Asymptotic behavior of the Tomonaga-Luttinger liquid in the vicinity of the phase-separated region is investigated in the one-dimensional $t\ensuremath{-}J$ model to study the universal property of the $c=1$ conformal field theory with U(1) symmetry near the $K\ensuremath{\rightarrow}\ensuremath{\infty}$ instability. By analogy to the spinless fermion, we argue that the compressibility behaves as $\ensuremath{\kappa}\ensuremath{\propto}{(J}_{c}\ensuremath{-}{J)}^{\ensuremath{-}1},$ and that the Drude weight is constant and changes to zero discontinuously at the phase boundary. This speculation is confirmed by analyzing the finite-size effect from the result of the exact diagonalization.Asymptotic behavior of the Tomonaga-Luttinger liquid in the vicinity of the phase-separated region is investigated in the one-dimensional $t\ensuremath{-}J$ model to study the universal property of the $c=1$ conformal field theory with U(1) symmetry near the $K\ensuremath{\rightarrow}\ensuremath{\infty}$ instability. By analogy to the spinless fermion, we argue that the compressibility behaves as $\ensuremath{\kappa}\ensuremath{\propto}{(J}_{c}\ensuremath{-}{J)}^{\ensuremath{-}1},$ and that the Drude weight is constant and changes to zero discontinuously at the phase boundary. This speculation is confirmed by analyzing the finite-size effect from the result of the exact diagonalization.

arXiv:cond-mat/9702126Physical review. B, Condensed matterNov 15, 19979 citations

Instability of a quasi-1D Luttinger liquid

V. S. Babichenko, Andrey Nikolaevich Kozlov

ZhETF Pisma RedaktsiiuMay 1, 19950 citations

Probing the Excitations of the Luttinger Liquids

孫允武

Jan 1, 20080 citations

Synthetic helical liquids with ultracold atoms in optical lattices

Jan Carl Budich, C. Laflamme, Ferdinand Tschirsich +2 more

We discuss a platform for the synthetic realization of key physical properties of helical Tomonaga Luttinger liquids (HTLLs) with ultracold fermionic atoms in one-dimensional optical lattices. The HTLL is a strongly correlated metallic state where spin polarization and propagation direction of the itinerant particles are locked to each other. We propose an unconventional one-dimensional Fermi-Hubbard model which, at quarter filling, resembles the HTLL in the long wavelength limit, as we demonstrate with a combination of analytical (bosonization) and numerical (density matrix renormalization group) methods. An experimentally feasible scheme is provided for the realization of this model with ultracold fermionic atoms in optical lattices. Finally, we discuss how the robustness of the HTLL against backscattering and imperfections, well known from its realization at the edge of two-dimensional topological insulators, is reflected in the synthetic one-dimensional scenario proposed here.We discuss a platform for the synthetic realization of key physical properties of helical Tomonaga Luttinger liquids (HTLLs) with ultracold fermionic atoms in one-dimensional optical lattices. The HTLL is a strongly correlated metallic state where spin polarization and propagation direction of the itinerant particles are locked to each other. We propose an unconventional one-dimensional Fermi-Hubbard model which, at quarter filling, resembles the HTLL in the long wavelength limit, as we demonstrate with a combination of analytical (bosonization) and numerical (density matrix renormalization group) methods. An experimentally feasible scheme is provided for the realization of this model with ultracold fermionic atoms in optical lattices. Finally, we discuss how the robustness of the HTLL against backscattering and imperfections, well known from its realization at the edge of two-dimensional topological insulators, is reflected in the synthetic one-dimensional scenario proposed here.

arXiv:1505.02800Physical Review BDec 14, 201511 citations

Tomonaga-Luttinger liquid aspects of one-dimensional Bose systems

光行得能

Jan 1, 20080 citations

Spin-gap phases in Tomonaga-Luttinger liquids

Masaaki Nakamura, Atsuhiro Kitazawa, K. Nomura

We give details of the analysis of critical properties of spin-gap phases in one-dimensional lattice electron models. In Tomonaga-Luttinger (TL) liquid theory, the spin-gap instability occurs when the backward scattering changes from repulsive to attractive. This transition point is shown to be equivalent to that of the level-crossing of the singlet and triplet excitation spectra, using the c=1 conformal field theory and the renormalization group. Based on this notion, the transition point between the TL liquid and the spin-gap phases can be determined with high-accuracy from the numerical data of finite-size clusters. We also discuss the boundary conditions and discrete symmetries to extract these excitation spectra. This technique is applied to the extended Hubbard model, the $t\ensuremath{-}J$ model, and the $t\ensuremath{-}J\ensuremath{-}{J}^{\ensuremath{'}}$ model, and their phase diagrams are obtained. We also discuss the relation between our results and analytical solutions in weak-coupling and low-density limits.We give details of the analysis of critical properties of spin-gap phases in one-dimensional lattice electron models. In Tomonaga-Luttinger (TL) liquid theory, the spin-gap instability occurs when the backward scattering changes from repulsive to attractive. This transition point is shown to be equivalent to that of the level-crossing of the singlet and triplet excitation spectra, using the c=1 conformal field theory and the renormalization group. Based on this notion, the transition point between the TL liquid and the spin-gap phases can be determined with high-accuracy from the numerical data of finite-size clusters. We also discuss the boundary conditions and discrete symmetries to extract these excitation spectra. This technique is applied to the extended Hubbard model, the $t\ensuremath{-}J$ model, and the $t\ensuremath{-}J\ensuremath{-}{J}^{\ensuremath{'}}$ model, and their phase diagrams are obtained. We also discuss the relation between our results and analytical solutions in weak-coupling and low-density limits.

arXiv:cond-mat/9904381Physical review. B, Condensed matterSep 15, 199922 citations

c=1

conformal field theory with U(1) symmetry near the $K\ensuremath{\rightarrow}\ensuremath{\infty}$ instability. By analogy to the spinless fermion, we argue that the compressibility behaves as $\ensuremath{\kappa}\ensuremath{\propto}{(J}_{c}\ensuremath{-}{J)}^{\ensuremath{-}1},$ and that the Drude weight is constant and changes to zero discontinuously at the phase boundary. This speculation is confirmed by analyzing the finite-size effect from the result of the exact diagonalization.