1,842 research outputs found
Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models
We consider several anisotropic extensions of the Belavin model, and show
that integrability holds also for the massive case for some specific relations
between the coupling constants. This is done by relating the S-matrix
factorization property to the exceptional solutions of the eight-vertex model.
The relation of exceptional solutions to the XXZ and six-vertex models is also
shown
Index theoretic characterization of d-wave superconductors in the vortex state
We employ index theoretic methods to study analytically the low energy
spectrum of a lattice d-wave superconductor in the vortex lattice state. This
allows us to compare singly quantized and doubly quantized
vortices, the first of which must always be accompanied by branch cuts.
For an inversion symmetric vortex lattice and in the presence of particle-hole
symmetry we prove an index theorem that imposes a lower bound on the number of
zero energy modes. Generic cases are constructed in which this bound exceeds
the number of zero modes of an equivalent lattice of doubly quantized vortices,
despite the identical point group symmetries. The quasiparticle spectrum around
the zero modes is doubly degenerate and exhibits a Dirac-like dispersion, with
velocities that become universal functions of in the limit of low
magnetic field. For weak particle-hole symmetry breaking, the gapped state can
be characterized by a topological quantum number, related to spin Hall
conductivity, which generally differs in the cases of the and
vortex lattices.Comment: 4 pages, 2 figures, 1 table (accepted for publication in PRL;
substantially rewritten for presentation clarity; references to quantum order
and visons omitted on referee's demand
Mixed state of a lattice d-wave superconductor
We study the mixed state in an extreme type-II lattice d-wave superconductor
in the regime of intermediate magnetic fields H_{c1} << H << H_{c2}. We analyze
the low energy spectrum of the problem dominated by nodal Dirac-like
quasiparticles with momenta near k_F=(\pm k_D,\pm k_D) and find that the
spectrum exhibits characteristic oscillatory behavior with respect to the
product of k_D and magnetic length l. The Simon-Lee scaling, predicted in this
regime, is satisfied only on average, with the magnitude of the oscillatory
part of the spectrum displaying the same 1/l dependence as its monotonous
``envelope'' part. The oscillatory behavior of the spectrum is due to the
inter-nodal interference enhanced by the singular nature of the low energy
eigenfunctions near vortices. We also study a separate problem of a single
vortex piercing an isolated superconducting grain of size L by L. Here we find
that the periodicity of the quasiparticle energy oscillations with respect to
k_D L is doubled relative to the case where the field is zero and the vortex is
absent, both such oscillatory behaviors being present at the leading order in
1/L. Finally, we review the overall features of the tunneling conductance
experiments in YBCO and BSCCO, and suggest an interpretation of the peaks at
5-20 meV observed in the tunneling local density of states in these materials.Comment: 16 pages, 11 figure
Thermodynamics of the quantum Landau-Lifshitz model
We present thermodynamics of the quantum su(1,1) Landau-Lifshitz model,
following our earlier exposition [J. Math. Phys. 50, 103518 (2009)] of the
quantum integrability of the theory, which is based on construction of
self-adjoint extensions, leading to a regularized quantum Hamiltonian for an
arbitrary n-particle sector. Starting from general discontinuity properties of
the functions used to construct the self-adjoint extensions, we derive the
thermodynamic Bethe Ansatz equations. We show that due to non-symmetric and
singular kernel, the self-consistency implies that only negative chemical
potential values are allowed, which leads to the conclusion that, unlike its
su(2) counterpart, the su(1,1) LL theory at T=0 has no instabilities.Comment: 10 page
Quantum integrability of the Alday-Arutyunov-Frolov model
We investigate the quantum integrability of the Alday-Arutyunov-Frolov (AAF)
model by calculating the three-particle scattering amplitude at the first
non-trivial order and showing that the S-matrix is factorizable at this order.
We consider a more general fermionic model and find a necessary constraint to
ensure its integrability at quantum level. We then show that the quantum
integrability of the AAF model follows from this constraint. In the process, we
also correct some missed points in earlier works.Comment: 40 pages; Replaced with published version. Appendix and comments
adde
Higher charges and regularized quantum trace identities in su(1,1) Landau-Lifshitz model
We solve the operator ordering problem for the quantum continuous integrable
su(1,1) Landau-Lifshitz model, and give a prescription to obtain the quantum
trace identities, and the spectrum for the higher-order local charges. We also
show that this method, based on operator regularization and renormalization,
which guarantees quantum integrability, as well as the construction of
self-adjoint extensions, can be used as an alternative to the discretization
procedure, and unlike the latter, is based only on integrable representations.Comment: 27 pages; misprints corrected, references adde
The r-matrix of the Alday-Arutyunov-Frolov model
We investigate the classical integrability of the Alday-Arutyunov-Frolov model, and show that the Lax connection can be reduced to a simpler 2 x 2 representation. Based on this result, we calculate the algebra between the L-operators and find that it has a highly non-ultralocal form. We then employ and make a suitable generalization of the regularization technique proposed by Mail let for a simpler class of non-ultralocal models, and find the corresponding r- and s-matrices. We also make a connection between the operator-regularization method proposed earlier for the quantum case, and the Mail let's symmetric limit regularization prescription used for non-ultralocal algebras in the classical theory.CAPESFAPESP [2011/20242-3
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