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 $hc/2e$ and doubly quantized $hc/e$ vortices, the first of which must always be accompanied by $Z_2$ 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 $\Delta_0/t$ 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 $hc/2e$ and $hc/e$ 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 su(1,1)su(1,1) 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