Bosons with density-dependent hopping on a one dimensional lattice have been shown to emulate anyonic particles with fractional exchange statistics. Leveraging this, we construct a Josephson junction setup, where an insulating barrier in the form of a Mott-insulator is sandwiched between two superfluid phases. This is obtained by spatially varying either the statistical phase or the strength of the on-site interaction potential on which the ground state of the system depends. Utilizing numerical methods such as exact diagonalization and density renormalization group theory, the ground state properties of this setup are investigated to understand the Josephson effect in a strongly correlated regime. The dynamical properties of this model for different configurations of this model are analyzed to find the configurations that can produce the Josephson effect. Furthermore, it is observed that continuous particle flow over time is achievable in this proposed model solely by creating an initial phase difference without any external biasing.
Bosons with density-dependent hopping on a one dimensional lattice have been shown to emulate anyonic particles with fractional exchange statistics. Leveraging this, we construct a Josephson junction setup, where an insulating barrier in the form of a Mott-insulator is sandwiched between two superfluid phases. This is obtained by spatially varying either the statistical phase or the strength of the on-site interaction potential on which the ground state of the system depends. Utilizing numerical methods such as exact diagonalization and density renormalization group theory, the ground state properties of this setup are investigated to understand the Josephson effect in a strongly correlated regime. The dynamical properties of this model for different configurations of this model are analyzed to find the configurations that can produce the Josephson effect. Furthermore, it is observed that continuous particle flow over time is achievable in this proposed model solely by creating an initial phase difference without any external biasing.
We study one-dimensional lattice anyons with extended Hubbard interactions at unit filling using bosonization and numerical simulations. The behavior can be continuously tuned from bosonic to fermionic statistics by adjusting the topological exchange angle θ, which leads to a competition of different instabilities. We present the bosonization theory in the presence of dynamic gauge fields, which predicts a phase diagram of four different gapped phases with distinct dominant correlations. Advanced numerical simulations determine and analyze the exact phase transitions between Mott insulator, charge density wave, dimerized state, and Haldane insulator, all of which meet at a multicritical line in the parameter space of anyonic angle θ, on-site interaction U, and nearest neighbor repulsion V. Superfluid and pair-superfluid phases are stable in a region of small V.
Using the Anyon–Hubbard Hamiltonian, we analyze the ground-state properties of anyons in a one-dimensional lattice. To this end we map the hopping dynamics of correlated anyons to an occupation-dependent hopping Bose–Hubbard model using the fractional Jordan–Wigner transformation. In particular, we calculate the quasi-momentum distribution of anyons, which interpolates between Bose–Einstein and Fermi–Dirac statistics. Analytically, we apply a modified Gutzwiller mean-field approach, which goes beyond a classical one by including the influence of the fractional phase of anyons within the many-body wavefunction. Numerically, we use the density-matrix renormalization group by relying on the ansatz of matrix product states. As a result it turns out that the anyonic quasi-momentum distribution reveals both a peak-shift and an asymmetry which mainly originates from the nonlocal string property. In addition, we determine the corresponding quasi-momentum distribution of the Jordan–Wigner transformed bosons, where, in contrast to the hard-core case, we also observe an asymmetry for the soft-core case, which strongly depends on the particle number density.
We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose–Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling, the system features a phase transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background—instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with two particles per site is destroyed completely by particle–hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a two-dimensional (2D) slab, localized along one spatial direction that is chosen spontaneously.
Recently optical lattices allow us to observe phase transition without the uncertainty posed by complex materials, and the simulations of these systems are an excellent bridge between materials-based condensed matter physics and cold atoms. In this way, the computational physics related to many-body problems have increased in importance. Using the density matrix renormalization group method, we studied a Hubbard model for anyons, which is an equivalent to a variant of the Bose-Hubbard model in which the bosonic hopping depends on the local density. This is an exact mapping between anyons and bosons in one dimension. The anyons interlope between bosons and fermions. For two anyons under particle exchange, the wave function acquires a fractional phase e iθ . We conclude that this system exhibits two phases: Mott-insulator and superfluid. We present the phase diagram for some angles. The Mott lobe increases with an increase of the statistical. We observed a reentrance phase transition for all lobes. We showed that the model studied is in the same universality class as the Bose-Hubbard model with two-body interactions.
Anyons are particles with intermediate quantum statistics whose wave function acquires a phase ${e}^{i\ensuremath{\theta}}$ by particle exchange. Inspired by proposals of simulating anyons using ultracold atoms trapped in optical lattices, we study a two-site anyonic Josephson junction, i.e., anyons confined in a one-dimensional double-well potential. We show, analytically and numerically, that many properties of anyonic Josephson junctions, such as Josephson frequency, imbalanced solutions, macroscopic quantum self-trapping, coherence visibility, and condensate fraction, crucially depend on the anyonic angle $\ensuremath{\theta}$. Our theoretical predictions are a solid benchmark for near-future experimental quantum simulations of anyonic matter in double-well potentials.
We use the density-matrix renormalization group method to investigate ground-state and dynamic properties of the one-dimensional Bose-Hubbard model, the effective model of ultracold bosonic atoms in an optical lattice. For fixed maximum site occupancy n b = 5, we calculate the phase boundaries between the Mott insulator and the "superfluid" phase for the lowest two Mott lobes. We extract the Tomonaga-Luttinger parameter from the density-density correlation function and determine accurately the critical interaction strength for the Mott transition. For both phases, we study the momentum distribution function in the homogeneous system, and the particle distribution and quasi-momentum distribution functions in a parabolic trap. With our zero-temperature method we determine the photoemission spectra in the Mott insulator and in the "superfluid" phase of the one-dimensional Bose-Hubbard model. In the insulator, the Mott gap separates the quasi-particle and quasi-hole dispersions. In the "superfluid" phase the spectral weight is concentrated around zero momentum.