2,937 research outputs found
Topology, the meson spectrum and the scalar glueball: three probes of conformality and the way it is lost
We discuss properties of non-Abelian gauge theories that change significantly
across the lower edge of the conformal window. Their probes are the topological
observables, the meson spectrum and the scalar glueball operator. The way these
quantities change tells about the way conformal symmetry is lost.Comment: 16 pages, 3 figures, contribution to Sakata Memorial KMI Workshop on
"Origin of Mass and Strong Coupling Gauge Theories (SCGT15)", 3-6 March 2015,
Nagoya Universit
Structure of Lefschetz thimbles in simple fermionic systems
The Picard-Lefschetz theory offers a promising tool to solve the sign problem
in QCD and other field theories with complex path-integral weight. In this
paper the Lefschetz-thimble approach is examined in simple fermionic models
which share some features with QCD. In zero-dimensional versions of the
Gross-Neveu model and the Nambu-Jona-Lasinio model, we study the structure of
Lefschetz thimbles and its variation across the chiral phase transition. We map
out a phase diagram in the complex four-fermion coupling plane using a thimble
decomposition of the path integral, and demonstrate an interesting link between
anti-Stokes lines and Lee-Yang zeros. In the case of nonzero mass, it is shown
that the approach to the chiral limit is singular because of intricate
cancellation between competing thimbles, which implies the necessity to sum up
multiple thimbles related by symmetry. We also consider a Chern-Simons theory
with fermions in -dimension and show how Lefschetz thimbles solve the
complex phase problem caused by a topological term. These prototypical examples
would aid future application of this framework to bona fide QCD.Comment: 37 pages, 17 figures. v2: minor changes, the version to appear in
JHE
Quasiparticle Berry curvature and Chern numbers in spin-orbit coupled bosonic Mott insulators
We study the ground-state topology and quasiparticle properties in bosonic
Mott insulators with two- dimensional spin-orbit couplings in cold atomic
optical lattices. We show that the many-body Chern and spin-Chern number can be
expressed as an integral of the quasihole Berry curvatures over the Brillouin
zone. Using a strong-coupling perturbation theory, for an experimentally
feasible spin-orbit coupling, we compute the Berry curvature and the spin Chern
number and find that these quantities can be generated purely by interactions.
We also compute the quasiparticle dispersions, spectral weights, and the
quasimomentum space distribution of particle and spin density, which can be
accessed in cold-atom experiments and used to deduce the Berry curvature and
Chern numbers
Spin-orbit coupling and semiclassical electron dynamics in noncentrosymmetric metals
Spin-orbit coupling of electrons with the crystal lattice plays a crucial
role in materials without inversion symmetry, lifting spin degeneracy of the
Bloch states and endowing the resulting nondegenerate bands with complex spin
textures and topologically nontrivial wavefunctions. We present a detailed
symmetry-based analysis of the spin-orbit coupling and the band degeneracies in
noncentrosymmetric metals. We systematically derive the semiclassical equations
of motion for fermionic quasiparticles near the Fermi surface, taking into
account both the spin-orbit coupling and the Zeeman interaction with an applied
magnetic field. Some of the lowest-order quantum corrections to the equations
of motions can be expressed in terms of a fictitious "magnetic field" in the
momentum space, which is related to the Berry curvature of the band
wavefunctions. The band degeneracy points or lines serve as sources of a
topologically nontrivial Berry curvature. We discuss the observable effects of
the wavefunction topology, focusing, in particular, on the modifications to the
Lifshitz-Onsager semiclassical quantization condition and the de Haas-van
Alphen effect in noncentrosymmetric metals.Comment: 38 LaTeX page
Strongly Correlated Topological Superconductors and Topological Phase Transitions via Green's Function
We propose several topological order parameters expressed in terms of Green's
function at zero frequency for topological superconductors, which generalizes
the previous work for interacting insulators. The coefficient in topological
field theory is expressed in terms of zero frequency Green's function. We also
study topological phase transition beyond noninteracting limit in this zero
frequency Green's function approach.Comment: 10 pages. Published versio
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