8 research outputs found
Pentaquarks with one heavy antiquark
Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2017, Tutor: Joan Soto i RieraThe aim of this project is to construct a complete classification of all possible ground wave functions of a pentaquark consisting of four light quarks and a heavy antiquark. The existence of such a particle has not been established yet, but the theoretical interest in studying properties of pentaquarks has raised since the discovery, in July 2015, of an exotic baryon consisting of three light quarks (two up and one down) and a heavy pair charm-anticharm. We will study the symmetries of the internal degrees of freedom of avour, colour and spin by computing the tensor product of irreducible representations of SU(3) and SU(2), and then identify which results correspond to particles that hold the quark model symmetry principles and thus could exist and might be discovered in the future
Lie groups and algebras in particle physics
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Laura Costa Farràs[en] The present document is a first introduction to the Theory of Lie Groups and Lie Algebras and their representations. Lie Groups verify the characteristics of both a group and a smooth manifold structure. They arise from the need to study continuous symmetries, which is exactly what is needed for some branches of modern Theoretical Physics and in particular for quantum mechanics.
The main objectives of this work are the following. First of all, to introduce the notion of a matrix Lie Group and see some examples, which will lead us to the general notion of Lie Group. From there, we will define the exponential map, which is the link to the notion of Lie Algebras. Every matrix Lie Group comes attached
somehow to its Lie Algebra. Next we will introduce some notions of Representation Theory. Using the detailed examples of SU(2) and SU(3), we will study how the irreducible representations of certain types of Lie Groups are constructed through their Lie Algebras. Finally, we will state a general classification for the irreducible
representations of the complex semisimple Lie Algebras
The Coming Decades of Quantum Simulation
Contemporary quantum technologies face major difficulties in fault tolerant
quantum computing with error correction, and focus instead on various shades of
quantum simulation (Noisy Intermediate Scale Quantum, NISQ) devices, analogue
and digital quantum simulators and quantum annealers. There is a clear need and
quest for such systems that, without necessarily simulating quantum dynamics of
some physical systems, can generate massive, controllable, robust, entangled,
and superposition states. This will, in particular, allow the control of
decoherence, enabling the use of these states for quantum communications (e.g.
to achieve efficient transfer of information in a safer and quicker way),
quantum metrology, sensing and diagnostics (e.g. to precisely measure phase
shifts of light fields, or to diagnose quantum materials). In this Chapter we
present a vision of the golden future of quantum simulators in the decades to
come
Topological properties of the long-range Kitaev chain with Aubry-Andr\'e-Harper modulation
We present a detailed study of the topological properties of the Kitaev chain
with long-range pairing terms and in the presence of an Aubry-Andr\'e-Harper
on-site potential. Specifically, we consider algebraically decaying
superconducting pairing amplitudes; the exponent of this decay is found to
determine a critical pairing strength, below which the chain remains
topologically trivial. Above the critical pairing, topological edge modes are
observed in the central gap. For sufficiently fast decay of the pairing, these
modes are identified as Majorana zero-modes. However, if the pairing term
decays slowly, the modes become massive Dirac modes. Interestingly, these
massive modes still exhibit a true level crossing at zero energy, which points
towards an initimate relation to Majorana physics. We also observe a clear lack
of bulk-boundary correspondence in the long-range system, where bulk
topological invariants remain constant, while dramatic changes appear in the
behavior at the edge of the system. In addition to the central gap around zero
energy, the Aubry-Andr\'e-Harper potential also leads to other energy gaps at
non-zero energy. As for the analogous short-range model, the edge modes in
these gaps can be characterized through a 2D Chern invariant. However, in
contrast to the short-range model, this topological invariant does not
correspond to the number of edge mode crossings anymore. This provides another
example for the weakening of the bulk-boundary correspondence occurring in this
model. Finally, we discuss possible realizations of the model with ultracold
atoms and condensed matter systems.Comment: 17 pages, 12 figures, comments are welcom
A hybrid quantum algorithm to detect conical intersections
Conical intersections are topologically protected crossings between the
potential energy surfaces of a molecular Hamiltonian, known to play an
important role in chemical processes such as photoisomerization and
non-radiative relaxation. They are characterized by a non-zero Berry phase,
which is a topological invariant defined on a closed path in atomic coordinate
space, taking the value when the path encircles the intersection
manifold. In this work, we show that for real molecular Hamiltonians, the Berry
phase can be obtained by tracing a local optimum of a variational ansatz along
the chosen path and estimating the overlap between the initial and final state
with a control-free Hadamard test. Moreover, by discretizing the path into
points, we can use single Newton-Raphson steps to update our state
non-variationally. Finally, since the Berry phase can only take two discrete
values (0 or ), our procedure succeeds even for a cumulative error bounded
by a constant; this allows us to bound the total sampling cost and to readily
verify the success of the procedure. We demonstrate numerically the application
of our algorithm on small toy models of the formaldimine molecule
(\ce{H2C=NH}).Comment: 15 + 10 pages, 4 figure
Initial state preparation for quantum chemistry on quantum computers
Quantum algorithms for ground-state energy estimation of chemical systems
require a high-quality initial state. However, initial state preparation is
commonly either neglected entirely, or assumed to be solved by a simple product
state like Hartree-Fock. Even if a nontrivial state is prepared, strong
correlations render ground state overlap inadequate for quality assessment. In
this work, we address the initial state preparation problem with an end-to-end
algorithm that prepares and quantifies the quality of initial states,
accomplishing the latter with a new metric -- the energy distribution. To be
able to prepare more complicated initial states, we introduce an implementation
technique for states in the form of a sum of Slater determinants that exhibits
significantly better scaling than all prior approaches. We also propose
low-precision quantum phase estimation (QPE) for further state quality
refinement. The complete algorithm is capable of generating high-quality states
for energy estimation, and is shown in select cases to lower the overall
estimation cost by several orders of magnitude when compared with the best
single product state ansatz. More broadly, the energy distribution picture
suggests that the goal of QPE should be reinterpreted as generating
improvements compared to the energy of the initial state and other classical
estimates, which can still be achieved even if QPE does not project directly
onto the ground state. Finally, we show how the energy distribution can help in
identifying potential quantum advantage
Higher-Order Topological Peierls Insulator in a Two-Dimensional Atom-Cavity System
: In this work, we investigate a two-dimensional system of ultracold bosonic atoms inside an optical cavity, and show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The latter corresponds to a 2D Peierls transition, generalizing the spontaneous bond dimerization driven by phonon-electron interactions in the 1D Su-Schrieffer-Heeger (SSH) model. Here the bosonic nature of the atoms plays a crucial role to generate the phase, as similar generalizations with fermionic matter do not lead to a plaquette structure. Similar to the SSH model, we show how this pattern opens a nontrivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states, that we characterize by means of a many-body topological invariant and through its entanglement structure. Finally, we demonstrate how this higher-order topological Peierls insulator can be readily prepared in atomic experiments through adiabatic protocols. Our work thus shows how atomic quantum simulators can be harnessed to investigate novel strongly correlated topological phenomena beyond those observed in natural materials