We present simple lattice realizations of symmetry-protected topological phases with q-form global symmetries where charged excitations have q spatial dimensions. Specifically, we construct d space-dimensional models supported on a (d + 1)-colorable graph by using a family of unitary phase gates, known as multiqubit control-Z gates in quantum information community. In our construction, charged ...

Explicit forms of IBM Hamiltonians with a generalized partial dynamical O(6) symmetry are presented and compared with empirical data in 162Dy. A dynamical symmetry corresponds to a situation in which the Hamiltonian is written in terms of the Casimir operators of a chain of nested algebras G1 ⊃ G2 ⊃ . . . ⊃ Gn , (1) and has the following properties. (i) Solvability. (ii) Quantum numbers related...

Given a close 3-form H ∈ Ω 0 (M), we define a twisted bracket on the space Γ(TM) ⊕ Ω 0 (M). We define the group of H-twisted Hamiltonian symmetries Ham(M, J;H) as well as Hamiltonian action of Lie group and moment map in the category of (twisted) generalized complex manifold, which leads to generalized complex reduction much the same way as symplectic reduction is constructed. The definitions a...

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Abstract We consider quantum many body systems with generalized symmetries, such as the higher form symmetries introduced recently, and ‘tensor symmetry’. a general of lattice Hamiltonians which allow certain level nonlocality. Based on assumption dual we explicitly construct low energy excited states. also derive ’t Hooft anomaly for after ‘gauging’ symmetries. A 3d system anomalous 1-form can...

Adding symmetry breaking constraints is one of the oldest ways of breaking variable symmetries for CSPs. For instance, it is well known that all the symmetries for the pigeon hole problem can be removed by ordering the variables. We have generalized this result to all CSPs where the variables are subject to an all different constraint. In such case it is possible to remove all variable symmetri...

Unconventional Superconductors Many novel superconductors show properties different from standard superconductors (overview); Aim of this lecture: • discuss structure of Cooper pairs from a symmetry point of view key symmetries: time reversal and inversion symmetry • learn the techniques of the phenomenological approach: generalized Ginzburg-Landau theories broken symmetries and order parameter...

An algorithm for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (DDEs) is presented. Recursion operators allow one to generate an infinite sequence of generalized symmetries. The existence of a recursion operator therefore guarantees the complete integrability of the DDE. The algorithm is based in part on the concept of dilation invari...

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalize...

We give explicit formulae for obtaining the binary sequences which produce Steinhaus triangles and generalized Pascal triangles with rotational and dihedral symmetries.