Enabling Adiabatic Passages Between Disjoint Regions in Parameter Space through Topological Transitions

We explore topological transitions in parameter space in order to enable adiabatic passages between regions adiabatically disconnected within a given parameter manifold. To this end, we study the Hamiltonian of two coupled qubits interacting with external magnetic fields, and make use of the analogy between the Berry curvature and magnetic fields in parameter space, with spectrum degeneracies associated to magnetic charges. Symmetry-breaking terms induce sharp topological transitions on these charge distributions, and we show how one can exploit this effect to bypass crossing degeneracies. We also investigate the curl of the Berry curvature, an interesting but as of yet not fully explored object, which together with its divergence uniquely defines this field. Finally, we suggest a simple method for measuring the Berry curvature, thereby showing how one can experimentally verify our results.Comment: 17 pages, 11 figure

Geodesic Paths for Quantum Many-Body Systems

We propose a method to obtain optimal protocols for adiabatic ground-state preparation near the adiabatic limit, extending earlier ideas from [D. A. Sivak and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)] to quantum non-dissipative systems. The space of controllable parameters of isolated quantum many-body systems is endowed with a Riemannian quantum metric structure, which can be exploited when such systems are driven adiabatically. Here, we use this metric structure to construct optimal protocols in order to accomplish the task of adiabatic ground-state preparation in a fixed amount of time. Such optimal protocols are shown to be geodesics on the parameter manifold, maximizing the local fidelity. Physically, such protocols minimize the average energy fluctuations along the path. Our findings are illustrated on the Landau-Zener model and the anisotropic XY spin chain. In both cases we show that geodesic protocols drastically improve the final fidelity. Moreover, this happens even if one crosses a critical point, where the adiabatic perturbation theory fails.Comment: 5 pages, 2 figures + 4 pages supplemen

Geodesic paths for quantum many-body systems

We propose a method to obtain optimal protocols for adiabatic ground-state preparation near the adiabatic limit, extending earlier ideas from [D. A. Sivak and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)] to quantum non-dissipative systems. The space of controllable parameters of isolated quantum many-body systems is endowed with a Riemannian quantum metric structure, which can be exploited when such systems are driven adiabatically. Here, we use this metric structure to construct optimal protocols in order to accomplish the task of adiabatic ground-state preparation in a fixed amount of time. Such optimal protocols are shown to be geodesics on the parameter manifold, maximizing the local fidelity. Physically, such protocols minimize the average energy fluctuations along the path. Our findings are illustrated on the Landau-Zener model and the anisotropic XY spin chain. In both cases we show that geodesic protocols drastically improve the final fidelity. Moreover, this happens even if one crosses a critical point, where the adiabatic perturbation theory fails.http://meetings.aps.org/link/BAPS.2016.MAR.F50.9First author draf

Lattice effects in the quasi-two-dimensional valence-bond-solid Mott insulator EtMe3_3P[Pd(dmit)2_2]2_2

The organic charge-transfer salt EtMe$_3$P[Pd(dmit)$_2$]$_2$ is a quasi-two-dimensional Mott insulator with localized spins $S$ = 1/2 residing on a distorted triangular lattice. Here we report measurements of the uniaxial thermal expansion coefficients $\alpha_i$ along the in-plane $i$ = $a$- and $c$-axis as well as along the out-of-plane $b$-axis for temperatures 1.4\,K $\leq$T$\leq$ 200\,K. Particular attention is paid to the lattice effects around the phase transition at $T_{VBS}$ = 25\,K into a low-temperature valence-bond-solid phase and the paramagnetic regime above where effects of short-range antiferromagnetic correlations can be expected. The salient results of our study include (i) the observation of strongly anisotropic lattice distortions accompanying the formation of the valence-bond-solid, and (ii) a distinct maximum in the thermal expansion coefficients in the paramagnetic regime around 40\,K. Our results demonstrate that upon cooling through $T_{VBS}$ the in-plane $c$-axis, along which the valence bonds form, contracts while the second in-plane $a$-axis elongates by the same relative amount. Surprisingly, the dominant effect is observed for the out-of-plane $b$-axis which shrinks significantly upon cooling through $T_{VBS}$. The pronounced anomaly in $\alpha_i$ around 40\,K is attributed to short-range magnetic correlations. It is argued that the position of this maximum, relative to that in the magnetic susceptibility around 70\,K, speaks in favor of a more anisotropic triangular-lattice scenario for this compound than previously thought.Comment: 6 pages, 4 figures, submitted to Phys. Rev.

