QUROPE Quantum Information Processing and Communication in Europe

Topological phases of matter possess intricate correlation patterns typically probed by entanglement entropies or entanglement spectra. In this Letter, we propose an alternative approach to assessing topologically induced edge states in free and interacting fermionic systems. We do so by focussing on the fermionic covariance matrix.

We introduce a family of strongly-correlated spin wave functions on arbitrary spin-1/2 and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore-Read states of particles at filling fraction 1/q, which are non-Abelian Fractional Quantum Hall states in 2D.

We propose infinite Matrix Product States (MPS) constructed from conformal field theories for describing 1D critical systems with open boundaries. To illustrate this, we consider a simple infinite MPS for a spin-1/2 chain and derive an inhomogeneous open Haldane-Shastry model. For the spin-1/2 open Haldane-Shastry model, we derive an exact expression for the two-point spin correlation function.

We develop a method of constructing excited states in one dimensional spin chains which are derived from the $SU(2)_1$ Wess-Zumino-Witten Conformal Field Theory (CFT) using a parent Hamiltonian approach. The resulting systems are equivalent to the Haldane-Shastry model.

We show that projected entangled-pair states (PEPS) can describe chiral topologically ordered phases. For that, we construct a simple PEPS for spin-1/2 particles in a two-dimensional lattice. We reveal a symmetry in the local projector of the PEPS that gives rise to the global topological character. We also extract characteristic quantities of the edge conformal field theory using the bulk-boundary correspondence.

In this work we numerically study critical phases in translation-invariant Z_N parafermion chains with both nearest- and next-nearest-neighbor hopping terms. The model can be mapped to a Z_N spin model with nearest-neighbor couplings via a generalized Jordan-Wigner transformation and translation invariance ensures that the spin model is always self-dual.

We provide a method for constructing finite temperature states of one-dimensional spin chains displaying quantum criticality. These models are constructed using correlators of products of quantum fields and have an analytical purification.

We propose 1D and 2D lattice wave functions constructed from the SU(n)1 Wess-Zumino-Witten (WZW) model and derive their parent Hamiltonians. When all spins in the lattice transform under SU(n) fundamental representations, we obtain a two-body Hamiltonian in 1D, including the SU(n) Haldane-Shastry model as a special case.

The Kalmeyer-Laughlin state, which is a lattice version of the bosonic Laughlin state at filling factor one half, has attracted much attention due to its topological and chiral spin liquid properties. Here we show that the Kalmeyer-Laughlin state on the torus can be expressed in terms of a correlator of conformal fields from the SU(2)1 Wess-Zumino-Witten model. This reveals an interesting underlying mathematical structure and provides a natural way to generalize the Kalmeyer-Laughlin state to arbitrary lattices on the torus.