Quantum simulation has the potential to investigate gauge theories in strongly-interacting regimes, which are up to now inaccessible through conventional numerical techniques. Here, we take a first step in this direction by implementing a Floquet-based method for studying Z 2 lattice gauge theories using two-component ultracold atoms in a double-well potential. For resonant periodic driving at the on-site interaction strength and an appropriate choice of the modulation parameters, the effective Floquet Hamiltonian exhibits Z 2 symmetry. We study the dynamics of the system for different initial states and critically contrast the observed evolution with a theoretical analysis of the full time-dependent Hamiltonian of the periodically-driven lattice model. We reveal challenges that arise due to symmetrybreaking terms and outline potential pathways to overcome these limitations. Our results provide important insights for future studies of lattice gauge theories based on Floquet techniques.Lattice gauge theories (LGTs) [1,2] are fundamental for our understanding of quantum many-body physics across different disciplines ranging from condensed matter [3-6] to high-energy physics [7]. However, theoretical studies of LGTs can be extremely challenging in particular in strongly-interacting regimes, where conventional computational methods are limited [8,9]. To overcome these limitations alternative numerical tools are currently developed, which enable out-of-equilibrium and finite density computations [10][11][12][13]. In parallel, the rapid progress in the field of quantum simulation [14][15][16][17] has sparked a growing interest in designing experimental platforms to explore the rich physics of LGTs [18][19][20][21][22][23][24][25]. State-of-the-art experiments are now able to explore the physics of static [26] as well as density-dependent gauge fields [27] and have engineered controlled few-body interactions [28][29][30], which are the basis for many proposed schemes to realize LGTs. First studies of the Schwinger model have been performed with quantum-classical algorithms [31] and a digital quantum computer composed of four trapped ions [32]. The challenge for analog quantum simulators mainly lies in the complexity to engineer gauge-invariant interactions between matter and gauge fields.Here, we explore the dynamics of a minimal model for Z 2 LGTs coupled to matter with ultracold atoms in periodically-driven double-well potentials [33]. An alternative technique was recently proposed for digital quantum simulation [34]. Z 2 LGTs are of high interest in condensed matter physics [13,[35][36][37] and topological quantum computation [38]. Our scheme is based on densitydependent laser-assisted tunneling techniques [39][40][41][42]. We use a mixture of bosonic atoms in two different internal states to encode the matter and gauge field degrees of freedom. The interaction between these states is engineered via resonant periodic modulation [43][44][45][46] of the on-site potential at the inter-species Hubbard interaction [47][48...

We compute the ground-state correlation functions of an exactly solvable chain of integer spins, recently introduced in [R. Movassagh and P. W. Shor, arXiv:1408.1657], whose ground state can be expressed in terms of a uniform superposition of all colored Motzkin paths. Our analytical results show that for spin s > 2 there is a violation of the cluster decomposition property. This has to be contrasted with s = 1, where the cluster property holds. Correspondingly, for s = 1 one gets a light-cone profile in the propagation of excitations after a local quench, while the cone is absent for s = 2, as shown by time dependent density-matrix renormalization group. Moreover, we introduce an original solvable model of half-integer spins, which we refer to as Fredkin spin chain, whose ground state can be expressed in terms of superposition of all Dyck paths. For this model we exactly calculate the magnetization and correlation functions, finding that for s = 1/2, a conelike propagation occurs, while for higher spins, s = 3/2 or greater, the colors prevent any cone formation and clustering is violated, together with square root deviation from the area law for the entanglement entropy

Artificial magnetic fields and spin-orbit couplings have been recently generated in ultracold gases in view of realizing topological states of matter and frustrated magnetism in a highlycontrollable environment. Despite being dynamically tunable, such artificial gauge fields are genuinely classical and exhibit no back-action from the neutral particles. Here we go beyond this paradigm, and demonstrate how quantized dynamical gauge fields can be created in mixtures of ultracold atoms in optical lattices. Specifically, we propose a protocol by which atoms of one species carry a magnetic flux felt by another species, hence realizing an instance of fluxattachment. This is obtained by combining coherent lattice modulation techniques with strong Hubbard interactions. We demonstrate how this setting can be arranged so as to implement lattice models displaying a local Z 2 gauge symmetry, both in one and two dimensions. We also provide a detailed analysis of a ladder toy model, which features a global Z 2 symmetry, and reveal the phase transitions that occur both in the matter and gauge sectors. Mastering flux-attachment in optical lattices envisages a new route towards the realization of strongly-correlated systems with properties dictated by an interplay of dynamical matter and gauge fields. arXiv:1810.02777v1 [cond-mat.quant-gas]

We demonstrate that hidden long range order is always present in the gapped phases of interacting fermionic systems on one dimensional lattices. It is captured by correlation functions of appropriate nonlocal charge and/or spin operators, which remain asymptotically finite. The corresponding microscopic orders are classified. The results are confirmed by DMRG numerical simulation of the phase diagram of the extended Hubbard model, and of a Haldane insulator phase.The behavior of strongly correlated electron systems has been widely investigated to understand the physics of several phenomena in condensed matter, ranging from the insulating regime to high-T c superconductivity. Due to the many degrees of freedom involved, many aspects of the micro-and macroscopic behavior of these systems remain unclear. Recently their simulation by means of ultracold gases of two-component fermionic atoms trapped onto optical lattices has opened new possibilities, leading for instance to the direct observation of the predicted magnetic [1] and Mott insulating (MI) phases [2]. The latter is efficiently modeled by the Hubbard Hamiltonian. In this case, it has been noticed quite recently [3] that in one dimension (1D) it is possible to identify a nonlocal order parameter in the MI phase, which displays long-range order (LRO); a result that is in agreement with Coleman-Hohenberg-Mermin-Wagner theorem [4] since no continuous symmetry of the system has been broken. The discovery envisaged a description of the underlying parity charge order, whose microscopic configurations are depicted below in the second cartoon of Fig.1: the Mott phase consists of a chain of single fermions with up and down spin, where fluctuations of pairs of empty and doubly occupied sites (holons and doublons) are bounded. The behavior is reminiscent of that observed in the insulating regime of a degenerate gas of bosonic atoms [5].In general, the observation of gapped phases in 1D systems is not believed to be necessarily related to the presence of some type of LRO, since the strong quantum fluctuation are expected to destroy any such order. In this Letter we show that LRO is instead hidden in every gapped phase of one dimensional correlated fermionic systems. The result is achieved by means of a general analysis of the bosonization treatment applied on a prototype lattice model Hamiltonian for these systems. We identify in the lattice the nonlocal parity and string operators responsible for the different types of LRO. As a byproduct, both charge and spin excitations turn out to be independently ordered, while local operators intrinsically generate both. It is tempting to conclude that nonlocal operators are "more fundamental" with respect to the usual local ones, at least for the description of the possible orders in the ground state phase diagram of these systems. To test our results we perform a density matrix renormalization group (DMRG) analysis at halffilling and zero temperature of the standard extended Hubbard case, focusing on the insulating phases.We star...