Quantum simulation of lattice gauge theories using Wilson fermions

Quantum simulators have the exciting prospect of giving access to real-time dynamics of lattice gauge theories, in particular in regimes that are difficult to compute on classical computers. Future progress towards scalable quantum simulation of lattice gauge theories, however, hinges crucially on the efficient use of experimental resources. As we argue in this work, due to the fundamental non-uniqueness of discretizing the relativistic Dirac Hamiltonian, the lattice representation of gauge theories allows for an optimization that up to now has been left unexplored. We exemplify our discussion with lattice quantum electrodynamics in two-dimensional space-time, where we show that the formulation through Wilson fermions provides several advantages over the previously considered staggered fermions. Notably, it enables a strongly simplified optical lattice setup and it reduces the number of degrees of freedom required to simulate dynamical gauge fields. Exploiting the optimal representation, we propose an experiment based on a mixture of ultracold atoms trapped in a tilted optical lattice. Using numerical benchmark simulations, we demonstrate that a state-of-the-art quantum simulator may access the Schwinger mechanism and map out its non-perturbative onset.Comment: 19 pages, 11 figure

Modified spin-wave theory with ordering vector optimization I: frustrated bosons on the spatially anisotropic triangular lattice

We investigate a system of frustrated hardcore bosons, modeled by an XY antiferromagnet on the spatially anisotropic triangular lattice, using Takahashi's modified spin-wave (MSW) theory. In particular we implement ordering vector optimization on the ordered reference state of MSW theory, which leads to significant improvement of the theory and accounts for quantum corrections to the classically ordered state. The MSW results at zero temperature compare favorably to exact diagonalization (ED) and projected entangled-pair state (PEPS) calculations. The resulting zero-temperature phase diagram includes a 1D quasi-ordered phase, a 2D Neel ordered phase, and a 2D spiraling ordered phase. We have strong indications that the various ordered or quasi-ordered phases are separated by spin-liquid phases with short-range correlations, in analogy to what has been predicted for the Heisenberg model on the same lattice. Within MSW theory we also explore the finite-temperature phase diagram. We find that the zero-temperature long-range-ordered phases turn into quasi-ordered phases (up to a Berezinskii-Kosterlitz-Thouless temperature), while zero-temperature quasi-ordered phases become short-range correlated at finite temperature. These results show that modified spin-wave theory is very well suited for describing ordered and quasi-ordered phases of frustrated XY spins (or, equivalently, of frustrated lattice bosons) both at zero and finite temperatures. While MSW theory, just as other theoretical methods, cannot describe spin-liquid phases, its breakdown provides a fast method for singling out Hamiltonians which may feature these intriguing quantum phases. We thus suggest a tool for guiding our search for interesting systems whose properties are necessarily studied with a physical quantum simulator.Comment: 40 pages, 16 figure

Increased Belief Instability in Psychotic Disorders Predicts Treatment Response to Metacognitive Training

BACKGROUND AND HYPOTHESIS: In a complex world, gathering information and adjusting our beliefs about the world is of paramount importance. The literature suggests that patients with psychotic disorders display a tendency to draw early conclusions based on limited evidence, referred to as the jumping-to-conclusions bias, but few studies have examined the computational mechanisms underlying this and related belief-updating biases. Here, we employ a computational approach to understand the relationship between jumping-to-conclusions, psychotic disorders, and delusions. STUDY DESIGN: We modeled probabilistic reasoning of 261 patients with psychotic disorders and 56 healthy controls during an information sampling task-the fish task-with the Hierarchical Gaussian Filter. Subsequently, we examined the clinical utility of this computational approach by testing whether computational parameters, obtained from fitting the model to each individual's behavior, could predict treatment response to Metacognitive Training using machine learning. STUDY RESULTS: We observed differences in probabilistic reasoning between patients with psychotic disorders and healthy controls, participants with and without jumping-to-conclusions bias, but not between patients with low and high current delusions. The computational analysis suggested that belief instability was increased in patients with psychotic disorders. Jumping-to-conclusions was associated with both increased belief instability and greater prior uncertainty. Lastly, belief instability predicted treatment response to Metacognitive Training at the individual level. CONCLUSIONS: Our results point towards increased belief instability as a key computational mechanism underlying probabilistic reasoning in psychotic disorders. We provide a proof-of-concept that this computational approach may be useful to help identify suitable treatments for individual patients with psychotic disorders

