues that are close in three-dimensional structural space but far from each other in their sequence positions. All existing machine-learning techniques relied on a sliding window of 10-20 amino acid residues to capture some 'short to intermediate' non-local interactions. Here, we employed Long Short-Term Memory (LSTM) Bidirectional Recurrent Neural Networks (BRNNs) which are capable of capturing long range interactions without using a window. We showed that the application of LSTM-BRNN to the prediction of protein structural properties makes the most significant improvement for residues with the most long-range contacts (|i-j| >19) over a previous window-based, deep-learning method SPIDER2. Capturing long-range interactions allows the accuracy of three-state secondary structure prediction to reach 84% and the correlation coefficient between predicted and actual solvent accessible surface areas to reach 0.80, plus a reduction of 5%, 10%, 5% and 10% in the mean absolute error for backbone ϕ , ψ , θ and τ angles, respectively, from SPIDER2. More significantly, 27% of 182724 40-residue models directly constructed from predicted C α atom-based θ and τ have similar structures to their corresponding native structures (6Å RMSD or less), which is 3% better than models built by ϕ and ψ angles. We expect the method to be useful for assisting protein structure and function prediction. The method is available as a SPIDER3 server and standalone package at http://sparks-lab.org . yaoqi.zhou@griffith.edu.au or yuedong.yang@griffith.edu.au. Supplementary data are available at Bioinformatics online.

A new γ-ray pulsar: PSR 0740-28

A new model of urban development in Latin America: The gated communities and fenced cities in the metropolitan areas of Santiago de Chile and Valparaíso

The non-trivial phase structure of the eigenstates of many-body quantum systems severely limits the applicability of quantum Monte Carlo, variational, and machine learning methods. Here, we study real-valued signful ground-state wave functions of frustrated quantum spin systems and, assuming that the tasks of finding wave function amplitudes and signs can be separated, show that the signs can be easily bootstrapped from the amplitudes. We map the problem of finding the sign structure to an auxiliary classical Ising model defined on a subset of the Hilbert space basis. We show that the Ising model does not exhibit significant frustrations even for highly frustrated parental quantum systems, and is solvable with a fully deterministic O(Klog K)-time combinatorial algorithm (where K is the Ising model size). Given the ground state amplitudes, we reconstruct the signs of the ground states of several frustrated quantum models, thereby revealing the hidden simplicity of many-body sign structures.

We provide information on a non-trivial structure of phase space of the cubic nonlinear Schrödinger (NLS) on a three-edge star graph. We prove that, in contrast to the case of the standard NLS on the line, the energy associated with the cubic focusing Schrödinger equation on the three-edge star graph with a free (Kirchhoff) vertex does not attain a minimum value on any sphere of constant L2-norm. We moreover show that the only stationary state with prescribed L2-norm is indeed a saddle point.

We report neutron scattering and transport measurements on semiconducting Rb$_{0.8}$Fe$_{1.5}$S$_2$, a compound isostructural and isoelectronic to the well-studied $A_{0.8}$Fe$_{y}$Se$_2 (A=$ K, Rb, Cs, Tl/K) superconducting systems. Both resistivity and DC susceptibility measurements reveal a magnetic phase transition at $T=275$ K. Neutron diffraction studies show that the 275 K transition originates from a phase with rhombic iron vacancy order which exhibits an in-plane stripe antiferromagnetic ordering below 275 K. In addition, interdigitated mesoscopically with the rhombic phase is an ubiquitous phase with $\sqrt{5}\times\sqrt{5}$ iron vacancy order. This phase has a magnetic transition at $T_N=425$ K and an iron vacancy order-disorder transition at $T_{S}=600$ K. These two different structural phases are closely similar to those observed in the isomorphous Se materials. Based on the close similarities of the in-plane antiferromagnetic structures, moments sizes, and ordering temperatures in semiconducting Rb$_{0.8}$Fe$_{1.5}$S$_2$ and K$_{0.81}$Fe$_{1.58}$Se$_2$, we argue that the in-plane antiferromagnetic order arises from strong coupling between local moments. Superconductivity, previously observed in the $A_{0.8}$Fe$_{y}$Se$_{2-z}$S$_z$ system, is absent in Rb$_{0.8}$Fe$_{1.5}$S$_2$, which has a semiconducting ground state. The implied relationship between stripe/block antiferromagnetism and superconductivity in these materials as well as a strategy for further investigation is discussed in this paper.

We extend our Wilsonian renormalization group (RG) analysis on the pionless nuclear effective field theory in the two-nucleon sector in two ways; on the one hand, (1) we enlarge the space of operators up to including those of [Formula: see text] in the S waves, and, on the other hand, (2) we consider the RG flows in higher partial waves (P and D waves). In the larger space calculations, we find, in addition to nontrivial fixed points, two "fixed lines" and a "fixed surface" which are related to marginal operators. In the higher partial wave calculations, we find similar phase structures to that of the S waves, but there are two relevant directions in the P waves at the nontrivial fixed points and three in the D waves. We explain the physical meaning of the P-wave phase structure by explicitly calculating the low-energy scattering amplitude. We also discuss the relation between the Legendre flow equation which we employ and the RG equation by Birse, McGovern and Richardson, and possible implementation of power divergence subtraction in higher partial waves.

Fully biodegradable blends with low shape memory recovery temperature were obtained based on poly(lactic acid) (PLA) and poly(propylene carbonate) (PPC). By virtue of their similar chemical structures, in situ cross-linking reaction initiated by dicumyl peroxide (DCP) between PLA and PPC chains was realized in PLA/PPC blends. Therefore, the compatibility between PLA and PPC was increased, which obviously changed the phase structures and increased the elongation at break of the blends. The compatibilized blends had a recovery performance at 45 °C. Combining the changes of phase structures, the mechanism of the shape memory was discussed. It was demonstrated that in situ compatibilization by dicumyl peroxide was effective to obtain eco-friendly PLA/PPC blends with good mechanical and shape memory properties.

