276 research outputs found
Exact results for spin dynamics and fractionization in the Kitaev Model
We present certain exact analytical results for dynamical spin correlation
functions in the Kitaev Model. It is the first result of its kind in
non-trivial quantum spin models. The result is also novel: in spite of presence
of gapless propagating Majorana fermion excitations, dynamical two spin
correlation functions are identically zero beyond nearest neighbor separation,
showing existence of a gapless but short range spin liquid. An unusual,
\emph{all energy scale fractionization}of a spin -flip quanta, into two
infinitely massive -fluxes and a dynamical Majorana fermion, is shown to
occur. As the Kitaev Model exemplifies topological quantum computation, our
result presents new insights into qubit dynamics and generation of topological
excitations.Comment: 4 pages, 2 figures. Typose corrected, figure made better, clarifying
statements and references adde
Decoherence Free Subspace and entanglement by interaction with a common squeezed bath
In this work we find explicitly the decoherence free subspace (DFS) for a two
two-level system in a common squeezed vacuum bath. We also find an orthogonal
basis for the DFS composed of a symmetrical and an antisymmetrical (under
particle permutation) entangled state. For any initial symmetrical state, the
master equation has one stationary state which is the symmetrical entangled
decoherence free state. In this way, one can generate entanglement via common
squeezed bath of the two systems. If the initial state does not have a definite
parity, the stationary state depends strongly on the initial conditions of the
system and it has a statistical mixture of states which belong to the DFS. We
also study the effect of the coupling between the two-level systems on the DFS.Comment: 4 pages, 1 figur
Zeta functions and Dynamical Systems
In this brief note we present a very simple strategy to investigate dynamical
determinants for uniformly hyperbolic systems. The construction builds on the
recent introduction of suitable functional spaces which allow to transform
simple heuristic arguments in rigorous ones. Although the results so obtained
are not exactly optimal the straightforwardness of the argument makes it
noticeable.Comment: 7 pages, no figuer
Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlev\'{e} Equation. I
The degenerate third Painlev\'{e} equation, , where ,
and , and the associated tau-function are studied via the
Isomonodromy Deformation Method. Connection formulae for asymptotics of the
general as and solution and general regular as and solution are obtained.Comment: 40 pages, LaTeX2
Exploring Contractor Renormalization: Tests on the 2-D Heisenberg Antiferromagnet and Some New Perspectives
Contractor Renormalization (CORE) is a numerical renormalization method for
Hamiltonian systems that has found applications in particle and condensed
matter physics. There have been few studies, however, on further understanding
of what exactly it does and its convergence properties. The current work has
two main objectives. First, we wish to investigate the convergence of the
cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This
is important because the linked cluster expansion used to evaluate this formula
non-perturbatively is not controlled by a small parameter. Here we present a
study of three different blocking schemes which reveals some surprises and in
particular, leads us to suggest a scheme for defining successive terms in the
cluster expansion. Our second goal is to present some new perspectives on CORE
in light of recent developments to make it accessible to more researchers,
including those in Quantum Information Science. We make some comparison to
entanglement-based approaches and discuss how it may be possible to improve or
generalize the method.Comment: Completely revised version accepted by Phy Rev B; 13 pages with added
material on entropy in COR
Perturbed Sachdev-Ye-Kitaev Model: A Polaron in the Hyperbolic Plane
We study the Sachdev-Ye-Kitaev (SYK₄) model with a weak SYK₂ term of magnitude Γ beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength, J/N ≪ Γ ≪ J/√N, fluctuations of the Schwarzian mode are suppressed, and the SYK₄ mean-field solution remains valid beyond the timescale t₀ ∼ N/J up to t∗∼J/Γ². The out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent 2πT, but its prefactor scales as T at low temperatures T ≤ Γ
Perturbed Sachdev-Ye-Kitaev model: a polaron in the hyperbolic plane
We study the SYK model with a weak SYK term of magnitude
beyond the simplest perturbative limit considered previously. For intermediate
values of the perturbation strength, ,
fluctuations of the Schwarzian mode are suppressed, and the SYK mean-field
solution remains valid beyond the timescale up to . Out-of-time-order correlation function displays at short time
intervals exponential growth with maximal Lyapunov exponent , but its
prefactor scales as at low temperatures .Comment: 12 page
Modulated Floquet Topological Insulators
Floquet topological insulators are topological phases of matter generated by
the application of time-periodic perturbations on otherwise conventional
insulators. We demonstrate that spatial variations in the time-periodic
potential lead to localized quasi-stationary states in two-dimensional systems.
These states include one-dimensional interface modes at the nodes of the
external potential, and fractionalized excitations at vortices of the external
potential. We also propose a setup by which light can induce currents in these
systems. We explain these results by showing a close analogy to px+ipy
superconductors
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