941 research outputs found
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
The Center symmetry and its spontaneous breakdown at high temperatures
We examine the role of the center Z(N) of the gauge group SU(N) in gauge
theories. In this pedagogical article, we discuss, among other topics, the
center symmetry and confinement and deconfinement in gauge theories and
associated finite-temperature phase transitions. We also look at universal
properties of domain walls separating distinct confined and deconfined bulk
phases, including a description of how QCD color-flux strings can end on
color-neutral domain walls, and unusual finite-volume dependence in which
quarks in deconfined bulk phase seem to be "confined".Comment: LaTex, 35 pages, 6 figures, uses sprocl.sty. To be published in the
Festschrift in honor of B.L. Ioffe, "At the Frontier of Particle Physics/
Handbook of QCD", edited by M. Shifma
An Introduction to Chiral Symmetry on the Lattice
The chiral symmetry of QCD is of central
importance for the nonperturbative low-energy dynamics of light quarks and
gluons. Lattice field theory provides a theoretical framework in which these
dynamics can be studied from first principles. The implementation of chiral
symmetry on the lattice is a nontrivial issue. In particular, local lattice
fermion actions with the chiral symmetry of the continuum theory suffer from
the fermion doubling problem. The Ginsparg-Wilson relation implies L\"uscher's
lattice variant of chiral symmetry which agrees with the usual one in the
continuum limit. Local lattice fermion actions that obey the Ginsparg-Wilson
relation have an exact chiral symmetry, the correct axial anomaly, they obey a
lattice version of the Atiyah-Singer index theorem, and still they do not
suffer from the notorious doubling problem. The Ginsparg-Wilson relation is
satisfied exactly by Neuberger's overlap fermions which are a limit of Kaplan's
domain wall fermions, as well as by Hasenfratz and Niedermayer's classically
perfect lattice fermion actions. When chiral symmetry is nonlinearly realized
in effective field theories on the lattice, the doubling problem again does not
arise. This review provides an introduction to chiral symmetry on the lattice
with an emphasis on the basic theoretical framework.Comment: (41 pages, to be published in Prog. Part. Nucl. Phys. Vol. 53, issue
1 (2004)
Perfect Actions with Chemical Potential
We show how to include a chemical potential \mu in perfect lattice actions.
It turns out that the standard procedure of multiplying the quark fields \Psi,
\bar\Psi at Euclidean time t by \exp(\pm \mu t), respectively, is perfect. As
an example, the case of free fermions with chemical potential is worked out
explicitly. Even after truncation, cut-off effects in the pressure and the
baryon density are small. Using a (quasi-)perfect action, numerical QCD
simulations for non-zero chemical potential become more powerful, because
coarse lattices are sufficient for extracting continuum physics.Comment: 10 pages, LaTex, 3 figure
Very High Precision Determination of Low-Energy Parameters: The 2-d Heisenberg Quantum Antiferromagnet as a Test Case
The 2-d spin 1/2 Heisenberg antiferromagnet with exchange coupling is
investigated on a periodic square lattice of spacing at very small
temperatures using the loop-cluster algorithm. Monte Carlo data for the
staggered and uniform susceptibilities are compared with analytic results
obtained in the systematic low-energy effective field theory for the staggered
magnetization order parameter. The low-energy parameters of the effective
theory, i.e.\ the staggered magnetization density , the spin stiffness , and the spin wave
velocity are determined with very high precision. Our study
may serve as a test case for the comparison of lattice QCD Monte Carlo data
with analytic predictions of the chiral effective theory for pions and
nucleons, which is vital for the quantitative understanding of the strong
interaction at low energies.Comment: 5 pages, 4 figures, 1 tabl
Meron-Cluster Solution of Fermion and Other Sign Problems
Numerical simulations of numerous quantum systems suffer from the notorious
sign problem. Important examples include QCD and other field theories at
non-zero chemical potential, at non-zero vacuum angle, or with an odd number of
flavors, as well as the Hubbard model for high-temperature superconductivity
and quantum antiferromagnets in an external magnetic field. In all these cases
standard simulation algorithms require an exponentially large statistics in
large space-time volumes and are thus impossible to use in practice.
Meron-cluster algorithms realize a general strategy to solve severe sign
problems but must be constructed for each individual case. They lead to a
complete solution of the sign problem in several of the above cases.Comment: 15 pages,LATTICE9
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