16,446 research outputs found
Approximating local observables on projected entangled pair states
Tensor network states are for good reasons believed to capture ground states
of gapped local Hamiltonians arising in the condensed matter context, states
which are in turn expected to satisfy an entanglement area law. However, the
computational hardness of contracting projected entangled pair states in two
and higher dimensional systems is often seen as a significant obstacle when
devising higher-dimensional variants of the density-matrix renormalisation
group method. In this work, we show that for those projected entangled pair
states that are expected to provide good approximations of such ground states
of local Hamiltonians, one can compute local expectation values in
quasi-polynomial time. We therefore provide a complexity-theoretic
justification of why state-of-the-art numerical tools work so well in practice.
We comment on how the transfer operators of such projected entangled pair
states have a gap and discuss notions of local topological quantum order. We
finally turn to the computation of local expectation values on quantum
computers, providing a meaningful application for a small-scale quantum
computer.Comment: 7 pages, 1 figure, minor changes in v
Pattern recognition on a quantum computer
By means of a simple example it is demonstrated that the task of finding and
identifying certain patterns in an otherwise (macroscopically) unstructured
picture (data set) can be accomplished efficiently by a quantum computer.
Employing the powerful tool of the quantum Fourier transform the proposed
quantum algorithm exhibits an exponential speed-up in comparison with its
classical counterpart. The digital representation also results in a
significantly higher accuracy than the method of optical filtering. PACS:
03.67.Lx, 03.67.-a, 42.30.Sy, 89.70.+c.Comment: 6 pages RevTeX, 1 figure, several correction
The Geometry of the Master Equation and Topological Quantum Field Theory
In Batalin-Vilkovisky formalism a classical mechanical system is specified by
means of a solution to the {\sl classical master equation}. Geometrically such
a solution can be considered as a -manifold, i.e. a super\m equipped with
an odd vector field obeying and with -invariant odd
symplectic structure. We study geometry of -manifolds. In particular, we
describe some construction of -manifolds and prove a classification theorem
(under certain conditions).
We apply these geometric constructions to obtain in natural way the action
functionals of two-dimensional topological sigma-models and to show that the
Chern-Simons theory in BV-formalism arises as a sigma-model with target space
. (Here stands for a Lie algebra and denotes
parity inversion.)Comment: 29 pages, Plain TeX, minor modifications in English are made by Jim
Stasheff, some misprints are corrected, acknowledgements and references adde
Duality Symmetry in the Schwarz-Sen Model
The continuous extension of the discrete duality symmetry of the Schwarz-Sen
model is studied. The corresponding infinitesimal generator turns out to be
local, gauge invariant and metric independent. Furthermore, commutes with
all the conformal group generators. We also show that is equivalent to the
non---local duality transformation generator found in the Hamiltonian
formulation of Maxwell theory. We next consider the Batalin--Fradkin-Vilkovisky
formalism for the Maxwell theory and demonstrate that requiring a local duality
transformation lead us to the Schwarz--Sen formulation. The partition functions
are shown to be the same which implies the quantum equivalence of the two
approaches.Comment: 10 pages, latex, small changes, final version to appear in Phys. Rev.
Intertwining Laplace Transformations of Linear Partial Differential Equations
We propose a generalization of Laplace transformations to the case of linear
partial differential operators (LPDOs) of arbitrary order in R^n. Practically
all previously proposed differential transformations of LPDOs are particular
cases of this transformation (intertwining Laplace transformation, ILT). We
give a complete algorithm of construction of ILT and describe the classes of
operators in R^n suitable for this transformation.
Keywords: Integration of linear partial differential equations, Laplace
transformation, differential transformationComment: LaTeX, 25 pages v2: minor misprints correcte
Functionals and the Quantum Master Equation
The quantum master equation is usually formulated in terms of functionals of
the components of mappings from a space-time manifold M into a
finite-dimensional vector space. The master equation is the sum of two terms
one of which is the anti-bracket (odd Poisson bracket) of functionals and the
other is the Laplacian of a functional. Both of these terms seem to depend on
the fact that the mappings on which the functionals act are vector-valued. It
turns out that neither this Laplacian nor the anti-bracket is well-defined for
sections of an arbitrary vector bundle. We show that if the functionals are
permitted to have their values in an appropriate graded tensor algebra whose
factors are the dual of the space of smooth functions on M, then both the
anti-bracket and the Laplace operator can be invariantly defined. Additionally,
one obtains a new anti-bracket for ordinary functionals.Comment: 21 pages, Late
Access to Government Information Is a Foundation of American Democracy—But the Courts Don\u27t Get It
String Network and U-Duality
We discuss the generalization of recently discovered BPS configurations,
corresponding to the planar string networks, to non-planar ones by considering
the U-duality symmetry of type II string theory in various dimensions. As an
explicit example, we analyze the string solutions in 8-dimensional space-time,
carrying SL(3) charges, and show that by aligning the strings along various
directions appropriately, one can obtain a string network which preserves 1/8
supersymmetry.Comment: 8 pages, latex, references added, minor modification
Zero-Mode Dynamics of String Webs
At sufficiently low energy the dynamics of a string web is dominated by zero
modes involving rigid motion of the internal strings. The dimension of the
associated moduli space equals the maximal number of internal faces in the web.
The generic web moduli space has boundaries and multiple branches, and for webs
with three or more faces the geometry is curved. Webs can also be studied in a
lift to M-theory, where a string web is replaced by a membrane wrapped on a
holomorphic curve in spacetime. In this case the moduli space is complexified
and admits a Kaehler metric.Comment: LaTeX, 17 pages, 5 eps figures; v2: references adde
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