43 research outputs found
Quasiparticles in Quantum Many-Body Systems
Topologically ordered phases flamboyance a cornucopia of intriguing phenomena that cannot be perceived in the conventional phases including the most striking property of hosting anyon quasiparticles having fractional charges and fractional statistics. Such phases were discovered with the remarkable experiment of the fractional quantum Hall effect and are drawing a lot of recognition.
Realization of these phases on lattice systems and study of the anyon quasiparticles there are important and interesting avenue to research in unraveling new physics, which can not be found in the continuum, and this thesis is an important contribution in that direction. Also such lattice models hosting anyons are particularly important to control the movement of anyons while experimentally implemented with ultra-cold atoms in optical lattices. We construct lattice models by implementing analytical states and parent Hamiltonians on two-dimensional plane hosting non-Abelian anyons, which are proposed candidates for quantum computations. Such lattice models are suitable to create both quasiholes and quasielectrons in the similar way and thereby avoiding the singularity problem for the quasielectrons in continuum. Anyons in these models are found to be well-screened with proper charges and right statistics. Going beyond two dimensions, we unravel the intriguing physics of topologically ordered phases of matter in fractional dimensions such as in the fractal lattices by employing our model constructions of analytical states and parent Hamiltonians there. We find the anyons to be well-screened with right charges and statistics for all dimensions. Our work takes the first step in bridging the gap between two dimensions and one dimension in addressing topological phases which reveal new physics. Our constructions are particularly important in this context since such lattices lack translational symmetry and hence become unsuitable for the fractional Chern insulator implementations. The special features of topologically ordered phases make these difficult to probe and hence the detection of topological quantum phase transitions becomes challenging. The existing probes suffer from shortcomings uo-to a large extent and therefore construction of new type of probes become important and are on high demand. The robustness of anyon properties draw our attention to propose these as detector of topological quantum phase transitions with significant advantages including the facts that these are numerically cheaper probes and are independent of the boundary conditions. We test our probe in three different examples and find that simple properties like anyon charges detect the transitions.Topologisch geordnete Phasen extravagieren ein Füllhorn faszinierender Phänomene, die in den herkömmlichen Phasen nicht wahrgenommen werden können, einschließlich der auffälligsten Eigenschaft, Quasiteilchen mit fraktionierten Ladungen und fraktion- ierten Statistiken aufzunehmen. Solche Phasen wurden mit dem bemerkenswerten Exper- iment des fraktionierten Quanten-Hall-Effekts entdeckt und finden viel Anerkennung.
Die Realisierung dieser Phasen auf Gittersystemen und die Untersuchung der Anyon- Quasiteilchen sind wichtige und interessante Wege zur Erforschung der Entschlüsselung neuer Physik, die im Kontinuum nicht zu finden sind, und diese These ist ein wichtiger Beitrag in diese Richtung. Auch solche Gittermodelle, die Anyons enthalten, sind beson- ders wichtig, um die Bewegung von Anyons zu steuern, während sie experimentell mit ultrakalten Atomen in optischen Gittern implementiert werden. Wir konstruieren Gittermodelle, indem wir analytische Zustände und Eltern-Hamiltonianer auf einer zwei- dimensionalen Ebene implementieren, die nicht-abelsche Anyons enthält, die als Kan- didaten für Quantenberechnungen vorgeschlagen werden. Solche Gittermodelle sind geeignet, sowohl Quasi-Löcher als auch Quasielektronen auf ähnliche Weise zu erzeu- gen und dadurch das Singularitätsproblem für die Quasielektronen im Kontinuum zu vermeiden. Jeder in diesen Modellen wird mit angemessenen Gebühren und richtigen Statistiken gut überprüft. Über zwei Dimensionen hinaus enträtseln wir die faszinierende Physik topologisch geordneter Phasen der Materie in fraktionierten Dimensionen wie in den fraktalen Gittern, indem wir dort unsere Modellkonstruktionen von analytischen Zuständen und Eltern-Hamiltonianern verwenden. Wir finden, dass die Anyons mit den richtigen Gebühren und Statistiken für alle Dimensionen gut überprüft werden. Unsere Arbeit macht den ersten Schritt, um die Lücke zwischen zwei Dimensionen und einer Dimension zu schließen und topologische Phasen anzugehen, die neue Physik enthüllen. Unsere Konstruktionen sind in diesem Zusammenhang besonders wichtig, da solche Gitter keine Translationssymmetrie aufweisen und