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Register a new userWigner crystal vs. Friedel oscillations in the 1D Hubbard model
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We analyze the fermion density of the one-dimensional Hubbard model using bosonization and numerical DMRG calculations. For finite systems we find a relatively sharp crossover even for moderate short range interactions into a region with $4k_F$ density waves as a function of density. The results show that the unstable fixed point of a spin-incoherent state can dominate the physical behavior in a large region of parameter space in finite systems. The crossover may be observable in ultra cold fermionic gases in optical lattices and in finite quantum wires.
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In one-dimensional quantum systems with strong long-range repulsion particles arrange in a quasi-periodic chain, the Wigner crystal. We demonstrate that besides the familiar phonons, such one-dimensional Wigner crystal supports an additional mode of elementary excitations, which can be identified with solitons in the classical limit. We compute the corresponding excitation spectrum and argue that the solitons have a parametrically small decay rate at low energies. We discuss implications of our results for the behavior of the dynamic structure factor.
Electron-electron interactions strongly affect the behavior of low-dimensional systems. In one dimension (1D), arbitrarily weak interactions qualitatively alter the ground state producing a Luttinger liquid (LL) which has now been observed in a number of experimental systems. Interactions are even more important at low carrier density, and in the limit when the long-ranged Coulomb potential is the dominant energy scale, the electron liquid is expected to become a periodically ordered solid known as the Wigner crystal. In 1D, the Wigner crystal has been predicted to exhibit novel spin and magnetic properties not present in an ordinary LL. However, despite recent progress in coupled quantum wires, unambiguous experimental demonstration of this state has not been possible due to the role of disorder. Here, we demonstrate using low-temperature single-electron transport spectroscopy that a hole gas in low-disorder carbon nanotubes with a band gap is a realization of the 1D Wigner crystal. Our observation can lead to unprecedented control over the behavior of the spatially separated system of carriers, and could be used to realize solid state quantum computing with long coherence times.
Under a perfect periodic potential, the electric current density induced by a constant electric field may exhibit nontrivial oscillations, so-called Bloch oscillations, with an amplitude that remains nonzero in the large system size limit. Such oscillations have been well studied for nearly noninteracting particles and observed in experiments. In this work, we revisit Bloch oscillations in strongly interacting systems. By analyzing the spin-1/2 XXZ chain, which can be mapped to a model of spinless electrons, we demonstrate that the current density at special values of the anisotropy parameter $Delta=-cos(pi/p)$ ($p=3,4,5,cdots$) in the ferromagnetic gapless regime behaves qualitatively the same as in the noninteracting case ($Delta=0$) even in the weak electric field limit. When $Delta$ deviates from these values, the amplitude of the oscillation under a weak electric field is suppressed by a factor of the system size. We estimate the strength of the electric field required to observe such a behavior using the Landau--Zener formula.
Conventional wisdom had long held that a composite particle behaves just like an ordinary Newtonian particle. In this paper, we derive the effective dynamics of a type-I Wigner crystal of composite particles directly from its microscopic wave function. It indicates that the composite particles are subjected to a Berry curvature in the momentum space as well as an emergent dissipationless viscosity. Therefore, contrary to the general belief, composite particles follow the more general Sundaram-Niu dynamics instead of the ordinary Newtonian one. We show that the presence of the Berry curvature is an inevitable feature for a dynamics consistent with the dipole picture of composite particles and Kohns theorem. Based on the dynamics, we determine the dispersions of magneto-phonon excitations numerically. We find an emergent magneto-roton mode which signifies the composite-particle nature of the Wigner crystal. It occurs at frequencies much lower than the magnetic cyclotron frequency and has a vanishing oscillator strength in the long wavelength limit.
The spatial Fourier spectrum of the electron density distribution in a finite 1D system and the distribution function of electrons over single-particle states are studied in detail to show that there are two universal features in their behavior, which characterize the electron ordering and the deformation of Wigner crystal by boundaries. The distribution function has a $delta$-like singularity at the Fermi momentum $k_F$. The Fourier spectrum of the density has a step-like form at the wavevector $2k_F$, with the harmonics being absent or vanishing above this threshold. These features are found by calculations using exact diagonalization method. They are shown to be caused by Wigner ordering of electrons, affected by the boundaries. However the common Luttinger liquid model with open boundaries fails to capture these features, because it overestimates the deformation of the Wigner crystal. An improvement of the Luttinger liquid model is proposed which allows one to describe the above features correctly. It is based on the corrected form of the density operator conserving the particle number.
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