We address the interplay between global and local gauge non-Abelian symmetries in lattice gauge theories with multicomponent scalar fields. We consider two-dimensional lattice scalar non-Abelian gauge theories with a local SOðN c Þ (N c ≥ 3) and a global OðN f Þ invariance, obtained by partially gauging a maximally OðN f N c Þ-symmetric multicomponent scalar model. Correspondingly, the scalar fields belong to the coset S N f N c −1 =SOðN c Þ, where S N is the N-dimensional sphere. In agreement with the Mermin-Wagner theorem, these lattice SOðN c Þ gauge models with N f ≥ 3 do not have finite-temperature transitions related to the breaking of the global non-Abelian OðN f Þ symmetry. However, in the zero-temperature limit they show a critical behavior characterized by a correlation length that increases exponentially with the inverse temperature, similarly to nonlinear OðNÞ σ models. Their universal features are investigated by numerical finite-size scaling methods. The results show that the asymptotic low-temperature behavior belongs to the universality class of the two-dimensional RP N f −1 model.

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We consider two-dimensional lattice SU(Nc) gauge theories with Nf real scalar fields transforming in the adjoint representation of the gauge group and with a global O(Nf) invariance. Focusing on systems with Nf≥ 3, we study their zero-temperature limit, to understand under which conditions a continuum limit exists, and to investigate the nature of the associated quantum field theory. Extending previous analyses, we address the role that the gauge-group representation and the quartic scalar potential play in determining the nature of the continuum limit (when it exists). Our results further corroborate the conjecture that the continuum limit of two-dimensional lattice gauge models with multiflavor scalar fields, when it exists, is associated with a σ model defined on a symmetric space that has the same global symmetry as the lattice model.

We study the ground-state properties of a quantum sunburst model, composed of a quantum Ising spin ring in a transverse field, symmetrically coupled to a set of ancillary isolated qubits, to maintain a residual translation invariance and also a Z 2 symmetry. The large-size limit is taken in two different ways: either by keeping the distance between any two neighboring ancillary qubits fixed or by fixing their number while increasing the ring size. Substantially different regimes emerge, depending on the various Hamiltonian parameters: For small energy scale δ of the ancillary subsystem and small ring-qubit interaction κ, we observe rapid and nonanalytic changes in proximity to the quantum transitions of the Ising ring, both first order and continuous, which can be carefully controlled by exploiting renormalization-group and finite-size scaling frameworks. Smoother behaviors are instead observed when keeping δ > 0 fixed and in the Ising disordered phase. The effect of an increasing number n of ancillary spins turns out to scale proportionally to √ n for sufficiently large values of n.