Related papers: The Generalized Lipkin-Meshkov-Glick Model and the…
We analyze the finite-size scaling exponents in the Lipkin-Meshkov-Glick model by means of the Holstein-Primakoff representation of the spin operators and the continuous unitary transformations method. This combination allows us to compute…
We consider an open spin chain model with GL(N) bulk symmetry that is broken to GL(M) x GL(N-M) by the boundary, which is a generalization of a model arising in string/gauge theory. We prove the integrability of this model by constructing…
In this paper we extend the Falicov-Kimball model (FKM) to the case where the "quasi-particles" entering the FKM are not "ordinary" fermions. As an example we first discuss how the FKM can be generalized to the case with spin-dependent…
We study 1+1 field-generalizations of the rational and elliptic Gaudin models. For ${\rm sl}(N)$ case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic curve. In ${\rm sl}(2)$ case we…
The pseudo-fermion functional renormalization group is generalized to treat spin Hamiltonians with finite magnetic fields, enabling its application to arbitrary spin lattice models with linear and bilinear terms in the spin operators. We…
We show that the classical model of Euler top (freely rotating, generally asymmetric rigid body), possibly supplemented with a rotor, corresponds to a generalized Lipkin-Meshkov-Glick (LMG) model describing phenomena of various branches of…
We solve the classical and quantum problems for the 1D sigma model with target space the flag manifold $\mathrm{U}(3)\over \mathrm{U}(1)^3$, equipped with the most general invariant metric. In particular, we explicitly describe all…
The Bethe ansatz equations of the fundamental Sp(2N) integrable model are solved by a peculiar configuration of roots leading us to determine the nature of the excitations. They consist of N elementary generalized spinons and N-1 composite…
The Sine-Gordon theory at $\frac{\beta^{2}}{8\pi} = \frac{2}{(2n+3)},\; n= 1,2,3 \cdots $ has a higher spin generalization of the $N=2$ supersymmetry with the central terms which arises from the affine quantum group $U_{q}( \hat{s \ell}…
In this paper we review the Myrzakulov Gravity models (MG-N, with $\mathrm{N = I, II, \ldots, VIII}$) and derive their respective metric-affine generalizations (MAMG-N), discussing also their particular sub-cases. The field equations of the…
We investigate the quantum Jaynes-Cummings model - a particular case of the Gaudin model with one of the spins being infinite. Starting from the Bethe equations we derive Baxter's equation and from it a closed set of equations for the…
The Lipkin-Meshkov-Glick (LMG) model was devised to test the validity of different approximate formalisms to treat many-particle systems. The model was constructed to be exactly solvable and yet non-trivial, in order to capture some of the…
The small polaron, an one-dimensional lattice model of interacting spinless fermions, with generic non-diagonal boundary terms is studied by the off-diagonal Bethe ansatz method. The presence of the Grassmann valued non-diagonal boundary…
By means of the Lee-Shrock transformation we generalize the 2D Gross-Neveu (GN$_2$) model to a U(1) gauge theory with charged fermion and scalar fields in 2D ($\chi U \phi_2$ model). The $\chi U \phi_2$ model is equivalent to the GN$_2$…
We study the ground state properties of the critical Lipkin-Meshkov-Glick model. Using the Holstein-Primakoff boson representation, and the continuous unitary transformation technique, we compute explicitly the finite-size scaling exponents…
We study quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(m|n)$-invariant $R$-matrix. We compute the norm of the Hamiltonian eigenstates. Using the notion of a generalized model we show…
The spectrum of the Lipkin-Meshkov-Glick model is exactly derived in the thermodynamic limit by means of a spin coherent states formalism. In the first step, a classical analysis allows one to distinguish between four distinct regions in…
We generalize the Kitaev's spin-1/2 model on the honeycomb by introducing a two-dimensional $Z_3$ clock model on the triangular lattice with three body interaction. We discuss various properties of this model and show that the low energy…
Geometric Brownian motion (GBM) is a standard model in stochastic differential equations. In this study, we consider a matrix-valued GBM with non-commutative matrices. Introduction of non-commutative matrices into the matrix-valued GBM…
We show that the SU(N) Fermi-Hubbard model (FHM) on two sites, where N is the number of flavors of each fermion, corresponds to an exactly solvable two-level many-boson model that Richardson [J. Math. Phys. 9, 1327 (1968)] analytically…