1,105 research outputs found
Lattice theory for nonrelativistic fermions in one spatial dimension
I derive a loop representation for the canonical and grand-canonical
partition functions for an interacting four-component Fermi gas in one spatial
dimension and an arbitrary external potential. The representation is free of
the "sign problem" irrespective of population imbalance, mass imbalance, and to
a degree, sign of the interaction strength. This property is in sharp contrast
with the analogous three-dimensional two-component interacting Fermi gas, which
exhibits a sign problem in the case of unequal masses, chemical potentials, and
repulsive interactions. The one-dimensional system is believed to exhibit many
phenomena in common with its three-dimensional counterpart, including an analog
of the BCS-BEC crossover, and nonperturbative universal few- and many-body
physics at scattering lengths much larger than the range of interaction, making
the theory an interesting candidate for numerical study. Positivity of the
probability measure for the partition function allows for a mean-field
treatment of the model; here, I present such an analysis for the interacting
Fermi gas in the SU(4) (unpolarized, mass-symmetric) limit, and demonstrate
that there exists a phase in which a continuum limit may be defined.Comment: 12 pages, 6 figures, references adde
Bipolaron-SO(5) Non-Fermi Liquid in a Two-channel Anderson Model with Phonon-assisted Hybridizations
We analyze non-Fermi liquid (NFL) properties along a line of critical points
in a two-channel Anderson model with phonon-assisted hybridizations. We succeed
in identifying hidden nonmagnetic SO(5) degrees of freedom for
valence-fluctuation regime and analyze the model on the basis of boundary
conformal field theory. We find that the NFL spectra along the critical line,
which is the same as those in the two-channel Kondo model, can be alternatively
derived by a fusion in the nonmagnetic SO(5) sector. The leading irrelevant
operators near the NFL fixed points vary as a function of Coulomb repulsion U;
operators in the spin sector dominate for large U, while those in the SO(5)
sector do for small U, and we confirm this variation in our numerical
renormalization group calculations. As a result, the thermodynamic singularity
for small U differs from that of the conventional two-channel Kondo problem.
Especially, the impurity contribution to specific heat is proportional to
temperature and bipolaron fluctuations, which are coupled electron-phonon
fluctuations, diverge logarithmically at low temperatures for small U.Comment: 16 pages, 4 figures, 3 table
Boundary-induced violation of the Dirac fermion parity and its signatures in local and global tunneling spectra of graphene
Extended defects in graphene, such as linear edges, break the translational
invariance and can also have an impact on the symmetries specific to massless
Dirac-like quasiparticles in this material. The paper examines the consequences
of a broken Dirac fermion parity in the framework of the effective boundary
conditions varying from the Berry-Mondragon mass confinement to a zigzag edge.
The parity breaking reflects the structural sublattice asymmetry of zigzag-type
edges and is closely related to the previously predicted time-reversal
symmetric edge states. We calculate the local and global densities of the edge
states and show that they carry a specific polarization, resembling, to some
extent, that of spin-polarized materials. The lack of the parity leads to a
nonanalytical particle-hole asymmetry in the edge-state properties. We use our
findings to interpret recently observed tunneling spectra in zigzag-terminated
graphene. We also propose a graphene-based tunneling device where the
particle-hole asymmetric edge states result in a strongly nonlinear
conductance-voltage characteristics, which could be used to manipulate the
tunneling transport.Comment: 8 pages, 5 figures, to be published in Phys. Rev.
Complexified Path Integrals and the Phases of Quantum Field Theory
The path integral by which quantum field theories are defined is a particular
solution of a set of functional differential equations arising from the
Schwinger action principle. In fact these equations have a multitude of
additional solutions which are described by integrals over a complexified path.
We discuss properties of the additional solutions which, although generally
disregarded, may be physical with known examples including spontaneous symmetry
breaking and theta vacua. We show that a consideration of the full set of
solutions yields a description of phase transitions in quantum field theories
which complements the usual description in terms of the accumulation of
Lee-Yang zeroes. In particular we argue that non-analyticity due to the
accumulation of Lee-Yang zeros is related to Stokes phenomena and the collapse
of the solution set in various limits including but not restricted to, the
thermodynamic limit. A precise demonstration of this relation is given in terms
of a zero dimensional model. Finally, for zero dimensional polynomial actions,
we prove that Borel resummation of perturbative expansions, with several
choices of singularity avoiding contours in the complex Borel plane, yield
inequivalent solutions of the action principle equations.Comment: 15 pages, 9 figures (newer version has better images
The Potts-q random matrix model : loop equations, critical exponents, and rational case
In this article, we study the q-state Potts random matrix models extended to
branched polymers, by the equations of motion method. We obtain a set of loop
equations valid for any arbitrary value of q. We show that, for q=2-2 \cos {l
\over r} \pi (l, r mutually prime integers with l < r), the resolvent satisfies
an algebraic equation of degree 2 r -1 if l+r is odd and r-1 if l+r is even.
