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We discuss the properties of non-abelian gauge theories formulated on manifolds with compactified dimensions and in the presence of fermionic fields coupled to magnetic backgrounds. We show that different phases may emerge, corresponding to…
We propose a practical protocol to generate and observe a non-Abelian geometric phase using a periodically driven Raman process in the hyperfne ground state manifold of atoms in a dilute ultracold gas. Our analysis is based upon recent…
Angular momentum $J=3/2$ holes in semiconductor heterostructures are showed to accumulate nonabelian geometric phases as a consequence of their motion. We provide a general framework for analyzing such a system and compute conductance…
We search a canonical basis of Dirac's observables for the classical non-Abelian Higgs model with fermions in the case of a trivial SU(2) principal bundle with a complex doublet of Higgs fields and with the fermions in a given…
New fundamental particles, charged under new gauge groups and only weakly coupled to the standard sector, could exist at fairly low energy scales. In this article we study a selection of such models, where the secluded group either contains…
Gauge theories, while describing fundamental interactions in nature, also emerge in a wide variety of physical systems. Abelian gauge fields have been predicted and observed in a number of novel quantum many-body systems, topological…
A general scheme for an adiabatic geometric phase gate is proposed which is maximally robust against parameter fluctuations. While in systems with SU(2) symmetry geometric phases are usually accompanied by dynamical phases and are thus not…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…
We study a scenario where the Standard Model is extended by a SU(2) gauge group in the dark sector. The three associated dark gauge bosons are stabilised via a custodial symmetry triggered by an additional dark SU(2) scalar doublet, thus…
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…
We analyze the phase diagram of the zeroth Landau level of bilayer graphene, taking into account the realistic effects of screening of the Coulomb interaction and the strong mixing between two degenerate sublevels. We identify robust…
The conventional formulation of the non-adiabatic (Aharonov-Anandan) phase is based on the equivalence class $\{e^{i\alpha(t)}\psi(t,\vec{x})\}$ which is not a symmetry of the Schr\"{o}dinger equation. This equivalence class when understood…
Owing to subtle issues concerning quantum fluctuations and gauge fixing, a formulation of a general procedure to specify the realization of non-Abelian gauge symmetry has evaded all earlier attempts. In this Letter, we discuss these…
We study gluodynamics in an external Abelian electromagnetic field within the dual superconductor approach. We show that the SU(2) gluodynamics should possess a deconfining phase transition at zero temperature at certain value of the…
The phase diagram of an SU(2)_L x SU(2)_R lattice Higgs-Yukawa model with finite lambda is constructed using mean field theory. The phase diagram bears a superficial resemblance to that for infinite lambda, however as lambda is decreased…
Geometric phase (GP) independent of energy and time rely only on the geometry of state space. It has been argued to have potential fault tolerance and plays an important role in quantum information and quantum computation. We present the…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
We study the phase structure of the 3D nonlocal compact U(1) lattice gauge theory coupled with a Higgs field by means of Monte-Carlo simulations. The nonlocal interactions among gauge variables are along the temporal direction and mimic the…
The non-Abelian geometric phase possesses the capability of enabling robust and fault-resilient unitary transformations, making it a cornerstone of holonomic quantum computation. This "all-geometric" approach has successfully advanced the…
We illustrate how geometric gauge forces and topological phase effects emerge in quantum systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices…