14,459 research outputs found
Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
Recently, it has been shown that two-dimensional bosonic symmetry-protected
topological(SPT) phases with on-site unitary symmetry can be completely
classified by the group cohomology class . Later, group
super-cohomology class was proposed as a partial classification for SPT phases
of interacting fermions. In this work, we revisit this problem based on the
mathematical framework of -extension of unitary braided tensor
category(UBTC) theory. We first reproduce the partial classifications given by
group super-cohomology, then we show that with an additional structure, a complete classification of SPT phases for
two-dimensional interacting fermion systems for a total symmetry group
can be achieved. We also discuss the classification of
interacting fermionic SPT phases protected by time-reversal symmetry.Comment: references added; published versio
3-D Velocity Regulation for Nonholonomic Source Seeking Without Position Measurement
We consider a three-dimensional problem of steering a nonholonomic vehicle to
seek an unknown source of a spatially distributed signal field without any
position measurement. In the literature, there exists an extremum seeking-based
strategy under a constant forward velocity and tunable pitch and yaw
velocities. Obviously, the vehicle with a constant forward velocity may exhibit
certain overshoots in the seeking process and can not slow down even it
approaches the source. To resolve this undesired behavior, this paper proposes
a regulation strategy for the forward velocity along with the pitch and yaw
velocities. Under such a strategy, the vehicle slows down near the source and
stays within a small area as if it comes to a full stop, and controllers for
angular velocities become succinct. We prove the local exponential convergence
via the averaging technique. Finally, the theoretical results are illustrated
with simulations.Comment: submitted to IEEE TCST;12 pages, 10 figure
Quantum phase transitions in a generalized compass chain with three-site interactions
We consider a class of one-dimensional compass models with XYZYZX-type of
three-site exchange interaction in an external magnetic field. We present the
exact solution derived by means of Jordan-Wigner transformation, and study the
excitation gap, spin correlations, and establish the phase diagram. Besides the
canted antiferromagnetic and polarized phases, the three-site interactions
induce two distinct chiral phases, corresponding to gapless spinless-fermion
systems having two or four Fermi points. We find that the component of
scalar chirality operator can act as an order parameter for these chiral
phases. We also find that the thermodynamic quantities including the Wilson
ratio can characterize the liquid phases. Finally, a nontrivial magnetoelectric
effect is explored, and we show that the polarization can be manipulated by the
magnetic field in the absence of electric field.Comment: 10 pages, 11 figure
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