Strong and weak symmetries and their spontaneous breaking distinguish different forms of symmetry and order in mixed states. We show that complete one- and two-point correlation functions, equivalently all two-site reduced density matrices, determine exact strong symmetry for continuous onsite unitary actions of connected groups: states with identical correlations have the same strong symmetry and character. We also present an algorithm to determine the maximal connected strong-symmetry sub-Lie group and its character from two-point correlations. Because such correlations are more accessible than full-state tomography, the algorithm is readily applicable to experiments ranging from condensed-matter systems to quantum simulators and circuits. We also identify group and representation-specific cases in which fewer correlations suffice.
We develop a nonperturbative functional framework for computing real-time correlation functions in strongly correlated systems. The framework is based on the spectral representation of correlation functions and dimensional regularization. Therefore, the nonperturbative spectral renormalization setup here respects all symmetries of the theories at hand. In particular, this includes space-time symmetries, as well as internal symmetries such as chiral symmetry, and gauge symmetries. Spectral renormalization can be applied within general functional approaches such as the functional renormalization group, Dyson-Schwinger equations, and two- or
n-particle irreducible approaches. As an application, we compute the full, nonperturbative, spectral function of the scalar field in the ${\ensuremath{\phi}}^{4}$-theory in
2+1 dimensions from spectral Dyson-Schwinger equations. We also compute the
s-channel spectral function of the full ${\ensuremath{\phi}}^{4}$-vertex in this theory.
Integrability of strongly correlated electron systems on open chains XIANG-YU GEIn recent years, there has been a strong increase of interest in models of strongly correlated electron systems in condensed matter physics, in particular in integrable onedimensional models.Examples of such models are the one-dimensional Hubbard model, the supersymmetric t-J model, the Hubbard-like model (Bariev's chain), the so-called extended Hubbard model (EKS model), the supersymmetric U model and the eight-state supersymmetric U model.The study of integrable open-boundary conditions for strongly correlated electron models is very important for physical applications, especially for gaining insights into the behaviour of more realistic systems.The important ingredient in Sklyanin's boundary quantum inverse scattering method (QISM), which has played a key role in recent advances in the study of lattice models with open-boundaries, is a new algebraic structure, the reflection equation algebra.In this thesis, a general graded reflection equation algebra is proposed and the corresponding graded (supersymmetry) boundary QISM is formulated.The formalism is applicable to all boundary lattice systems where an invertible i?-matrix exists.As applications, some important integrable boundary conditions for various strongly correlated electron models with quantum superalgebra symmetries are constructed, including:1. Presentation of integrable open-boundary conditions for the one-dimensional qdeformed supersymmetric Essler-Korepin-Schoutens (EKS) extended Hubbard model.Determination of three different diagonal boundary if-matrices and of nine classes of integrable open-boundary conditions.Construction of the exactly solvable Hamiltonian with open-boundary terms for quantum superalgebra U q (gl(2\2)) symmetry; 2. Establishment of the quantum integrability of open-boundary conditions for the one-dimensional ^-deformed supersymmetric U model with quantum superalgebra U q (gl(2\l)} symmetry.Determination of diagonal boundary if-matrices and of integrable open-boundary conditions.Solution of the boundary system by means of the coordinate space Bethe ansatz technique, and derivation of the Bethe ansatz equations;