1,853 research outputs found
Digital quantum simulation of lattice gauge theories in three spatial dimensions
In the present work, we propose a scheme for digital formulation of lattice
gauge theories with dynamical fermions in 3+1 dimensions. All interactions are
obtained as a stroboscopic sequence of two-body interactions with an auxiliary
system. This enables quantum simulations of lattice gauge theories where the
magnetic four-body interactions arising in two and more spatial dimensions are
obtained without the use of perturbation theory, thus resulting in stronger
interactions compared with analogue approaches. The simulation scheme is
applicable to lattice gauge theories with either compact or finite gauge
groups. The required bounds on the digitization errors in lattice gauge
theories, due to the sequential nature of the stroboscopic time evolution, are
provided. Furthermore, an implementation of a lattice gauge theory with a
non-abelian gauge group, the dihedral group , is proposed employing the
aforementioned simulation scheme using ultracold atoms in optical lattices.Comment: 38 pages, 5 figure
Stability for a continuous SOS-interface model in a randomly perturbed periodic potential
We consider the Gibbs-measures of continuous-valued height configurations on
the -dimensional integer lattice in the presence a weakly disordered
potential. The potential is composed of Gaussians having random location and
random depth; it becomes periodic under shift of the interface perpendicular to
the base-plane for zero disorder. We prove that there exist localized
interfaces with probability one in dimensions , in a
`low-temperature' regime. The proof extends the method of
continuous-to-discrete single- site coarse graining that was previously applied
by the author for a double-well potential to the case of a non-compact image
space. This allows to utilize parts of the renormalization group analysis
developed for the treatment of a contour representation of a related
integer-valued SOS-model in [BoK1]. We show that, for a.e. fixed realization of
the disorder, the infinite volume Gibbs measures then have a representation as
superpositions of massive Gaussian fields with centerings that are distributed
according to the infinite volume Gibbs measures of the disordered
integer-valued SOS-model with exponentially decaying interactions
Quantum Crystals and Spin Chains
In this note, we discuss the quantum version of the melting crystal corner in
one, two, and three dimensions, generalizing the treatment for the quantum
dimer model. Using a mapping to spin chains we find that the two--dimensional
case (growth of random partitions) is integrable and leads directly to the
Hamiltonian of the Heisenberg XXZ ferromagnet. The three--dimensional case of
the melting crystal corner is described in terms of a system of coupled XXZ
spin chains. We give a conjecture for its mass gap and analyze the system
numerically.Comment: 34 pages, 26 picture
Quantum incompressibility of a falling Rydberg atom, and a gravitationally-induced charge separation effect in superconducting systems
Freely falling point-like objects converge towards the center of the Earth.
Hence the gravitational field of the Earth is inhomogeneous, and possesses a
tidal component. The free fall of an extended quantum object such as a hydrogen
atom prepared in a high principal-quantum-number stretch state, i.e., a
circular Rydberg atom, is predicted to fall more slowly that a classical
point-like object, when both objects are dropped from the same height from
above the Earth. This indicates that, apart from "quantum jumps," the atom
exhibits a kind of "quantum incompressibility" during free fall in
inhomogeneous, tidal gravitational fields like those of the Earth. A
superconducting ring-like system with a persistent current circulating around
it behaves like the circular Rydberg atom during free fall. Like the electronic
wavefunction of the freely falling atom, the Cooper-pair wavefunction is
"quantum incompressible." The ions of the ionic lattice of the superconductor,
however, are not "quantum incompressible," since they do not possess a globally
coherent quantum phase. The resulting difference during free fall in the
response of the nonlocalizable Cooper pairs of electrons and the localizable
ions to inhomogeneous gravitational fields is predicted to lead to a charge
separation effect, which in turn leads to a large repulsive Coulomb force that
opposes the convergence caused by the tidal, attractive gravitational force on
the superconducting system. A "Cavendish-like" experiment is proposed for
observing the charge separation effect induced by inhomogeneous gravitational
fields in a superconducting circuit. This experiment would demonstrate the
existence of a novel coupling between gravity and electricity via
macroscopically coherent quantum matter.Comment: `2nd Vienna Symposium for the Foundations of Modern Physics'
Festschrift MS for Foundations of Physic
Hamiltonian submanifolds of regular polytopes
We investigate polyhedral -manifolds as subcomplexes of the boundary
complex of a regular polytope. We call such a subcomplex {\it -Hamiltonian}
if it contains the full -skeleton of the polytope. Since the case of the
cube is well known and since the case of a simplex was also previously studied
(these are so-called {\it super-neighborly triangulations}) we focus on the
case of the cross polytope and the sporadic regular 4-polytopes. By our results
the existence of 1-Hamiltonian surfaces is now decided for all regular
polytopes.
Furthermore we investigate 2-Hamiltonian 4-manifolds in the -dimensional
cross polytope. These are the "regular cases" satisfying equality in Sparla's
inequality. In particular, we present a new example with 16 vertices which is
highly symmetric with an automorphism group of order 128. Topologically it is
homeomorphic to a connected sum of 7 copies of . By this
example all regular cases of vertices with or, equivalently, all
cases of regular -polytopes with are now decided.Comment: 26 pages, 4 figure
Dobrushin Interfaces via Reflection Positivity
We study the interfaces separating different phases of 3D systems by means of
the Reflection Positivity method. We treat discrete non-linear sigma-models,
which exhibit power-law decay of correlations at low temperatures, and we prove
the rigidity property of the interface.
Our method is applicable to the Ising and Potts models, where it simplifies
the derivation of some known results. The method also works for large-entropy
systems of continuous spins.Comment: 48 pages, 4 figures; updated for publication (to appear in CMP
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