daher für die fraktionierten Chern- Isolatorimplementierungen ungeeignet werden. Die besonderen Merkmale topologisch geordneter Phasen machen es schwierig, diese zu untersuchen, und daher wird die Detek- tion topologischer Quantenphasenübergänge schwierig. Die vorhandenen Sonden leiden in hohem Maße unter Mängeln, weshalb die Konstruktion neuer Sondenarten wichtig wird und eine hohe Nachfrage besteht. Die Robustheit der Anyon-Eigenschaften lenkt unsere Aufmerksamkeit darauf, diese als Detektor für topologische Quantenphasenübergänge mit signifikanten Vorteilen vorzuschlagen, einschließlich der Tatsache, dass dies numerisch billigere Sonden sind und von den Randbedingungen unabhängig sind. Wir testen unsere Sonde in drei verschiedenen Beispielen und stellen fest, dass einfache Eigenschaften wie Ladungen die Übergänge erfassen
Chain and ladder models with two-body interactions and analytical ground states
We consider a family of spin-1/2 models with few-body, SU(2) invariant
Hamiltonians and analytical ground states related to the 1D Haldane-Shastry
wavefunction. The spins are placed on the surface of a cylinder, and the
standard 1D Haldane-Shastry model is obtained by placing the spins with equal
spacing in a circle around the cylinder. Here, we show that another interesting
family of models with two-body exchange interactions is obtained if we instead
place the spins along one or two lines parallel to the cylinder axis, giving
rise to chain and ladder models, respectively. We can change the scale along
the cylinder axis without changing the radius of the cylinder. This gives us a
parameter that controls the ratio between the circumference of the cylinder and
all other length scales in the system. We use Monte Carlo simulations and
analytical investigations to study how this ratio affects the properties of the
models. If the ratio is large, we find that the two legs of the ladder decouple
into two chains that are in a critical phase with Haldane-Shastry-like
properties. If the ratio is small, the wavefunction reduces to a product of
singlets. In between, we find that the behavior of the correlations and the
Renyi entropy depends on the distance considered. For small distances the
behavior is critical, and for long distances the correlations decay
exponentially and the entropy shows an area law behavior. The distance up to
which there is critical behavior gets larger and larger as the ratio increases.Comment: 19 pages, 16 figure
Generalized Triple-Component Fermions: Lattice Model, Fermi arcs, and Anomalous Transport
We generalize the construction of time-reversal symmetry-breaking
triple-component semimetals, transforming under the pseudospin-1
representation, to arbitrary (anti-)monopole charge , with in
the crystalline environment. The quasiparticle spectra of such systems are
composed of two dispersing bands with pseudospin projections and
energy dispersions , where , and one completely flat band at
zero energy with . We construct simple tight-binding models for such
spin-1 excitations on a cubic lattice and address the symmetries of the
generalized triple-component Hamiltonian. In accordance to the bulk-boundary
correspondence, triple-component semimetals support branches of
topological Fermi arc surface states and also accommodate a \emph{large}
anomalous Hall conductivity (in the plane), given by the separation of the triple-component nodes (in units of
). Furthermore, we compute the longitudinal magnetoconductivity, planar
Hall conductivity, and magneto thermal conductivity in these systems, which
increase as for sufficiently weak magnetic fields () due to the
nontrivial Berry curvature in the medium. A generalization of our construction
to arbitrary integer spin systems is also highlighted.Comment: 18 Pages, 8 Figures: Published version in Phys. Rev.
Shot noise classification of different conductance plateaus in a quantum point contact at the edge
The filling is the simplest paradigmatic example of a fractional
quantum Hall state, which contains counter-propagating edge modes. These modes
can be either in the coherent or equilibrated to different extents, on top of
the possible edge reconstruction. In the coherent regime, two distinct
renormalization group fixed points have been previously proposed, namely
Kane-Fischer-Polchinski and Wang-Meir-Gefen. In the equilibration regime,
different degree of thermal equilibration can exist, while charge is fully
equilibrated. Here, we show that these rich variety of models can give rise to
three possible conductance plateaus at (recently observed in
experiments), (we predict), and (observed earlier in
experiments) in a quantum point contact geometry. We identify different
mechanisms for \emph{electrical shot noise} generation at these plateaus, which
provides an experimentally accessible venue for distinguishing among the
distinct models.Comment: 12 pages, 6 figure