We construct three models to describe the scenario where two eternal black holes are separated by a flat space, and can eventually be entangled by exchanging radiation. In the doubly holographic setup, we compute the entanglement entropy and mutual information among subsystems and obtain the dynamic phase structure of the entanglement. The formation of entanglement between these two black holes is delayed by the space which the radiation must travel through. If the black holes exchange sufficient Hawking modes, the final state is characterized by a connected entanglement wedge; otherwise, the final entanglement wedge contains two separate islands. In the former case, the entanglement wedge of the black holes forms at the time scale proportional to the size of the flat space between them. While in both cases, the unitarity of the evolution is preserved. When the sizes of the black holes are not equal, we observe a loss of entanglement between the smaller black hole and the radiation at late times. On the field theory side, we consider two Sachdev-Ye-Kitaev (SYK) clusters coupled to a Majorana chain, which resemble two black holes connected by a radiation region. We numerically compute the same entanglement measures and obtain similar phase structures as the bulk results. In general, a time delay of the entanglement between the SYK clusters is found in cases with a long Majorana chain. In particular, when the SYK clusters are different in size, similar entanglement loss between the smaller SYK cluster and the Majorana chain is observed. Finally, we investigate a chain model composed of EPR clusters with particles exchanging between neighboring clusters and reproduce the features of entanglement observed in the previous models.

The potential energy surface of Si2B2H4, explored ab initio at the MP2/6-31G* and density functional theory, Becke3LYP/6-311+G** levels, is rich in detail. Twelve minima were found out of the 39 stationary points located. 1,3-Disiladiboretene (1a), with a puckered four-membered ring, is predicted to be the global minimum. Its calculated inversion barrier (1.2 kcal/mol), however, is much lower than that of the analogous 1,3-diboretene (17.0 kcal/mol). The relative energies of two other Si2B2H4 isomers (5 and 7) with B−H−Si bridges are only 2.0 kcal/mol above 1a. The relative energies of 9 and 15a, both with planar pentacoordinate borons, are 7.3 and 27.1 kcal/mol. The acyclic (18) and linear (22a,b) isomers are noncompetitive energetically. Many other Si2B2H4 silaboranes, possessing similar structures and bonding as the corresponding carboranes, are calculated to be saddle points. In general, hydrogen bridging and cyclic π-delocalization stabilize Si2B2H4 isomers, while structures with multiply bonded silicon are unfavorable.

Since the genesis of condensed matter physics, strongly correlated fermionic systems have shown a variety of fascinating properties and remain a vital topic in the field. Such systems arise through electronic interaction, and despite decades of intensive research, no holistic approach to solving this problem has been found. During that time, physicists have compiled a wealth of individual experimental and theoretical results, which together give an invaluable insight into these materials, and, in some instances, can explain correlated phenomena. However, there are several systems that stubbornly refuse to fall completely in line with current theoretical descriptions, among them the high-\( T_c{}\) cuprates and heavy fermion compounds. Although the two material classes have been around for the better part of the last 50 years, large portions of their respective phase diagram are still under intensive debate. Recent experiments in several electron-doped cuprates compounds, e.g. neodymium cerium copper oxide (Nd\(_{2x}\)Ce\(_x\)CuO\(_4\)), reveal a charge ordering about an antiferromagnetic ground state. So far, it has not been conclusively clarified how this intertwining of charge and spin polarization comes about and how it can be reconciled with a rigorous theoretical description. The heavy-fermion semimetals, on the other hand, have enjoyed renewed scientific interest with the discovery of topological Kondo insulators, a new material class offering a unique interface of topology, symmetry breaking, and correlated phenomena. In this context, samarium hexaboride (SmB\(_6\)) has emerged as a prototypical system, which may feature a topological ground state. In this thesis, we present a spin rotational invariant auxiliary particle approach to investigate the propensities of interacting electrons towards forming new states of order. In particular, we study the onset of spin and charge order in high-\( T_c{}\) cuprate systems and Kondo lattices, as well as the interplay of magnetism and topology. To that end, we use a sophisticated mean-field approximation of bosonic auxiliary particles augmented by a stability analysis of the saddle point via Gaussian fluctuations. The latter enables the derivation of dynamic susceptibilities, which describe the response of the system under external fields and offer a direct comparison to experiments. Both the mean-field and fluctuation formalisms require a numerical tool that is capable of extremizing the saddle point equations, on the one hand, and reliably solving a loop integral of the susceptibility-type, on the other. A full, from scratch derivation of the formalism tailored towards a software implementation, is provided and pedagogically reviewed. The auxiliary particle method allows for a rigorous description of incommensurate magnetic order and compares well to other established numerical and analytical techniques. Within our analysis, we employ the two-dimensional one-band Hubbard as well as the periodic Anderson model as minimal Hamiltonians for the high-\( T_c{}\) cuprates and Kondo systems, respectively. For the former, we observe a regime of intertwined charge- and spin-order in the electron-doped regime, which matches recent experimental observations in the cuprate material Nd\(_{2x}\)Ce\(_x\)CuO\(_4\). Furthermore, we localize the emergence of a Kondo regime in the periodic Anderson model and establish the magnetic phase diagram of the two-band model for topological Kondo insulators. The emerging antiferromagnetic ground state can be characterized by its topological properties and shows, for a non-trivial phase, topologically protected hinge modes.