(3+1) Massive Dirac Fermions with Ultracold Atoms in Optical Lattices

We propose the experimental realization of (3+1) relativistic Dirac fermions using ultracold atoms in a rotating optical lattice or, alternatively, in a synthetic magnetic field. This approach has the advantage to give mass to the Dirac fermions by coupling the ultracold atoms to a Bragg pulse. A dimensional crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the anisotropy of the lattice. We also discuss under which conditions the interatomic potentials give rise to relativistically invariant interactions among the Dirac fermions

Simulation of gauge transformations on systems of ultracold atoms

We show that gauge transformations can be simulated on systems of ultracold atoms. We discuss observables that are invariant under these gauge transformations and compute them using a tensor network ansatz that escapes the phase problem. We determine that the Mott-insulator-to-superfluid critical point is monotonically shifted as the induced magnetic flux increases. This result is stable against the inclusion of a small amount of entanglement in the variational ansatz.Comment: 14 pages, 6 figure

Effective Theory and Breakdown of Conformal Symmetry in a Long-Range Quantum Chain

We deal with the problem of studying the symmetries and the effective theories of long-range models around their critical points. A prominent issue is to determine whether they possess (or not) conformal symmetry (CS) at criticality and how the presence of CS depends on the range of the interactions. To have a model, both simple to treat and interesting, where to investigate these questions, we focus on the Kitaev chain with long-range pairings decaying with distance as power-law with exponent alpha. This is a quadratic solvable model, yet displaying non-trivial quantum phase transitions. Two critical lines are found, occurring respectively at a positive and a negative chemical potential. Focusing first on the critical line at positive chemical potential, by means of a renormalization group approach we derive its effective theory close to criticality. Our main result is that the effective action is the sum of two terms: a Dirac action S-D, found in the short-range Ising universality class, and an "anomalous" CS breaking term SAN. While SD originates from low-energy excitations in the spectrum, SAN originates from the higher energy modes where singularities develop, due to the long-range nature of the model. At criticality SAN flows to zero for alpha > 2, while for alpha infinity the ELI is restored. In order to test the validity of the determined effective theory, we compared the two-fermion static correlation functions and the von Neumann entropy obtained from them with the ones calculated on the lattice, finding agreement. These results explain two observed features characteristic of long-range models, the hybrid decay of static correlation functions within gapped phases and the area-law violation for the von Neumann entropy. The proposed scenario is expected to hold in other long-range models displaying quasiparticle excitations in ballistic regime. From the effective theory one can also see that new phases emerge for alpha infinity) model, are not altered. This also shows that the long-range paired Kitaev chain provides an example of a long-range model in which the value of a where the CS is broken does not coincide with the value at which the critical exponents start to differ from the ones of the corresponding short-range model. At variance, for the second critical line, having negative chemical potential, only SAN (So) is present for 1 2). Close to this line, where the minimum of the spectrum coincides with the momentum where singularities develop, the critical exponents change where CS is broken. \ua9 2016 Elsevier Inc

(3+1) massive Dirac fermions with ultracold atoms in frustrated cubic optical lattices

We propose the experimental realization of (3+1) relativistic Dirac fermions using ultracold atoms in a cubic optical lattice in a frustrating magnetic field which can be realized by rotating the lattice or, alternatively, using a synthetic gauge field. We show that it is possible to give mass to the Dirac fermions by coupling the ultracold atoms to a Bragg pulse: the method relies on the peculiar position of the Dirac points in the (magnetic) Brillouin zone, and it would not generally work for other lattices (e.g., for honeycomb lattices). A dimensional crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the anisotropy of the lattice. Finally, we also discuss under which conditions the interatomic potentials give rise to relativistically invariant interactions among the Dirac fermions

Singular dynamics and emergence of nonlocality in long-range quantum models

We discuss how nonlocality originates in long-range quantum systems and how it affects their dynamics at and out of equilibrium. We focus in particular on the Kitaev chains with long-range pairings and on the quantum Ising chain with long-range antiferromagnetic coupling (both having a powerlaw decay with exponent \uce\ub1). By studying the dynamic correlation functions, we find that for every finite \uce\ub1 two different behaviours can be identified, one typical of short-range systems and the other connected with locality violation. The latter behaviour is shown related also with the known power-law decay tails previously observed in the static correlation functions, and originated by modesiXhaving in general energies far from the minima of the spectrum-where particular singularities develop as a consequence of the long-rangedness of the system. We refer to these modes as to 'singular' modes, and as to 'singular dynamics' to their dynamics. For the Kitaev model they are manifest, at finite \uc2\ua3\, in derivatives of the quasiparticle energy, the order of the derivatives at which the singularity occurs is increasing with \uce\ub1. The features of the singular modes and their physical consequences are clarified by studying an effective theory for them and by a critical comparison of the results from this theory with the lattice ones. Moreover, a numerical study of the effects of the singular modes on the time evolution after various types of global quenches is performed. We finally present and discuss the presence of singular modes and their consequences in interacting long-range systems by investigating in the long-range Ising quantum chain, both in the deep paramagnetic regime and at criticality, where they also play a central role for the breakdown of conformal invariance