Many-body localization in a quantum simulator with programmable random disorder

When a system thermalizes it loses all local memory of its initial conditions. This is a general feature of open systems and is well described by equilibrium statistical mechanics. Even within a closed (or reversible) quantum system, where unitary time evolution retains all information about its initial state, subsystems can still thermalize using the rest of the system as an effective heat bath. Exceptions to quantum thermalization have been predicted and observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize in spite of strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. Here we experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium. We observe the essential signatures of MBL: memory retention of the initial state, a Poissonian distribution of energy level spacings, and entanglement growth in the system at long times. Our platform can be scaled to higher numbers of spins, where detailed modeling of MBL becomes impossible due to the complexity of representing such entangled quantum states. Moreover, the high degree of control in our experiment may guide the use of MBL states as potential quantum memories in naturally disordered quantum systems.Comment: 9 pages, 9 figure

Complete devil's staircase and crystal--superfluid transitions in a dipolar XXZ spin chain: A trapped ion quantum simulation

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many meta-stable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization, and quasiexact numerical techniques (density-matrix renormalization group and infinite time evolving block decimation). We find that the complete devil's staircase -- an infinite sequence of crystal states existing at vanishing tunneling -- spreads to a succession of lobes similar to the Mott-lobes found in Bose--Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar two-dimensional models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long range (algebraic) correlations, opposed to models with nearest-neighbor tunneling which show exponential decay of correlations

Temperament Systems Influence Emotion Induction but not Makam Recognition Performance in Turkish Makam Music

We tested how induced emotions and Turkish makam recognition are influenced by participation in an ear training classes, and if either is influenced by the temperament system employed. The ear training class was attended by 19 music students and was based on the Hicaz makam presented as a between-subjects factor in either unfamiliar Turkish Original Temperament (OT, pitches unequally divided into 24 intervals) or familiar Western Equal Temperament (ET, pitches equally divided into 12 intervals). Before the and after the class, participants listened to 20 music excerpts from five different Turkish makams (in both OT and ET versions). Emotion-induction was assessed via GEMS-25, and participants were also asked to identify the makam that was present in the excerpt. The unfamiliar original temperament was experienced as less vital and more uneasy before the ear training class, and recognition of the Hicaz makam increased after ear training classes (independent of the temperament system employed). Results suggest that unfamiliar temperament systems are experienced as less vital and more uneasy. Furthermore, being exposed to this temperament system for just one hour does not seem to be enough to change participants’ mental representations of it or their emotional responses to it

Biological and Pharmacokinetic Studies with β-Peptides

Interactions and cleavage reactions of β-amino acids and β-oligopeptides (up to nine residues, carrying the side chains of Ala, Val, Leu, Ile, Phe, Ser, Lys, and Hop) with biological systems, such as the most potent peptidases (pronase, proteinase K, 20S proteasome), microorganisms (Pseudomonas aeruginosa and Pseudomonas putida), and mammalian blood (intravenous application to rats) have been investigated and compared with ?-peptides. The results are: i) the three peptidases do not cleave β-peptides at all (within 24 h), and they are not inhibited by a β-peptide; ii) except for certain 3-aminobutanoic-acid (β-HAla) derivatives, neither free, nor N-acetyl-β-amino acids, nor β-peptides (offered as sole N and C source) lead to growth of the two bacteria tested; iii) two water-soluble β-heptapeptides (with Lys side chains) were shown to have elimination half-lives t1/2(β) of 3 and 10 h at 100- and 30-ng/ml levels, respectively, in the rodent blood – much larger than those of α-peptides. Thus, the preliminary results described here confirm the much greater stability of β-peptides, as compared to α-peptides, towards metabolization processes, but they also suggest that there may be interactions (by hitherto unknown mechanisms) between the worlds of α- and β-peptides

Z_2-Regge versus Standard Regge Calculus in two dimensions

We consider two versions of quantum Regge calculus. The Standard Regge Calculus where the quadratic link lengths of the simplicial manifold vary continuously and the Z_2-Regge Model where they are restricted to two possible values. The goal is to determine whether the computationally more easily accessible Z_2 model still retains the universal characteristics of standard Regge theory in two dimensions. In order to compare observables such as average curvature or Liouville field susceptibility, we use in both models the same functional integration measure, which is chosen to render the Z_2-Regge Model particularly simple. Expectation values are computed numerically and agree qualitatively for positive bare couplings. The phase transition within the Z_2-Regge Model is analyzed by mean-field theory.Comment: 21 pages, 16 ps-figures, to be published in Phys. Rev.