Tomonaga-Luttinger liquid (TLL) theory is a canonical formalism used to describe one-dimensional (1D) metals, where the low energy physics is determined by collective bosonic excitations. In this work, we present a theoretical model to compute the parameters of Tomonaga-Luttinger liquid (TLL) in multi-wall nanotubes (MWNTs). MWNTs introduce additional complexity to the usual fermionic chains due to interactions and hybridization between their multiple coaxial shells. We consider a model in which conducting paths along the length of the MWNTs are randomly distributed among the shells. Since the valley degree of freedom remains a good quantum number, the TLL description in addition to spin and charge, contains also valley degree of freedom, hence four mode description applies. The values of all four TLL parameters are obtained for this model. A surprising outcome is that the compressibility of the holon mode becomes a universal quantity, while the parameters of neutral modes will depend on the details of inter-shell coupling. Finally, we propose experiments where our predictions can be tested.
Tomonaga-Luttinger liquid (TLL) theory is a canonical formalism used to describe one-dimensional (1D) metals, where the low energy physics is determined by collective bosonic excitations. In this work, we present a theoretical model to compute the parameters of Tomonaga-Luttinger liquid (TLL) in multi-wall nanotubes (MWNTs). MWNTs introduce additional complexity to the usual fermionic chains due to interactions and hybridization between their multiple coaxial shells. We consider a model in which conducting paths along the length of the MWNTs are randomly distributed among the shells. Since the valley degree of freedom remains a good quantum number, the TLL description in addition to spin and charge, contains also valley degree of freedom, hence four mode description applies. The values of all four TLL parameters are obtained for this model. A surprising outcome is that the compressibility of the holon mode becomes a universal quantity, while the parameters of neutral modes will depend on the details of inter-shell coupling. Finally, we propose experiments where our predictions can be tested.
The eect of electronic many-body interactions in one-dimensional (1D) systems is drastically enhanced compared to higher dimensions due to the restricted phasespace, often leading to strong electronic correlations. It can be shown that due to a breakdown of the Fermi liquid theory, the ground state at low temperatures becomes a Tomonaga-Luttinger liquid (TLL). In a TLL, the strength of electronic correlations is characterized by the Luttinger parameter K, ranging between K = 0 and K = 1, where K = 1 describes non-interacting electrons. Various systems, such as single-walled carbon nanotubes, 1D atomic metal chains, and MoS 2 mirror twin boundaries, have been reported to host TLLs, in which spin-degeneracy is intact.
The paradigmatic state of a 1D collective metal, the Tomonaga-Luttinger liquid (TLL), offers us an exact analytic solution for a strongly interacting quantum system not only for infinite systems at zero temperature but also at finite temperature and with a boundary. Potentially, these results are of high relevance for technology as they could lay the foundation for a many-body description of various nanostructures. For this to happen, we need expressions for local (i.e., spatially resolved) correlations as a function of frequency. In this study, we find such expressions and study their outcome. Based on our analytic expressions we are able to identify two distinct cases of TLL which we call Coulomb metal and Hund metal, respectively. We argue that these two cases span all the situations possible in nanotubes made out of p-block elements. From an applications viewpoint, it is crucial to capture the fact that the end of the 1D system can be coupled with the external environment and emit electrons into it. We discuss such coupling on two levels for both Coulomb and Hund metals: i) in the zeroth order approximation, the coupling modifies the 1D system's boundary conditions; ii) stronger coupling, when the environment can self-consistently modify the 1D system, we introduce spatially dependent TLL parameters. In case ii) we were able to capture the presence of plasmon-polariton particles, thus building a link between TLL and the field of nano-optics.
