22,706 research outputs found
A Characterization of in Terms of Character Zeros
The aim of this paper is to classify the finite nonsolvable groups in which
every irreducible character of even degree vanishes on at most two conjugacy
classes. As a corollary, it is shown that are the only nonsolvable
groups in which every irreducible character of even degree vanishes on just one
conjugacy class.Comment: 11 page
Two-parameter Quantum Group of Exceptional Type G_2 and Lusztig's Symmetries
We give the defining structure of two-parameter quantum group of type G_2
defined over a field {\Bbb Q}(r,s) (with r\ne s), and prove the Drinfel'd
double structure as its upper and lower triangular parts, extending an earlier
result of [BW1] in type A and a recent result of [BGH1] in types B, C, D. We
further discuss the Lusztig's Q-isomorphisms from U_{r,s}(G_2) to its
associated object U_{s^{-1},r^{-1}}(G_2), which give rise to the usual
Lusztig's symmetries defined not only on U_q(G_2) but also on the centralized
quantum group U_q^c(G_2) only when r=s^{-1}=q. (This also reflects the
distinguishing difference between our newly defined two-parameter object and
the standard Drinfel'd-Jimbo quantum groups). Some interesting (r,s)-identities
holding in U_{r,s}(G_2) are derived from this discussion.Comment: 34 pages. Pacific J. Math. (to appear in its simplified version
Multitask Deep Learning with Spectral Knowledge for Hyperspectral Image Classification
In this letter, we propose a multitask deep learning method for
classification of multiple hyperspectral data in a single training. Deep
learning models have achieved promising results on hyperspectral image
classification, but their performance highly rely on sufficient labeled
samples, which are scarce on hyperspectral images. However, samples from
multiple data sets might be sufficient to train one deep learning model,
thereby improving its performance. To do so, we trained an identical feature
extractor for all data, and the extracted features were fed into corresponding
Softmax classifiers. Spectral knowledge was introduced to ensure that the
shared features were similar across domains. Four hyperspectral data sets were
used in the experiments. We achieved higher classification accuracies on three
data sets (Pavia University, Pavia Center, and Indian Pines) and competitive
results on the Salinas Valley data compared with the baseline. Spectral
knowledge was useful to prevent the deep network from overfitting when the data
shared similar spectral response. The proposed method tested on two deep CNNs
successfully shows its ability to utilize samples from multiple data sets and
enhance networks' performance.Comment: Accepted by IEEE GRS
Attractive electron-electron interaction induced by geometric phase in a Bloch band
We investigate electron pairing in the presence of the Berry curvature field
that ubiquitously exists in ferromagnetic metals with spin-orbit coupling. We
show that a sufficiently strong Berry curvature field on the Fermi surface can
transform a repulsive interaction between electrons into an attractive one in
the p-wave channel. We also reveal a topological possibility for turning an
attractive s-wave interaction into one in the p-wave channel, even if the Berry
curvature field only exists inside the Fermi surface (circle). We speculate
that these novel mechanism might be relevant to the recently discovered
ferromagnetic superconductors such as UGe and URhGe.Comment: 4 pages, 3 figure
Are degenerate groundstates induced by spontaneous symmetry breakings in quantum phase transitions?
