Ultracold fermions and the SU(N) Hubbard model

We investigate the fermionic SU(N) Hubbard model on the two-dimensional square lattice for weak to moderate interactions using renormalization group and mean-field methods. For the repulsive case U>0 at half filling and small N the dominant tendency is towards breaking of the SU(N) symmetry. For N>6 staggered flux order takes over as the dominant instability, in agreement with the large-N limit. Away from half filling for N=3 two flavors remain half filled by cannibalizing the third flavor. For U<0 and odd N a full Fermi surface coexists with a superconductor. These results may be relevant to future experiments with cold fermionic atoms in optical lattices.     

SU(2) symmetry in a Hubbard model with spin-orbit coupling

We study the underlying symmetry in a spin-orbit coupled tight-binding model with Hubbard interaction. It is shown that, in the absence of the on-site interaction, the system possesses the SU(2) symmetry arising from the time reversal symmetry. The influence of the on-site interaction on the symmetry depends on the topology of the networks: The SU(2) symmetry is shown to be the spin rotation symmetry of a simply-connected lattice even in the presence of the Hubbard interaction. On the contrary, the on-site interaction breaks the SU(2) symmetry of a multi-connected lattice. This fact indicates that a discrete spin-orbit coupled system has exclusive features from its counterpart in a continuous system. The obtained rigorous result is illustrated by a simple ring system.     

Ground states of the SU(N) Heisenberg model

The SU(N) Heisenberg model with various single-row representations is investigated by quantum Monte Carlo simulations. While the zero-temperature phase boundary agrees qualitatively with the theoretical predictions based on the 1/N expansion, some unexpected features are also observed. For N> or =5 with the fundamental representation, for example, it is suggested that the ground states possess exact or approximate U(1) degeneracy. In addition, for the representation of Young tableau with more than one column, the ground state shows no valence-bond-solid order even at N greater than the threshold value.     

Solution of the SU(N) massless thirring model

In the present work a method is proposed of constructing the eigenvectors and finding the quantum numbers of SU(N) symmetric massless theories with four-fermion interaction for an arbitrary value of N.     

Two-scale analysis of the SU(N) kondo model

We show how to resolve coherent low-energy features embedded in a broad high-energy background by use of a fully self-consistent calculation for composite particle operators. The method generalizes the formulation of Roth, which linearizes the dynamics of composite operators at any energy scale. Self-consistent equations are derived and analyzed in the case of the single-impurity SU(N) Kondo model.     

Decorated star-triangle relations and exact integrability of the one-dimensional Hubbard model

The exact integrability of the one-dimensional Hubbard model is demonstrated with the help of a novel set of triangle relations, the decorated star-triangle relations. The covering two-dimensional statistical mechanical model obeys the star-triangle or Yang-Baxter relation. A conjecture is presented for the eigenvalues of the transfer matrix.     

Coherent states associated with the groups SU(N) and SU(N, 1)

The coherent-state basis is constructed for symmetric representations of the groups SU(N) and SU(N, 1) and its properties are studied. The evolution of coherent states is considered. A relationship between the SU(N) coherent states and the Glauber coherent states is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 83–89, January, 1990.     

The integrability criterion in SU(2) Chern-Simons gauge theory

We prove that the multiplicity spaces appearing in Chern-Simons theory, as defioned by Segal, vanish unless they are associated to integrable representations. This and other links with conformal field theory are examined.Supported in part by NSF Mathematics Postdoctoral Fellowship DMS-9007255     

On the gauge hierarchy in the SU(5) model

It is explicitly shown that in the SU(5) prototype for grand unified theories, the decoupling of superheavy gauge bosons as well as Higgses from the light gauge particles is complete and therefore a gauge interaction hierarchy is possible.     

The integrable SU(N) Heisenberg model at finite temperature

We derive an exact integral representation for the free energy of the integrable SU(N) Heisenberg model with arbitrary color.     

On the CPA treatment of Magnetic Disordered Hubbard model (II)

In this contribution we continue the treatment of the model based on the Hubbard hamiltonian in which the stochastic fields acting at the sites of the atoms can assume arbitrary directions and values due to accepted distribution. The averaging procedure introduced by Brandt and Gross to study the behaviour of the magnetically disordered system is used for a model with stochastically localized magnetic fields, resulting from magnetic moments, at the atomic sites, as previously in I. The coherent potential approximation-like method is employed. The selfconsistency problem is regarded as well as the thermodynamic consequences like density of states, localization function, magnetization, high temperature susceptibility and dc conductivity as functions of temperature are discussed.Supported in part by Polish Academy of Science, Problem MR I. 9. Partly done at Institute of Physics and Chemistry of Metals, Silesian University, Katowice, Poland     

The Branching Rules for SU(2N)⊃(SU(N)⊃O(N)⊃O(3))⊗SU(2) and the Highest Weight States for SU(N) and O(N)

Simple analytical recurrent formulae of the branching rules for group chain SU(2N)⊃(SU(N)⊃O(N)⊃O(3))⊗SU(2) are obtained. The highest weight states for the irreducible representations [2^al^b] or {nS} of group SU(N) and for the irreducible representations (2^α1^β) or (υS) of group O(N) are constructed respectively     

sl(N) Onsager's algebra and integrability

We define ansl(N) analog of Onsager's algebra through a finite set of relations that generalize the Dolan-Grady defining relations for the original Onsager's algebra. This infinite-dimensional Lie algebra is shown to be isomorphic to a fixed-point subalgebra ofsl(N) loop algebra with respect to a certain involution. As the consequence of the generalized Dolan-Grady relations a Hamiltonian linear in the generators ofsl(N) Onsager's algebra is shown to posses an infinite number of mutually commuting integrals of motion.