47,845 research outputs found
Phase Diagram of the Spin-Orbital model on the Square Lattice
We study the phase diagram of the spin-orbital model in both the weak and
strong limits of the quartic spin-orbital exchange interaction. This allows us
to study quantum phase transitions in the model and to approach from both sides
the most interesting intermediate-coupling regime and in particular the
SU(4)-symmetric point of the Hamiltonian. It was suggested earlier by Li et al
[Phys.Rev.Lett. vol. 81, 3527 (1999)] that at this point the ground state of
the system is a plaquette spin-orbital liquid. We argue that the state is more
complex. There is plaquette order, but it is anisotropic: bonds in one
direction are stronger than those in the perpendicular direction. This order is
somewhat similar to that found recently in the frustrated J_1-J_2 Heisenberg
spin model.Comment: 8 pages, 4 Postscript figure
A generalization of the injectivity condition for Projected Entangled Pair States
We introduce a family of tensor network states that we term semi-injective
Projected Entangled-Pair States (PEPS). They extend the class of injective PEPS
and include other states, like the ground states of the AKLT and the CZX models
in square lattices. We construct parent Hamiltonians for which semi-injective
PEPS are unique ground states. We also determine the necessary and sufficient
conditions for two tensors to generate the same family of such states in two
spatial dimensions. Using this result, we show that the third cohomology
labeling of Symmetry Protected Topological phases extends to semi-injective
PEPS.Comment: 63 page
Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque
New exact analytic solutions are introduced for the rotational motion of a
rigid body having two equal principal moments of inertia and subjected to an
external torque which is constant in magnitude. In particular, the solutions
are obtained for the following cases: (1) Torque parallel to the symmetry axis
and arbitrary initial angular velocity; (2) Torque perpendicular to the
symmetry axis and such that the torque is rotating at a constant rate about the
symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial
angular velocity perpendicular to the symmetry axis, with the torque being
fixed with the body. In addition to the solutions for these three forced cases,
an original solution is introduced for the case of torque-free motion, which is
simpler than the classical solution as regards its derivation and uses the
rotation matrix in order to describe the body orientation. This paper builds
upon the recently discovered exact solution for the motion of a rigid body with
a spherical ellipsoid of inertia. In particular, by following Hestenes' theory,
the rotational motion of an axially symmetric rigid body is seen at any instant
in time as the combination of the motion of a "virtual" spherical body with
respect to the inertial frame and the motion of the axially symmetric body with
respect to this "virtual" body. The kinematic solutions are presented in terms
of the rotation matrix. The newly found exact analytic solutions are valid for
any motion time length and rotation amplitude. The present paper adds further
elements to the small set of special cases for which an exact solution of the
rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The
following typos present in the Journal version are HERE corrected: 1)
Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3)
Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6
A computational group theoretic symmetry reduction package for the SPIN model checker
Symmetry reduced model checking is hindered by two problems: how to identify state space symmetry when systems are not fully symmetric, and how to determine equivalence of states during search. We present TopSpin, a fully automatic symmetry reduction package for the Spin model checker. TopSpin uses the Gap computational algebra system to effectively detect state space symmetry from the associated Promela specification, and to choose an efficient symmetry reduction strategy by classifying automorphism groups as a disjoint/wreath product of subgroups. We present encouraging experimental results for a variety of Promela examples
Squark production in R-symmetric SUSY with Dirac gluinos: NLO corrections
R-symmetry leads to a distinct realisation of SUSY with a significantly
modified coloured sector featuring a Dirac gluino and a scalar colour octet
(sgluon). We present the impact of R-symmetry on squark production at the 13
TeV LHC. We study the total cross sections and their NLO corrections from all
strongly interacting states, their dependence on the Dirac gluino mass and
sgluon mass as well as their systematics for selected benchmark points. We find
that tree-level cross sections in the R-symmetric model are reduced compared to
the MSSM but the NLO K-factors are generally larger in the order of ten to
twenty per cent. In the course of this work we derive the required DREG
DRED transition counterterms and necessary on-shell renormalisation constants.
The real corrections are treated using FKS subtraction, with results cross
checked against an independent calculation employing the two cut phase space
slicing method.Comment: 46 pages, 15 figures; updated to match published versio
The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
We present a compendium of numerical simulation techniques, based on tensor
network methods, aiming to address problems of many-body quantum mechanics on a
classical computer. The core setting of this anthology are lattice problems in
low spatial dimension at finite size, a physical scenario where tensor network
methods, both Density Matrix Renormalization Group and beyond, have long proven
to be winning strategies. Here we explore in detail the numerical frameworks
and methods employed to deal with low-dimension physical setups, from a
computational physics perspective. We focus on symmetries and closed-system
simulations in arbitrary boundary conditions, while discussing the numerical
data structures and linear algebra manipulation routines involved, which form
the core libraries of any tensor network code. At a higher level, we put the
spotlight on loop-free network geometries, discussing their advantages, and
presenting in detail algorithms to simulate low-energy equilibrium states.
Accompanied by discussions of data structures, numerical techniques and
performance, this anthology serves as a programmer's companion, as well as a
self-contained introduction and review of the basic and selected advanced
concepts in tensor networks, including examples of their applications.Comment: 115 pages, 56 figure
Nuclear matter in the chiral limit and the in-medium chiral condensate
We investigate nuclear matter, i.e. the nuclear equation-of-state (EOS) as
well as the relativistic mean fields in the chiral limit. The investigations
are based on a chiral nucleon-nucleon EFT interaction where the explicit and
implicit pion mass dependence is known up to next-to-leading order. The nuclear
bulk properties are found to remain fairly stable in the chiral limit. Based on
the same interaction the in-medium scalar condensate is derived, both in
Hartree-Fock approximation as well as from the Brueckner G-matrix, making
thereby use of the Hellman-Feynman theorem. Short distance physics which
determines the reduction of the in-medium nucleon mass is found to play only a
minor role for the reduction of the chiral condensate.Comment: 30 pages, 5 figs. To appear in Nuclear Physics
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