Self-Dual Transitive Spin 1/2 Models

H. Moraal

P. Lecheminant, Kiyohito Totsuka

We investigate the low-energy properties of a generalized quantum sine–Gordon model in one dimension with a self-dual symmetry. This model describes a class of quantum phase transitions that stems from the competition of different orders. This SU ( N ) self-dual sine–Gordon model is shown to be equivalent to an SO ( N ) 2 conformal field theory perturbed by a current–current interaction, which is related to an integrable fermionic model introduced by Andrei and Destri. In the context of spin-chain problems, we give several realizations of this self-dual sine–Gordon model and discuss the universality class of the transitions.

M. S. Ramkarthik, Pranay Barkataki

Loïc Turban

Introduces a family of D-dimensional q-state quantum Potts models with multi-spin interactions, which are self-dual for any D. These models are introduced using their (d=D+1)-dimensional classical formulations and the transfer matrix technique. The self-duality is proved on the quantum Hamiltonian. In the limit q to infinity the ground state energy is obtained exactly and the phase transition is first-order. A 1/q expansion allows one to get an approximate expression for the line in the (q,D)-plane separating regions where the transition changes from first- to second-order.

Eiichi Bannaĭ, Etsuko Bannai

Loïc Turban, Jean‐Marc Debierre

The quantum Hamiltonian formulation of the q-state Potts model on a linear chain is generalised by introducing models with m-spin interactions. These models are self-dual for any values of q and m and have a first-order transition when q and/or m are large enough. The line in the (q,m) plane where the latent heat vanishes is approximately located using 1/q and 1/m expansions.