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We investigate the infrared properties of SU ( N ) k conformal field theory perturbed by its adjoint primary field in 1 + 1 dimensions. The latter field theory is shown to govern the low-energy properties of various SU( N ) spin chain problems. In particular, using a mapping onto k -leg SU( N ) spin ladder, a massless renormalization group flow to SU ( N ) 1 criticality is predicted when N and k have no common divisor. The latter result extends the well-known massless flow between SU ( 2 ) k and SU(2) 1 Wess–Zumino–Novikov–Witten theories when k is odd in connection to the Haldane's conjecture on SU(2) Heisenberg spin chains. A direct approach is presented in the simplest N = 3 and k = 2 case to investigate the existence of this massless flow. [ABSTRACT FROM AUTHOR]

Four-spin exchange interaction has been raising intriguing questions regarding the exotic phase transitions it induces in two-dimensional quantum spin systems. In this context, we investigate the effects of a cyclic four-spin exchange in the quasi-1D limit by considering a general N-leg spin ladder. We show by means of a low-energy approach that depending on its sign, this ring exchange interaction can engender either a staggered or a uniform dimerization from the conventional phases of spin ladders. The resulting quantum phase transition is found to be described by the SU(2)N conformal field theory. This result, as well as the fractional value of the central charge at the transition, is further confirmed by a large-scale numerical study performed by means of exact diagonalization and density matrix renormalization group approaches for N≤4. [ABSTRACT FROM AUTHOR]

Abstract: The physical properties of arbitrary half-integer spins fermionic cold atoms loaded into a one-dimensional optical lattice are investigated by means of a conformal field theory approach. We show that for attractive interactions two different superfluid phases emerge for : A BCS pairing phase, and a molecular superfluid phase which is formed from bound-states made of 2N fermions. In the low-energy approach, the competition between these instabilities and charge-density waves is described in terms of parafermionic degrees of freedom. The quantum phase transition for is universal and shown to belong to the Ising and three-state Potts universality classes respectively. In contrast, for , the transition is non-universal. For a filling of one atom per site, a Mott transition occurs and the nature of the possible Mott-insulating phases are determined. [Copyright &y& Elsevier]