Field-induced length changes in the spin-liquid candidate κ\kappa-(BEDT-TTF)2_2Cu2_2(CN)3_3

Measurements of the coefficient of thermal expansion on the spin-liquid candidate $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ have revealed distinct and strongly anisotropic lattice effects around 6 K - a possible spin-liquid instability. In order to study the effects of a magnetic field on the low-temperature spin-liquid state, dilatometric measurements have been conducted both as a function of temperature at \emph{B} = const. and as a function of field at \emph{T} = const. While the 6 K anomaly is found to be insensitive to magnetic fields \emph{B} $\leq$ 10 T, the maximum field applied, surprisingly strong \emph{B}-induced effects are observed for magnetic fields applied along the in-plane \emph{b}-axis. Above a threshold field of 0.5 T < \emph{B}$_c$ $\leq$ 1 T, a jump-like anomaly is observed in the \emph{b}-axis lattice parameter. This anomaly, which is located at 8.7 K at \emph{B} = 1 T, grows in size and shifts to lower temperatures with increasing the magnetic field. Although the anomaly bears resemblance to a first-order phase transition, the lack of hysteresis suggests otherwise.Comment: 3 pages, 3 figures, proceedings of ISCOM 2011, physica status solidi (c)(in press

Magnetic Field-Induced Lattice Effects in a Quasi-2D Organic Conductor Close to the Mott Metal-Insulator Transition

We present ultra-high-resolution dilatometric studies in magnetic fields on a quasi-two-dimensional organic conductor $\kappa$-(D8-BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br, which is located close to the Mott metal-insulator (MI) transition. The obtained thermal expansion coefficient, $\alpha(T)$, reveals two remarkable features: (i) the Mott MI transition temperature $T_{MI}$ = (13.6 $\pm$ 0.6)\,K is insensitive to fields up to 10\,T, the highest applied field; (ii) for fields along the interlayer \emph{b}-axis, a magnetic-field-induced (FI) phase transition at $T_{FI}$ = (9.5 $\pm$ 0.5)\,K is observed above a threshold field $H_c \sim$ 1 T, indicative of a spin reorientation with strong magneto-elastic coupling.Comment: 5 pages, 4 figure

LExecutor: Learning-Guided Execution

Executing code is essential for various program analysis tasks, e.g., to detect bugs that manifest through exceptions or to obtain execution traces for further dynamic analysis. However, executing an arbitrary piece of code is often difficult in practice, e.g., because of missing variable definitions, missing user inputs, and missing third-party dependencies. This paper presents LExecutor, a learning-guided approach for executing arbitrary code snippets in an underconstrained way. The key idea is to let a neural model predict missing values that otherwise would cause the program to get stuck, and to inject these values into the execution. For example, LExecutor injects likely values for otherwise undefined variables and likely return values of calls to otherwise missing functions. We evaluate the approach on Python code from popular open-source projects and on code snippets extracted from Stack Overflow. The neural model predicts realistic values with an accuracy between 79.5% and 98.2%, allowing LExecutor to closely mimic real executions. As a result, the approach successfully executes significantly more code than any available technique, such as simply executing the code as-is. For example, executing the open-source code snippets as-is covers only 4.1% of all lines, because the code crashes early on, whereas LExecutor achieves a coverage of 51.6%.Comment: Accepted in research track of the ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering (ESEC/FSE) 202