We show how 1+1-dimensional fermionic symmetry-protected topological states (SPTs, i.e. nontrivial short-range entangled gapped phases of quantum matter whose boundary exhibits 't Hooft anomaly and bulk cannot be deformed into a trivial tensor product state under finite-depth local unitary transformations only in the presence global symmetries), indeed can unwound to by enlarging Hilbert space ...

We compute the correlation functions of the eigenvalues in the Gaussian unitary ensemble using the fermionic replica method. We show that non-trivial saddle points, which break replica symmetry, must be included in the calculation in order to correctly reproduce the exact asymptotic behaviour of the correlation functions at a large distance.

The embedding diagrams of representations of the N = 2 superconformal algebra with central charge c = 3 are given. Some non-unitary representations possess subsingular vectors that are systematically described. The structure of the embedding diagrams is largely defined by the spectral flow symmetry. As an additional consistency check the action of the spectral flow on the characters is calculat...

We consider a model which effectively restricts the functional integral of Yang–Mills theories to the fundamental modular region. Using algebraic arguments, we prove that this theory has the same divergences as ordinary Yang Mills theory in the Landau gauge and that it is unitary. The restriction of the functional integral is interpreted as a kind of spontaneous breakdown of the BRS symmetry.

We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. derive a Wigner-type result for operator involving all Pauli matrices: in this case, isometry group consists unitary or anti-unitary conjugations. In Bloch sphere model means that coincides classical symmetry O(3). On other hand, generated by qubit ‘‘clock” and ‘‘shift” operators, we ...

We consider a possible generalization of the random matrix theory, which involves the maximization of Tsallis’ q-parametrized entropy. We discuss the dependence of the spacing distribution on q using a nonextensive generalization of Wigner’s surmises for ensembles belonging to the orthogonal, unitary and symplectic symmetry universal classes. PACS numbers: 03.65.-w, 05.45.Mt, 05.30.Ch