This generalizes the presently-known cases of q=1, 2, 3. We then derive for any
0 \leq q \leq 4 the Potts-q critical exponents and string susceptibility.Comment: 7 pages, submitted to Phys. Letters
The scaling limit of the energy correlations in non integrable Ising models
We obtain an explicit expression for the multipoint energy correlations of a
non solvable two-dimensional Ising models with nearest neighbor ferromagnetic
interactions plus a weak finite range interaction of strength , in a
scaling limit in which we send the lattice spacing to zero and the temperature
to the critical one. Our analysis is based on an exact mapping of the model
into an interacting lattice fermionic theory, which generalizes the one
originally used by Schultz, Mattis and Lieb for the nearest neighbor Ising
model. The interacting model is then analyzed by a multiscale method first
proposed by Pinson and Spencer. If the lattice spacing is finite, then the
correlations cannot be computed in closed form: rather, they are expressed in
terms of infinite, convergent, power series in . In the scaling limit,
these infinite expansions radically simplify and reduce to the limiting energy
correlations of the integrable Ising model, up to a finite renormalization of
the parameters. Explicit bounds on the speed of convergence to the scaling
limit are derived.Comment: 75 pages, 11 figure
Collinearity, convergence and cancelling infrared divergences
The Lee-Nauenberg theorem is a fundamental quantum mechanical result which
provides the standard theoretical response to the problem of collinear and
infrared divergences. Its argument, that the divergences due to massless
charged particles can be removed by summing over degenerate states, has been
successfully applied to systems with final state degeneracies such as LEP
processes. If there are massless particles in both the initial and final
states, as will be the case at the LHC, the theorem requires the incorporation
of disconnected diagrams which produce connected interference effects at the
level of the cross-section. However, this aspect of the theory has never been
fully tested in the calculation of a cross-section. We show through explicit
examples that in such cases the theorem introduces a divergent series of
diagrams and hence fails to cancel the infrared divergences. It is also
demonstrated that the widespread practice of treating soft infrared divergences
by the Bloch-Nordsieck method and handling collinear divergences by the
Lee-Nauenberg method is not consistent in such cases.Comment: 29 pages, 17 figure
Electron-positron pair creation in a vacuum by an electromagnetic field in 3+1 and lower dimensions
We calculate the probability of electron-positron pair creation in vacuum in
3+1 dimensions by an external electromagnetic field composed of a constant
uniform electric field and a constant uniform magnetic field, both of arbitrary
magnitudes and directions. The same problem is also studied in 2+1 and 1+1
dimensions in appropriate external fields and similar results are obtained.Comment: REVTeX, 10 pages, no figure, a brief note and some more references
added in the proo
The Euler-Heisenberg Lagrangian beyond one loop
We review what is presently known about higher loop corrections to the
Euler-Heisenberg Lagrangian and its Scalar QED analogue. The use of those
corrections as a tool for the study of the properties of the QED perturbation
series is outlined. As a further step in a long-term effort to prove or
disprove the convergence of the N photon amplitudes in the quenched
approximation, we present a parameter integral representation of the three-loop
Euler-Heisenberg Lagrangian in 1+1 dimensional QED, obtained in the worldline
formalism.Comment: 11 pages, 2 figures, talk given by Christian Schubert at QFEXT11,
Benasque, Spain, Sept. 18-24, 2011, to appear in the conference proceeding
Conformal invariance in 2-dimensional discrete field theory
A discretized massless wave equation in two dimensions, on an appropriately
chosen square lattice, exactly reproduces the solutions of the corresponding
continuous equations. We show that the reason for this exact solution property
is the discrete analog of conformal invariance present in the model, and find
more general field theories on a two-dimensional lattice that exactly solve
their continuous limit equations. These theories describe in general
non-linearly coupled bosonic and fermionic fields and are similar to the
Wess-Zumino-Witten model.Comment: 18 pages, RevTeX, 2 figures included; revision of title and
introductio
- …