SciPost Physics

SciPost Physics Vol. 4 issue 2 (February 2018)

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• A Generalized Construction of Calabi-Yau Models and Mirror Symmetry

  Per Berglund, Tristan Hubsch

  SciPost Phys. 4, 009 (2018) · published 20 February 2018 | Toggle abstract · pdf

  We extend the construction of Calabi-Yau manifolds to hypersurfaces in non-Fano toric varieties, requiring the use of certain Laurent defining polynomials, and explore the phases of the corresponding gauged linear sigma models. The associated non-reflexive and non-convex polytopes provide a generalization of Batyrev's original work, allowing us to construct novel pairs of mirror models. We showcase our proposal for this generalization by examining Calabi-Yau hypersurfaces in Hirzebruch n-folds, focusing on n=3,4 sequences, and outline the more general class of so-defined geometries.

• Electronic structure of the candidate 2D Dirac semimetal SrMnSb2: a combined experimental and theoretical study

  S. V. Ramankutty, J. Henke, A. Schiphorst, R. Nutakki, S. Bron, G. Araizi-Kanoutas, S. K. Mishra, Lei Li, Y. K. Huang, T. K. Kim, M. Hoesch, C. Schlueter, T. -L. Lee, A. de Visser, Zhicheng Zhong, Jasper van Wezel, E. van Heumen, M. S. Golden

  SciPost Phys. 4, 010 (2018) · published 21 February 2018 | Toggle abstract · pdf

  SrMnSb$_2$ is suggested to be a magnetic topological semimetal. It contains square, 2D Sb planes with non-symmorphic crystal symmetries that could protect band crossings, offering the possibility of a quasi-2D, robust Dirac semi-metal in the form of a stable, bulk (3D) crystal. Here, we report a combined and comprehensive experimental and theoretical investigation of the electronic structure of SrMnSb$_2$, including the first ARPES data on this compound. SrMnSb$_2$ possesses a small Fermi surface originating from highly 2D, sharp and linearly dispersing bands (the Y-states) around the (0,$\pi$/a)-point in $k$-space. The ARPES Fermi surface agrees perfectly with that from bulk-sensitive Shubnikov de Haas data from the same crystals, proving the Y$-$states to be responsible for electrical conductivity in SrMnSb$_2$. DFT and tight binding (TB) methods are used to model the electronic states, and both show good agreement with the ARPES data. Despite the great promise of the latter, both theory approaches show the Y-states to be gapped above E$_F$, suggesting trivial topology. Subsequent analysis within both theory approaches shows the Berry phase to be zero, indicating the non-topological character of the transport in SrMnSb$_2$, a conclusion backed up by the analysis of the quantum oscillation data from our crystals.

• Quantum quench dynamics of the attractive one-dimensional Bose gas via the coordinate Bethe ansatz

  Jan C. Zill, Tod M. Wright, Karen V. Kheruntsyan, Thomas Gasenzer, Matthew J. Davis

  SciPost Phys. 4, 011 (2018) · published 25 February 2018 | Toggle abstract · pdf

  We use the coordinate Bethe ansatz to study the Lieb-Liniger model of a one-dimensional gas of bosons on a finite-sized ring interacting via an attractive delta-function potential. We calculate zero-temperature correlation functions for seven particles in the vicinity of the crossover to a localized solitonic state and study the dynamics of a system of four particles quenched to attractive interactions from the ideal-gas ground state. We determine the time evolution of correlation functions, as well as their temporal averages, and discuss the role of bound states in shaping the postquench correlations and relaxation dynamics.

• The grin of Cheshire cat resurgence from supersymmetric localization

  Daniele Dorigoni, Philip Glass

  SciPost Phys. 4, 012 (2018) · published 27 February 2018 | Toggle abstract · pdf

  First we compute the $\mbox{S}^2$ partition function of the supersymmetric $\mathbb{CP}^{N-1}$ model via localization and as a check we show that the chiral ring structure can be correctly reproduced. For the $\mathbb{CP}^1$ case we provide a concrete realisation of this ring in terms of Bessel functions. We consider a weak coupling expansion in each topological sector and write it as a finite number of perturbative corrections plus an infinite series of instanton-anti-instanton contributions. To be able to apply resurgent analysis we then consider a non-supersymmetric deformation of the localized model by introducing a small unbalance between the number of bosons and fermions. The perturbative expansion of the deformed model becomes asymptotic and we analyse it within the framework of resurgence theory. Although the perturbative series truncates when we send the deformation parameter to zero we can still reconstruct non-perturbative physics out of the perturbative data in a nice example of Cheshire cat resurgence in quantum field theory. We also show that the same type of resurgence takes place when we consider an analytic continuation in the number of chiral fields from $N$ to $r\in\mathbb{R}$. Although for generic real $r$ supersymmetry is still formally preserved, we find that the perturbative expansion of the supersymmetric partition function becomes asymptotic so that we can use resurgent analysis and only at the end take the limit of integer $r$ to recover the undeformed model.

• Quantum dynamics in transverse-field Ising models from classical networks

  Markus Schmitt, Markus Heyl

  SciPost Phys. 4, 013 (2018) · published 28 February 2018 | Toggle abstract · pdf

  The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field Ising models that can be solved efficiently using Monte Carlo techniques. Our perturbative construction encodes time-evolved quantum states of spin-1/2 systems in a network of classical spins with local couplings and can be directly generalized to other spin systems and higher spins. Using this construction we compute the transient dynamics in one, two, and three dimensions including local observables, entanglement production, and Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy of this approach by comparisons to exact results. We include a mapping to equivalent artificial neural networks, which were recently introduced to provide a universal structure for classical network wave functions.