Related papers: A set of exactly solvable Ising models with half-o…
A family of two-dimensional (2D) spin-1/2 models have been constructed to realize Kitaev's sixteen-fold way of anyon theories. Defining a one-dimensional (1D) path through all the lattice sites, and performing the Jordan-Wigner…
A novel exact solution of the multichannel spin-$S$ Kondo model is presented, based on a lattice path integral approach of the single channel spin-1/2 case. The spin exchange between the localized moment and the host is of $XXZ$-type,…
We consider the exact solution of a many-body problem of spin-$s$ particles interacting through an arbitrary U(1) invariant factorizable $S$-matrix. The solution is based on a unified formulation of the quantum inverse scattering method for…
Ultra-cold alkali atoms trapped in two distinct hyperfine states in an external magnetic field can mimic magnetic systems of spin 1/2 particles. We describe the spin-dependent effective interaction as a spin-spin interaction. As a…
We find all the exact eigenstates and eigenvalues of a spin-1/2 model on square lattice: $H=16g \sum_i S^y_i S^x_{i+x} S^y_{i+x+y} S^x_{i+y}$. We show that the ground states for $g<0$ and $g>0$ have different quantum orders described by Z2A…
We study a model of strongly correlated fermions in one dimension with extended N=2 supersymmetry. The model is related to the spin $S=1/2$ XXZ Heisenberg chain at anisotropy $\Delta=-1/2$ with a real magnetic field on the boundary. We…
We continue our work on lattice models of webs, which generalise the well-known loop models to allow for various kinds of bifurcations [arXiv:2101.00282, arXiv:2107.10106]. Here we define new web models corresponding to each of the rank-two…
We construct models describing interaction between a spin $s$ and a single bosonic mode using a quantum inverse scattering procedure. The boundary conditions are generically twisted by generic matrices with both diagonal and off-diagonal…
A special case of the Gaudin model related to the superalgebra $osp(1,2)$ is investigated. An exact solution for the model in the spin-1/2 representation is presented. A complete set of commuting observables is diagonalized and the…
It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin-1/2 spin-1…
A non-hermitian deformation of the one-dimensional transverse Ising model is shown to have the property of quasi-hermiticity. The transverse Ising chain is obtained from the starting non-hermitian Hamiltonian through a similarity…
The electronic and magnetic structure, including the Heisenberg model exchange interaction parameters, was explored for the recently proposed novel cuprate Cu$_2$F$_5$. Using the DFT+U calculation, it is shown that the compound is formed by…
The spin-1/2 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the…
A gas of strongly interacting spinless p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively…
We write down a class of two-dimensional quantum spin-1/2 Hamiltonians whose eigenspectra are exactly solvable via the Jordan-Wigner transformation. The general structure corresponds to a suitable grid composed of XY or XX-Ising spin chains…
We perform a duality transformation that allows one to express the partition function of the d-dimensional Ising model with random nearest neighbor coupling in terms of new spin variables defined on the square plaquettes of the lattice. The…
Using the representation of the quantum group $SL_q$(2) by the Weyl ope\-ra\-tors of the canonical commutation relations in quantum mechanics, we construct and solve a new vertex model on a square lattice. Random variables on horizontal…
We present a simple criterion for solvability of lattice spin systems on the basis of the graph theory and the simplicial homology. The lattice systems satisfy algebras with graphical representations. It is shown that the null spaces of…
Exactly solvable Hamiltonians with spin liquid ground states have proven to be extremely useful, not only because they unambiguously demonstrate that these phases can arise in systems of interacting spins but also as a pedagogical…
We consider a lattice formulation of the four dimensional N=1 Wess-Zumino model in terms of the Ginsparg-Wilson relation. This formulation has an exact supersymmetry on the lattice. The lattice action is invariant under a deformed…