6,061 research outputs found
Gauge-invariant implementation of the Abelian Higgs model on optical lattices
We present a gauge-invariant effective action for the Abelian Higgs model
(scalar electrodynamics) with a chemical potential on a 1+1 dimensional
lattice. This formulation provides an expansion in the hopping parameter
which we test with Monte Carlo simulations for a broad range of the
inverse gauge coupling and small values of the scalar
self-coupling . In the opposite limit of infinitely large ,
the partition function can be written as a traced product of local tensors
which allows us to write exact blocking formulas. Their numerical
implementation requires truncations but there is no sign problem for arbitrary
values of . We show that the time continuum limit of the blocked transfer
matrix can be obtained numerically and, in the limit of infinite
and with a spin-1 truncation, the small volume energy spectrum is identical to
the low energy spectrum of a two-species Bose-Hubbard model in the limit of
large onsite repulsion. We extend this procedure for finite and
derive a spin-1 approximation of the Hamiltonian. It involves new terms
corresponding to transitions among the two species in the Bose-Hubbard model.
We propose an optical lattice implementation involving a ladder structure.Comment: 10 pages, 9 figure
Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
Abelian and non-Abelian gauge theories are of central importance in many
areas of physics. In condensed matter physics, Abelian U(1) lattice gauge
theories arise in the description of certain quantum spin liquids. In quantum
information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In
particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge
theory of the strong interactions between quarks and gluons, is
non-perturbatively regularized on a lattice. Quantum link models extend the
concept of lattice gauge theories beyond the Wilson formulation, and are well
suited for both digital and analog quantum simulation using ultracold atomic
gases in optical lattices. Since quantum simulators do not suffer from the
notorious sign problem, they open the door to studies of the real-time
evolution of strongly coupled quantum systems, which are impossible with
classical simulation methods. A plethora of interesting lattice gauge theories
suggests itself for quantum simulation, which should allow us to address very
challenging problems, ranging from confinement and deconfinement, or chiral
symmetry breaking and its restoration at finite baryon density, to color
superconductivity and the real-time evolution of heavy-ion collisions, first in
simpler model gauge theories and ultimately in QCD.Comment: 27 pages, 6 figures, invited contribution to the "Annalen der Physik"
topical issue "Quantum Simulation", guest editors: R. Blatt, I. Bloch, J. I.
Cirac, and P. Zolle
Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
Can high energy physics be simulated by low-energy, non-relativistic,
many-body systems, such as ultracold atoms? Such ultracold atomic systems lack
the type of symmetries and dynamical properties of high energy physics models:
in particular, they manifest neither local gauge invariance nor Lorentz
invariance, which are crucial properties of the quantum field theories which
are the building blocks of the standard model of elementary particles.
However, it turns out, surprisingly, that there are ways to configure atomic
system to manifest both local gauge invariance and Lorentz invariance. In
particular, local gauge invariance can arise either as an effective, low
energy, symmetry, or as an "exact" symmetry, following from the conservation
laws in atomic interactions. Hence, one could hope that such quantum simulators
may lead to new type of (table-top) experiments, that shall be used to study
various QCD phenomena, as the confinement of dynamical quarks, phase
transitions, and other effects, which are inaccessible using the currently
known computational methods.
In this report, we review the Hamiltonian formulation of lattice gauge
theories, and then describe our recent progress in constructing quantum
simulation of Abelian and non-Abelian lattice gauge theories in 1+1 and 2+1
dimensions using ultracold atoms in optical lattices.Comment: A review; 55 pages, 14 figure
Ordering in a frustrated pyrochlore antiferromagnet proximate to a spin liquid
We perform a general study of spin ordering on the pyrochlore lattice with a
3:1 proportionality of two spin polarizations. Equivalently, this describes
valence bond solid conformations of a quantum dimer model on the diamond
lattice. We determine the set of likely low temperature ordered phases, on the
assumption that the ordering is weak, i.e the system is close to a ``U(1)''
quantum spin liquid in which the 3:1 proportionality is maintained but the
spins are strongly fluctuating. The nature of the 9 ordered states we find is
determined by a ``projective symmetry'' analysis. All the phases exhibit
translational and rotational symmetry breaking, with an enlarged unit cell
containing 4 to 64 primitive cells of the underlying pyrochlore. The simplest
of the 9 phases is the same ``R'' state found earlier in a theoretical study of
the ordering on the magnetization plateau in the materials \cdaf and
\hgaf. We suggest that the spin/dimer model proposed therein undergoes a direct
transition from the spin liquid to the R state, and describe a field theory for
the universal properties of this critical point, at zero and non-zero
temperatures
Solvable Hydrodynamics of Quantum Integrable Systems
The conventional theory of hydrodynamics describes the evolution in time of
chaotic many-particle systems from local to global equilibrium. In a quantum
integrable system, local equilibrium is characterized by a local generalized
Gibbs ensemble or equivalently a local distribution of pseudo-momenta. We study
time evolution from local equilibria in such models by solving a certain
kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local
pseudo-momentum density. Explicit comparison with density matrix
renormalization group time evolution of a thermal expansion in the XXZ model
shows that hydrodynamical predictions from smooth initial conditions can be
remarkably accurate, even for small system sizes. Solutions are also obtained
in the Lieb-Liniger model for free expansion into vacuum and collisions between
clouds of particles, which model experiments on ultracold one-dimensional Bose
gases.Comment: 6+5 pages, published versio
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