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Register a new userFractionalization via $mathbb{Z}_{2}$ Gauge Fields at a Cold Atom Quantum Hall Transition
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We study a single species of fermionic atoms in an effective magnetic field at total filling factor $ u_{f}=1$, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a $ u_{f} =1 $ fermionic integer quantum Hall state to $ u_{b} =1/4 $ bosonic fractional quantum Hall state as a function of detuning. The transition is in the $(2+1)$-D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a $mathbb{Z}_{2}$ gauge field, and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.
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Topological quantum paramagnets are exotic states of matter, whose magnetic excitations have a topological band structure, while the ground state is topologically trivial. Here we show that a simple model of quantum spins on a honeycomb bilayer hosts a time-reversal-symmetry protected $mathbb{Z}_2$ topological quantum paramagnet ({em topological triplon insulator}) in the presence of spin-orbit coupling. The excitation spectrum of this quantum paramagnet consists of three triplon bands, two of which carry a nontrivial $mathbb{Z}_2$ index. As a consequence, there appear two counterpropagating triplon excitation modes at the edge of the system. We compute the triplon edge state spectrum and the $mathbb{Z}_2$ index for various parameter choices. We further show that upon making one of the Heisenberg couplings stronger, the system undergoes a topological quantum phase transition, where the $mathbb{Z}_2$ index vanishes, to a different topological quantum paramagnet. In this case the counterpopagating triplon edge modes are disconnected from the bulk excitations and are protected by a chiral and a unitary symmetry. We discuss possible realizations of our model in real materials, in particular d$^{4}$ Mott insulators, and their potential applications.
The dynamics of ultracold neutral atoms subject to a non-Abelian gauge field is investigated. In particular we analyze in detail a simple experimental scheme to achieve a constant, but non-Abelian gauge field, and discuss in the frame of this gauge field the non-Abelian Aharanov-Bohm effect. In the last part of this paper, we discuss intrinsic non-Abelian effects in the dynamics of cold atomic wavepackets.
This article is a report of Projet bibliographique of M1 at Ecole Normale Superieure. In this article we reviewed the historical developments in artificial gauge fields and spin-orbit couplings in cold atom systems. We resorted to origins of literatures to trace the ideas of the developments. For pedagogical purposes, we tried to work out examples carefully and clearly, to verified the validity of various approximations and arguments in detail, and to give clear physical and mathematical pictures of the problems that we discussed. The first part of this article introduced the fundamental concepts of Berry phase and Jaynes-Cummings model. The second part reviewed two schemes to generate artificial gauge fields with N-pod scheme in cold atom systems. The first one is based on dressed-atom picture which provide a method to generate non-Abelian gauge fields with dark states. The second one is about rotating scheme which is achieved earlier historically. Non-Abelian gauge field inevitably leads to spin-orbit coupling. We reviewed some developments in achieve spin-orbital coupling theoretically and experimentally. The fourth part was devoted to recently developed idea of optical flux lattice that provides a possibility to reach the strongly correlated regime in cold atom systems. We developed a geometrical interpretation based on Coopers theory. Some useful formulae and their proofs were listed in the Appendix.
It has been proposed that an extended version of the Hubbard model which potentially hosts rich possibilities of correlated physics may be well simulated by the transition metal dichalcogenide (TMD) moir{e} heterostructures. Motivated by recent reports of continuous metal insulator transition (MIT) at half filling, as well as correlated insulators at various fractional fillings in TMD moir{e} heterostructures, we propose a theory for the potentially continuous MIT with fractionalized electric charges. The charge fractionalization at the MIT will lead to experimental observable effects, such as a large universal resistivity jump and interaction driven bad metal at the MIT, as well as special scaling of the quasi-particle weight with the tuning parameter. These predictions are different from previously proposed theory for continuous MIT.
We investigate the rich quantum phase diagram of Wegners theory of discrete Ising gauge fields interacting with $U(1)$ symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model reduces to (i) pure $mathbb{Z}_2$ even and odd gauge theories, (ii) free fermions in a static background of deconfined $mathbb{Z}_2$ gauge fields, (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. We develop a local transformation that maps the lattice gauge theory onto a model of $mathbb{Z}_2$ gauge-invariant spin $1/2$ degrees of freedom. Using the mapping, we perform numerical density matrix renormalization group calculations that corroborate our understanding of the limits identified above. Moreover, in the absence of the magnetic plaquette term, we reveal signatures of topologically ordered Dirac semimetal and staggered Mott insulator phases at half-filling. At strong coupling, the lattice gauge theory displays fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, we predict that in the ground state dimers form compact clusters, whose hopping is suppressed exponentially in their size. We determine the band structure of the smallest clusters numerically using exact diagonalization.
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