In one-dimensional conductors, Coulomb interactions result in correlated electronic systems called Tomonaga-Luttinger liquids (TLL). The TLL physics also applies to other many-body phenomena, providing complementary viewpoints while benefiting from the powerful TLL framework. One such phenomenon is the low-energy conductance suppression of a quantum coherent conductor embedded in a dissipative circuit, an effect called dynamical Coulomb blockade. Here we investigate the basic class of mesoscopic circuits constituted by a short single-channel quantum conductor in series with a resistance R. Remarkably, such circuits can be mapped on a TLL of interaction parameter 1/(1+Re^2/h), with an impurity. From this mapping, generalized to realistic dissipative circuits, a scaling law for the suppressed conductance is derived at R=h/e^2, and small deviations computed for R \neq h/e^2. We find that the scaling law is obeyed by our data for arbitrary quantum channels, emulated by a Ga(Al)As quantum point contact, and by the recent data of Mebrahtu et al. [Nature 488, 61 (2012)] obtained using a carbon nanotube. This demonstrates a highly tunable test-bed for TLL physics, and consolidates a recently proposed phenomenological expression for the conductance of a quantum channel in a linear circuit.
The concept of Tomonaga--Luttinger liquids (TLL) on the basis of the free-boson models is ubiquitous in theoretical descriptions of low-energy properties in one-dimensional quantum systems. In this work, we develop a squeezed-field path-integral description for gapless one-dimensional systems beyond the free-boson picture of the TLL paradigm. In the squeezed-field description, the parameter of the Bogoliubov transformation for the TL Hamiltonian becomes a dynamical squeezing field, and its fluctuations give rise to corrections to the free-boson results. We derive an effective nonlinear Lagrangian describing the dispersion relation of the squeezing field, and interactions between the excitations of the TLL and the squeezing modes. Using the effective Lagrangian, we analyze the imaginary-time correlation function of a vertex operator in the non-interacting limit. We show that a side-band branch emerges due to the fluctuation of the squeezing field, in addition to the standard branch of the free-boson model of the TLL paradigm. Furthermore, we perturbatively analyze the spectral function of the density fluctuations for an ultracold Bose gas in one dimension. We evaluate the renormalized values of the phase velocities and spectral weights of the TLL and side-band branches due to the interaction between the TLL and the squeezing modes. At zero temperature, the renormalized dispersion relations are linear in the momentum, but at nonzero temperatures, these acquire a nonlinear dependence on the momentum due to the thermal population of the excitation branches.
Abstract The Tomonaga–Luttinger liquid (TLL) theory describes the low-energy excitations of strongly correlated one-dimensional (1D) fermions. In the past years, a number of studies have provided a detailed understanding of this universality class. More recently, theoretical investigations that go beyond the standard low-temperature, linear-response TLL regime have been developed. While these provide a basis for understanding the dynamics of the spin-incoherent Luttinger liquid, there are few experimental investigations in this regime. Here we report the observation of a thermally induced, spin-incoherent Luttinger liquid in a 6Li atomic Fermi gas confined to 1D. We use Bragg spectroscopy to measure the suppression of spin-charge separation and the decay of correlations as the temperature is increased. Our results probe the crossover between the coherent and incoherent regimes of the Luttinger liquid and elucidate the roles of the charge and the spin degrees of freedom in this regime.
The one-dimensional (1D) Yang-Gaudin model--an integrable δ-function interacting Fermi gas, serves as a paradigm in quantum many-body physics, encompassing phenomena from spin-charge separation to the Luther-Emery liquid. However, a consistent description of the Luther-Emery liquid and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like pairing states in the 1D attractive Fermi gas remains elusive. In this work, we develop a universal Tomonaga-Luttinger liquid (TLL) theory to describe the FFLO state both for the case of weak and strong binding between fermions of opposite spins. We rigorously derive a low-energy effective Hamiltonian using bosonization, revealing the emergence of a two-component TLL: one exhibiting spin-charge coupling in the weak binding regime, and another featuring charge-charge separation in the strong binding regime. For the weak binding regime, we further derive renormalization-group equations for the sine-Gordon term in the spin sector and show that this term undergoes a relevant-irrelevant phase transition driven by the magnetic field. We further analyze the dynamical correlation functions of the FFLO pairing state based on the effective Hamiltonian we constructed. Finally, we discuss experiments using ultracold atoms to elucidate the Luther-Emery liquid behavior and the subtle phenomena of spin-charge coupling and charge-charge separation.