We derive an analytic expression for the zero temperature Fourier transform of the density-density correlation function of a multicomponent Luttinger liquid with different velocities. By employing Schwinger identity and a generalized Feynman identity
exact integral expressions are derived, and approximate analytical forms are given for frequencies close to each component singularity. We find power-like singularities and compute the corresponding exponents. Numerical results are shown for the case of three components.
We derive the dynamical structure factor for an inhomogeneous Tomonaga-Luttinger liquid as can be formed in a confined strongly interacting one-dimensional gas. In view of current experimental progress in the field, we provide a simple analytic expre
ssion for the light-scattering cross section, requiring only the knowledge of the density dependence of the ground-state energy, as they can be extracted e.g. from exact or Quantum Monte Carlo techniques, and a Thomas-Fermi description. We apply the result to the case of one-dimensional quantum bosonic gases with dipolar interaction in a harmonic trap, using an energy functional deduced from Quantum Monte Carlo computations. We find an universal scaling behavior peculiar of the Tomonaga-Luttinger liquid, a signature that can be eventually probed by Bragg spectroscopy in experimental realizations of such systems.
We determine the phase diagram and the momentum distribution for a one-dimensional Bose gas with repulsive short range interactions in the presence of a two-color lattice potential, with incommensurate ratio among the respective wave lengths, by usin
g a combined numerical (DMRG) and analytical (bosonization) analysis. The system displays a delocalized (superfluid) phase at small values of the intensity of the secondary lattice V2 and a localized (Bose glass-like) phase at larger intensity V2. We analyze the localization transition as a function of the height V2 beyond the known limits of free and hard-core bosons. We find that weak repulsive interactions unfavor the localized phase i. e. they increase the critical value of V2 at which localization occurs. In the case of integer filling of the primary lattice, the phase diagram at fixed density displays, in addition to a transition from a superfluid to a Bose glass phase, a transition to a Mott-insulating state for not too large V2 and large repulsion. We also analyze the emergence of a Bose-glass phase by looking at the evolution of the Mott-insulator lobes when increasing V2. The Mott lobes shrink and disappear above a critical value of V2. Finally, we characterize the superfluid phase by the momentum distribution, and show that it displays a power-law decay at small momenta typical of Luttinger liquids, with an exponent depending on the combined effect of the interactions and of the secondary lattice. In addition, we observe two side peaks which are due to the diffraction of the Bose gas by the second lattice. This latter feature could be observed in current experiments as characteristics of pseudo-random Bose systems.
We determine the excitation spectrum of a bosonic dipolar quantum gas in a one-dimensional geometry, from the dynamical density-density correlation functions simulated by means of Reptation Quantum Monte Carlo techniques. The excitation energy is alw
ays vanishing at the first vector of the reciprocal lattice in the whole crossover from the liquid-like at low density to the quasi-ordered state at high density, demonstrating the absence of a roton minimum. Gaps at higher reciprocal lattice vectors are seen to progressively close with increasing density, while the quantum state evolves into a quasi-periodic structure. The simulational data together with the uncertainty-principle inequality also provide a rigorous proof of the absence of long-range order in such a super-strongly correlated system. Our conclusions confirm that the dipolar gas is in a Luttinger-liquid state, significantly affected by the dynamical correlations. The connection with ongoing experiments is also discussed.
We calculate the excitation modes of a 1D dipolar quantum gas confined in a harmonic trap with frequency $omega_0$ and predict how the frequency of the breathing n=2 mode characterizes the interaction strength evolving from the Tonks-Girardeau value
$omega_2=2omega_0$ to the quasi-ordered, super-strongly interacting value $omega_2=sqrt{5}omega_0$. Our predictions are obtained within a hydrodynamic Luttinger-Liquid theory after applying the Local Density Approximation to the equation of state for the homogeneous dipolar gas, which are in turn determined from Reptation Quantum Monte Carlo simulations. They are shown to be in quite accurate agreement with the results of a sum-rule approach. These effects can be observed in current experiments, revealing the Luttinger-liquid nature of 1D dipolar Bose gases.
Recent experiments have revealed the role of staggered Dzialoshinskii-Moriya interaction in the magnetized phase of an antiferromagnetic spin 1/2 two-leg ladder compound under a uniform magnetic field. We derive a low energy effective field theory de
scribing a magnetized two-leg ladder with a weak staggered Dzialoshinskii-Moriya interaction. This theory predicts the persistence of the spin gap in the magnetized phase, in contrast to standard two-leg ladders, and the presence of bound states in the excitation spectrum. Such bound states are observable in Raman scattering measurements. These results are then extended to intermediate Dzialoshinskii-Moriya interaction using Exact Diagonalizations.
