The momentum distribution function n(k) and spin-correlation function S(k) are determined for the one-dimensional large-U Hubbard model with various electron densities. The present work is featured with an application of the Bethe-ansatz wave function, which has a simple form in the large-U limit for any electron density. Namely, its charge degrees of freedom are expressed as a Slater determinant of spinless fermions, while its spin degrees of freedom are equivalent to the one-dimensional S=(1/2 Heisenberg model. The singularity of n(k) at k=
kF is analyzed from the system size dependence. In addition to the
kF singularity, n(k) has a weak singularity at k=3
kF; however, no detectable singularity is present at 2
kF, which one might expect from the spinless fermion wave function. The singularity of S(k) at 2
kF is also examined in detail. It is concluded from the size dependence that, when the system is away from half-filling, the nature of the singularity at 2
kF is different from that in the Heisenberg model. The results are compared with the behavior in the weak-correlation regime examined with the perturbation calculation, the prediction of g-ology, and recent Monte Carlo calculations.
We theoretically investigate one-dimensional (1D) $\mathrm{SU}(\ensuremath{\kappa}$) fermions in the regime of spin-incoherent Luttinger liquid. We specifically focus on the Tonks-Girardeau gas limit where its density is sufficiently low that effective repulsions between atoms become infinite. In such case, spin exchange energy of 1D $\mathrm{SU}(\ensuremath{\kappa}$) fermions vanishes and all spin configurations are degenerate, which automatically puts them into a spin-incoherent regime. In this limit, we are able to express the single-particle density matrices in terms of those of anyons. This allows us to numerically simulate the number of particles up to
N=32. We numerically calculate single-particle density matrices in two cases: (1) equal populations for each spin components (balanced) and (2) all
Sz manifolds included. In contrast to noninteracting multicomponent fermions, the momentum distributions are broadened due to strong interactions. As $\ensuremath{\kappa}$ increases, the momentum distributions are less broadened for fixed
N, while they are more broadened for fixed number of particles per spin component. We then compare numerically calculated high-momentum tails with analytical predictions which are proportional to
1/p4, in good agreement. Thus, our theoretical study provides a comparison with the experiments of repulsive multicomponent alkaline-earth fermions with a tunable $\mathrm{SU}(\ensuremath{\kappa}$) spin symmetry in the spin-incoherent regime.
We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems, the equal-time oneparticle Green’s function at arbitrary particle density is expressed as a multiple integral form. Our formula reproduces previously known results in the following three limits: the zero-temperature, the infinite-temperature and the free fermion limits. PACS numbers: 05.30.-d, 71.10.Fd, 02.30.Ik 1
We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems, the equal-time one-particle Green's function at arbitrary particle density is expressed as a multiple-integral form. Our formula reproduces previously known results in the following three limits: the zero-temperature, the infinite-temperature and the free fermion limits.
Using a path integral approach and bosonization, we calculate the low-energy asymptotics of the one particle Green's function for a "magnetically incoherent" one dimensional strongly interacting electron gas at temperatures much greater than the typical exchange energy but much lower than the Fermi energy. The Green's function exhibits features reminiscent of spin-charge separation, with exponential spatial decay and scaling behavior with interaction dependent anomalous exponents inconsistent with any unitary conformal field theory. We compute the tunneling density of states at low energies and find that it is a power law in energy with exponent 1/(4g)-1, where g is the Luttinger interaction parameter in the charge sector. The underlying physics is made transparent by the simplicity of the approach. Our results generalize those of Cheianov and Zvonarev [Phys. Rev. Lett. 92, 176401 (2004)]].
We present a calculation of the one-particle equal time correlation function.(x) for the one-dimensional (1D) Hubbard model in the infinite U limit. We consider the zero temperature spin incoherent regime, which is obtained by first taking the limit U --> infinity and then the limit T --> 0. Using the determinant representation for.(x), we derive analytical expressions for both large and small x at an arbitrary filling factor 0 < rho < 1/ 2. The large x asymptotics of rho(x) is found to be remarkably accurate starting from x sin(2 pi rho) similar to 1. We find that the one-particle momentum distribution function rho(k) is a smooth function of k, and. rho'(k) is peaked at k = 2k(F) in contrast to spin-coherent liquid obeying the Luttinger theorem.