Recently, emergent symmetry is one of fast-growing intriguing issues in
many-body systems. Its roles and consequential physics have not been well
understood in quantum phase transitions. Emergent symmetry of degenerate
groundstates is discussed in possible connection to spontaneous symmetry
breaking within the Landau theory. For a clear discussion, a quantum spin-
plaquette chain system is shown to have rich emergent symmetry phenomena in its
groundstates. A covering symmetry group over all emergent symmetries
responsible for degenerate groundstates in the plaquette chain system is found
to correspond to a largest common symmetry group of constituent Hamiltonians
describing the plaquette system. Consequently, this result suggests that, as a
guiding symmetry principle in quantum phase transitions, {\it degenerate
groundstates are induced by a spontaneous breaking of symmetries belonging to a
largest common symmetry group of continent Hamiltonians describing a given
system but can have more symmetries than the largest common symmetry}.Comment: 18 pages,18 figure
Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach
We propose a method to construct universal order parameters for quantum phase
transitions in many-body lattice systems. The method exploits the
-orthogonality of a few near-degenerate lowest states of the Hamiltonian
describing a given finite-size system, which makes it possible to perform
finite-size scaling and take full advantage of currently available numerical
algorithms. An explicit connection is established between the fidelity per site
between two -orthogonal states and the energy gap between the ground state
and low-lying excited states in the finite-size system. The physical
information encoded in this gap arising from finite-size fluctuations clarifies
the origin of the universal order parameter.We demonstrate the procedure for
the one-dimensional quantum formulation of the -state Potts model, for
and 5, as prototypical examples, using finite-size data obtained from
the density matrix renormalization group (DMRG) algorithm.Comment: 4 pages, 4 figure
Duality and ground-state phase diagram for the quantum XYZ model with arbitrary spin in one spatial dimension
Five duality transformations are unveiled for the quantum XYZ model with
arbitrary spin in one spatial dimension. The presence of these duality
transformations drastically reduces the entire ground-state phase diagram to
two {\it finite} regimes - the principal regimes, with all the other ten
regimes dual to them. Combining with the determination of critical points from
the conventional order parameter approach and/or the fidelity approach to
quantum phase transitions, we are able to map out the ground-state phase
diagram for the quantum XYZ model with arbitrary spin . This is explicitly
demonstrated for and 2. As it turns out, all the critical points,
with central charge , are self-dual under a respective duality
transformation for half-integer as well as integer spin . However, in the
latter case, the presence of the so-called symmetry protected topological
phase, i.e., the Haldane phase, results in extra lines of critical points with
central charge , which is not self-dual under any duality
transformation.Comment: 4+ pages, 5 figure
Ground-state phase diagram of the two-dimensional t-J model
The ground-state phase diagram of the two-dimensional t-J model is
investigated in the context of the tensor network algorithm in terms of the
graded Projected Entangled-Pair State representation of the ground-state wave
functions. There is a line of phase separation between the Heisenberg
anti-ferromagnetic state without hole and a hole-rich state. For both J=0.4t
and J=0.8t, a systematic computation is performed to identify all the competing
ground states for various dopings. It is found that, besides a possible
Nagaoka's ferromagnetic state, the homogeneous regime consists of four
different phases: one phase with charge and spin density wave order coexisting
with a p_x (p_y)-wave superconducting state, one phase with the symmetry mixing
of d+s-wave superconductivity in the spin-singlet channel and p_x (p_y)-wave
superconductivity in the spin-triplet channel in the presence of an
anti-ferromagnetic background, one superconducting phase with extended s-wave
symmetry, and one superconducting phase with p_x (p_y)-wave symmetry in a
ferromagnetic background.Comment: 4+ pages, 3 figures, and 1 tabl
Fidelity mechanics: analogues of the four thermodynamic laws and Landauer's principle
Fidelity mechanics is formalized as a framework to investigate quantum
critical phenomena in quantum many-body systems. This is achieved by
introducing fidelity temperature to properly quantify quantum fluctuations,
which, together with fidelity entropy and fidelity internal energy, constitute
three basic state functions in fidelity mechanics, thus enabling us to
formulate analogues of the four thermodynamic laws and Landauer's principle at
zero temperature. Fidelity flows are defined and may be interpreted as an
alternative form of renormalization group flows. Thus, both stable and unstable
fixed points are characterized in terms of fidelity temperature and fidelity
entropy: divergent fidelity temperature for unstable fixed points and zero
fidelity temperature and (locally) maximal fidelity entropy for stable fixed
points. In addition, an inherently fundamental role of duality is clarified,
resulting in a canonical form of the Hamiltonian in fidelity mechanics.
Dualities, together with symmetry groups and factorizing fields, impose the
constraints on a fidelity mechanical system, thus shaping fidelity flows from
an unstable fixed point to a stable fixed point.
A detailed analysis of fidelity mechanical state functions is presented for
the quantum XY model, the transverse field quantum Ising chain in a
longitudinal field, the spin- XYZ model and the XXZ model in a magnetic
field.Comment: 56 pages, 23 figures and 2 table
On self-dual negacirculant codes of index two and four
In this paper, we study a special kind of factorization of over
with a prime power when
with and is a prime. Given such a infinitely
many such 's exist that admit as a primitive root by the Artin
conjecture in arithmetic progressions. This number theory conjecture is known
to hold under GRH. We study the double (resp. four)-negacirculant codes over
finite fields of co-index such 's, including the exact
enumeration of the self-dual subclass, and a modified Varshamov-Gilbert bound
on the relative distance of the codes it contains.Comment: Design, Codes and Cryptography,201
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