Zero modes of various graphene confiurations from the index theorem

In this article we consider a graphene sheet that is folded in various compact geometries with arbitrary topology described by a certain genus, g. While the Hamiltonian of these systems is defined on a lattice one can take the continuous limit. The obtained Dirac-like Hamiltonian describes well the low energy modes of the initial system. Starting from first principles we derive an index theorem that corresponds to this Hamiltonian. This theorem relates the zero energy modes of the graphene sheet with the topology of the compact lattice. For g = 0 and g = 1 these results coincide with the analytical and numerical studies performed for fullerene molecules and carbon nanotubes while for higher values of g they give predictions for more complicated molecules

Graphene with geometrically induced vorticity

At half filling, the electronic structure of graphene can be modeled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field an everywhere-real Kekulé modulation of the hopping matrix elements can correspond to a nonreal Higgs field with nontrivial vorticity. This provides a natural setting for fractionally charged vortices with localized zero modes. For fullerenelike molecules we employ the index theorem to demonstrate the existence of six low-lying states that do not depend strongly on the Kekulé-induced mass gap

Seeing topological edge and bulk currents in time-of-flight images

5 pags., 5 figs.Here we provide a general methodology to directly measure the topological currents emerging in the optical lattice implementation of the Haldane model. Alongside the edge currents supported by gapless edge states, transverse currents can emerge in the bulk of the system whenever the local potential is varied in space, even if it does not cause a phase transition. In optical lattice implementations the overall harmonic potential that traps the atoms provides the boundaries of the topological phase that supports the edge currents, as well as providing the potential gradient across the topological phase that gives rise to the bulk current. Both the edge and bulk currents are resilient to several experimental parameters such as trapping potential, temperature, and disorder. We propose to investigate the properties of these currents directly from time-of-flight images with both short-time and long-time expansions.This work was supported by the EPSRC Grant No. EP/R020612/1; Spanish Projects PGC2018-094792-B-I00 (MCIU/AEI/FEDER, EU), PGC2018-094180-B-I00 (MCIU /AEI/FEDER, EU), and FIS2015-63770-P (MINECO /FEDER, EU); CAM/FEDER Project No. S2018/TCS-4342 (QUITEMAD-CM), and CSIC Research Platform PTI-001

Break-in’ Point: Somatic narratives: The convergence of arts and science in the transformation of temporal communities

Break-in’ Point, a 2012 arts and science performance and community engagement research initiative, was presented in the spring and fall semesters at the University of Leeds in the United Kingdom at Stage@Leeds. The outcome of a collaboration between dance artist A3 and theoretical physicist A2, under the direction of performance researcher A1, Break-in’ Point is based on a series of real-life encounters at intersections of arts and science – exploring force, risk, exposure and resilience. The Break-in’ Point performance offered an interrogation of the critical point at which physical, mental, and/or emotional strength give way under stress – causing structural degeneration and the experience of what lies beyond. This article is an examination of the performance, reviewing and analysing it as an imagined somatic zone – embodied encounters that transcend temporal bound-ness, compelling and igniting new possibilities – that engaged spiritual and epistemological transformation of performers and audiences. The article addresses three main periods in the life of Break-in’ Point: (1) the development period – script building and rehearsals, (2) the performance – live encounters between and among performers and audiences and (3) beyond the theatre – digital engagements in the classroom and pedagogy. The article contributes new concepts and new ways of thinking about science education, the role of digital technology in pedagogy, dance/theatre public engagement and community arts practices as practices of healing, health and resilience

Exploring interacting chiral spin chains in terms of black hole physics

In this paper we explore the properties of a one-dimensional spin chain in the presence of chiral interactions, focusing on the system's transition to distinct chiral phases for various values of the chiral coupling. By employing the mean-field theory approximation we establish a connection between this chiral system and a Dirac particle in the curved spacetime of a black hole. Surprisingly, the black-hole horizon coincides with the interface between distinct chiral phases. We examine the chiral properties of the system for homogeneous couplings and in scenarios involving position-dependent couplings that correspond to black-hole geometries. To determine the significance of interactions in the chiral chain we employ bosonization techniques and derive the corresponding Luttinger liquid model. Furthermore, we investigate the classical version of the model to understand the impact of the chiral operator on the spins and gain insight into the observed chirality. Our findings shed light on the behavior of the spin chain under the influence of the chiral operator, elucidating the implications of chirality in various contexts, including black-hole physics

Universality of Z3 parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms

Parafermions are Zn generalizations of Majorana quasiparticles, with fractional non-Abelian statistics. They can be used to encode topological qudits and perform Clifford operations by their braiding. Here we investigate the generation of quantum gates by allowing Z3 parafermions to interact in order to achieve universality. In particular, we study the form of the nontopological gate that arises through direct short-range interaction of the parafermion edge modes in a Z3 parafermion chain. We show that such an interaction gives rise to a dynamical phase gate on the encoded ground space, generating a non-Clifford gate which can be tuned to belong to even levels of the Clifford hierarchy. We illustrate how to access highly noncontextual states using this dynamical gate. Finally, we propose an experiment that simulates the braiding and dynamical evolutions of the Z3 topological states with Rydberg atom technology

Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation

We develop a consistent perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover the truncated Wigner approximation, where the evolution is still classical but the initial conditions are distributed according to the Wigner transform of the initial density matrix. Further corrections can be characterized as quantum scattering events, which appear in the form of a nonlinear response of the observable to an infinitesimal displacement of the field along its classical evolution. At the end of the paper we give a few numerical examples to test the formalism.Comment: published versio

Quantum circuits for spin and flavor degrees of freedom of quarks forming nucleons

We discuss the quantum-circuit realization of the state of a nucleon in the scope of simple symmetry groups. Explicit algorithms are presented for the preparation of the state of a neutron or a proton as resulting from the composition of their quark constituents. We estimate the computational resources required for such a simulation and design a photonic network for its implementation. Moreover, we highlight that current work on three-body interactions in lattices of interacting qubits, combined with the measurement-based paradigm for quantum information processing, may also be suitable for the implementation of these nucleonic spin states.Comment: 5 pages, 2 figures, RevTeX4; Accepted for publication in Quantum Information Processin

Quantum phases and dynamics of geometric phase in a quantum spin chain system under linear quench

We study the quantum phases of anisotropic XY spin chain system in presence and absence of adiabatic quench. A connection between geometric phase and criticality is established from the dynamical behaviour of the geometric phase for a quench induced quantum phase transition in a quantum spin chain. We predict XX criticality associated with a sequence of non-contractible geometric phases.Comment: 9 pages, 3 figures, one reference added. arXiv admin note: significant text overlap with arXiv:0908.329