The Lagrangian (action) formulation of the Chalker-Coddington network model for plateauplateau transitions in quantum Hall effect is presented based on a model of fermions hopping on Manhattan Lattice (ML). The dimensionless Landauer resistance is considered and its average is calculated over the random U(1) phases with constant distribution on the circle. The Lagrangian of the resultant model ...

We introduce new $U_q\mathfrak{sl}_2$-invariant boundary conditions for the open XXZ spin chain. For generic values of $q$ we couple bulk Hamiltonian to an infinite-dimensional Verma module on one or both boundaries chain, and $q=e^{\frac{i\pi}{p}}$ a $2p$-th root unity $ - its $p$-dimensional analogue. Both cases are parametrised by continuous "spin" $\alpha\in\mathbb{C}$. To motivate our cons...

We introduce a family of quantum R\'enyi fidelities and discuss their symmetry resolution. express the symmetry-resolved as Fourier transforms charged fidelities, for which we derive exact formulas fermionic Gaussian states. These results also yield formula total states, expect to have applications beyond scope this paper. investigate in XX spin chain focus on (i) between thermal states (ii) re...

We obtain exact formulas for the time-dependence of a few physical observables open XX spin chain with Lindbladian dynamics. Our analysis is based on fact that Lindblad equation an arbitrary quadratic system N N fermions explicitly solved in terms diagonalization 4N\times4N display="inline"><mm...

The ferromagnetic integrable SU(3) spin chain provides the one loop anomalous dimension of single trace operators involving the three complex scalars of N = 4 supersymmetric Yang-Mills. We construct the non-linear sigma model describing the continuum limit of the SU(3) spin chain. We find that this sigma model corresponds to a string moving with large angular momentum in the five-sphere in AdS5...

We begin with a review of the antiferromagnetic spin 1/2 Heisenberg chain. In particular, we show that the model has particle-like excitations with spin 1/2, and we compute the exact bulk S matrix. We then review our recent work which generalizes these results. We first consider an integrable alternating spin 1/2 spin 1 chain. In addition to having excitations with spin 1/2, this model also has...

Localization may survive in periodically driven (Floquet) quantum systems, but is generally unstable for aperiodic drives. In this Letter, we identify a hidden conservation law originating from chiral symmetry disordered spin-$\frac{1}{2}$ XX chain. This protects indefinitely long-lived localization general---even aperiodic---drives. Therefore, rather counterintuitively, adding further potentia...