12p-K-6 Tomonaga-Luttinger Liquid

Masaki Oshikawa

Masao Ogata, Hidetoshi Fukuyama

Isabelle Bouchoule, R. Citro, T. Duty +5 more

Akira Furusaki

Quantum impurity problems in Tomonaga-Luttinger liquids (TLLs) are reviewed with emphasis on their analogy to the Kondo problem in Fermi liquids. First, the problem of a static impurity in a spinless TLL is considered, which is related to the model studied in the context of the macroscopic quantum coherence. In the low-energy limit the TLL is essentially cut into two pieces when interaction is repulsive. The orthogonality catastrophe in a TLL is then discussed. Finally, the Kondo effect of a spin-1/2 impurity in a one-dimensional repulsively interacting electron liquids (a spinful TLL) is reviewed. Regardless of the sign of the exchange coupling, the impury spin is completely screened in the ground state. The leading low-temperature contributions to thermodynamic quantities come from boundary contributions of a bulk leading irrelevant operator.

Masahiro Sato

Abstract. Uniform-field effects for frustrated odd-leg integer-spin tubes (cylinder type spin systems) are investigated in the weak interchain-coupling regime. We predict that, as the field exceeds the spin gap, a two-component Tomonaga-Luttinger liquid (TLL) appears due to the condensation of the doubly degenerate lowest magnons. Furthermore, it is argued that when the uniform field is so strong that the second lowest magnons are also condensed, the two-component TLL is destroyed and a new one-component TLL emerges. This quantum phase transition may be detected as a magnetization cusp. Keywords: integer-spin tube, frustration, Tomonaga-Luttinger liquid, magnetization cusp, nonlinear sigma model, bosonization PACS: 75.10.Jm, 75.40.Cx, 75.50.Ee In one-dimensional (1D) gapped isotropic spin systems, a uniform magnetic field, which causes the rotation symmetry to reduce to a U(1) one, generally removes the gap and induces a magnon-condensed phase regarded as a Tomonaga-Luttinger liquid (TLL) [1] with central charge c = 1. Zamolodchikov’s c theorem [2] actually predicts that a c = 1 TLL state tends to occur in U(1) symmetric 1D systems. However, frustration often breaks such conventional scenarios. In this short paper, we focus on the field-induced critical phases in frustrated integer-spin tubes, and discuss the possibility of the existence of an unconventional two-component TLL (we call this c = 1 + 1 state in this paper) and a quantum phase transition. Here, the tube means a ladder with a periodic boundary condition along the interchain (rung) direction. For more details, refer to Ref. [3]. The N(finite)-leg spin tube Hamiltonian is given by

Naira Grigoryan, Piotr Chudziński

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.