Temperature and magnetic field-dependent correlators of the exactly integrable (1+1)-dimensional gas of impenetrable fermions

Temperature-Dependent Periodicity of the Persistent Current in Strongly Interacting Systems

The persistent current in small isolated rings enclosing magnetic flux is the current circulating in equilibrium in the absence of an external excitation. While initially studied in superconducting and normal metals, recently, atomic persistent currents have been generated in ultracold gases spurring a new wave of theoretical investigations. Nevertheless, our understanding of the persistent currents in interacting systems is far from complete, especially at finite temperatures. Here we consider the fermionic one-dimensional Hubbard model and show that in the strong-interacting limit, the current can change its flux period and sign (diamagnetic or paramagnetic) as a function of temperature, features that cannot be explained within the single-particle or Luttinger liquid techniques. Also, the magnitude of the current can counterintuitively increase with temperature, in addition to presenting different rates of decay depending on the polarization of the system. Our work highlights the properties of the strongly interacting multicomponent systems that are missed by conventional approximation techniques, but can be important for the interpretation of experiments on persistent currents in ultracold gases.

Momentum distribution and tunneling density of states of one-dimensional Fermionic [Formula: see text] Hubbard model

We study the one-dimensional Fermionic Hubbard model with [Formula: see text] spin symmetry in the incommensurate filling case. The basic properties of Green's function, momentum distribution and tunneling density of states of the system at low temperature are studied in the frame work of Luttinger liquid theory combined with Bethe Ansatz solutions for arbitrary interaction. In the strong interacting case, the system enters the spin-incoherent regime at intermediate temperature [Formula: see text] and we obtain the Green's function and tunneling density of states by generalizing the path integral approach for the [Formula: see text] case to the [Formula: see text] case in this regime. The theoretical results we obtained agree qualitatively with the experiments on the one-dimensional alkaline earth atomic system with [Formula: see text] spin symmetry. The similarities and difference between the one-dimensional [Formula: see text] Fermionic Hubbard system at large N and the one-dimensional spinless Bosonic system are also investigated.

Singular responses of spin-incoherent Luttinger liquids

When a local potential changes abruptly in time, an electron gas responds by shifting to a new state which at long times is orthogonal to the one in the absence of the local potential. This is known as Anderson's orthogonality catastrophe and it is relevant for the so-called x-ray edge or Fermi-edge singularity, and for tunneling into an interacting one-dimensional system of fermions. It often happens that the finite frequency response of the photon absorption or the tunneling density of states exhibits a singular behavior as a function of frequency: [Formula: see text], where ω(th) is a threshold frequency and α is an exponent characterizing the singular response. In this review singular responses of spin-incoherent Luttinger liquids are reviewed. Such responses most often do not fall into the familiar form above, but instead typically exhibit logarithmic corrections and display a much higher universality in terms of the microscopic interactions in the theory. Specific predictions are made, the current experimental situation is summarized and key outstanding theoretical issues related to spin-incoherent Luttinger liquids are highlighted.

Green's function for magnetically incoherent interacting electrons in one dimension

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)]].

Nonunitary spin-charge separation in a one-dimensional fermion gas

In this Letter we report exact results on the infrared asymptotics of the one-particle dynamical correlation function of the gas of impenetrable spin 1/2 fermions at infinitesimal temperature. The correlation function shows signs of spin-charge separation with scaling behavior in the charge part and exponential decay as a function of the space coordinate in the spin part. Surprisingly, the anomalous dimensions in the charge part do not correspond to any unitary conformal field theory. We find that the fermion spectral weight has a power law divergency at low energy with the anomalous exponent -1/2.