We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points invariant under the permutational symmetry S_{q} in two dimensions, and we show how one of these scattering solutions describes the ferromagnetic and square lattice antiferromagnetic critical lines of the q-state Potts model. Other solutions we determine should correspond to new critical lines. In particular, we obtain that a S_{q}-invariant fixed point can be found up to the maximal value q=(7+sqrt[17])/2. This is larger than the usually assumed maximal value 4 and leaves room for a second-order antiferromagnetic transition at q=5.

A typical working condition in the study of quantum quenches is that the initial state produces a distribution of quasiparticle excitations with an opposite-momentum-pair structure. In this work we investigate the dynamical and stationary properties of the entanglement entropy after a quench from initial states which do not have such structure: instead of pairs of excitations they generate ν-plets of correlated excitations with ν > 2. Our study is carried out focusing on a system of non-interacting fermions on the lattice. We study the time evolution of the entanglement entropy showing that the standard semiclassical formula is not applicable. We propose a suitable generalisation which correctly describes the entanglement entropy evolution and perfectly matches numerical data. We finally consider the relation between the thermodynamic entropy of the stationary state and the diagonal entropy, showing that when there is no pair structure their ratio depends on the details of the initial state and lies generically between 1/2 and 1.

The higher fusion level logarithmic minimal models LM(P, P ′ ; n) have recently been constructed as the diagonal GKO cosets (A +∆ P,P ′ ;2 r,s,ℓχ (N ) r,s;ℓ (q) for s-type boundary conditions with r = 1, s = 1, 2, 3, . . ., ℓ = 0, 1, 2. The P, P ′ dependence enters only in the fractional power of q in the prefactor and ℓ = 0, 2 labels the Neveu-Schwarz sectors (r + s even) and ℓ = 1 labels the Ramond sectors (r + s odd). Combinatorially, the finitized characters involve Motzkin and Riordan polynomials defined in terms of q-trinomial coefficients. Using the Hamiltonian limit and the finitized characters we argue, from examples of finite lattice calculations, that there exist reducible yet indecomposable representations for which the Virasoro dilatation operator L 0 exhibits rank-2 Jordan cells confirming that these theories are indeed logarithmic. We relate these results to the N = 1 superconformal representation theory.

We use the Quench Action approach to study the non-equilibrium dynamics after a quantum quench in the Hubbard model in the limit of infinite interaction. We identify a variety of lowentangled initial states for which we can directly compute the overlaps with the Hamiltonian's eigenstates. For these initial states, we analytically find the rapidity distributions of the stationary state characterising the expectation values of all local observables. Some of the initial states considered are not reflection symmetric and lead to non-symmetric rapidity distributions. To study such cases, we have to introduce a generalised form for the reduced entropy which measures the entropy restricted to states with non-zero overlap. The initial states considered are of direct experimental realisability and also represent ideal candidates for studying non-equilibrium dynamics in the Hubbard model for finite interactions. arXiv:1707.01073v2 [cond-mat.stat-mech]