Phase transitions of a quasi-one-dimensional Fermi gas are studied by the use of the renormalization group method for the fermion system without the bosonization. Intrachain backward and forward scatterings, pair electron hopping between different chains and exchange scattering of electrons in different chains are taken account of. Pair electron hopping gives rise to the singlet and triplet superconductor phase transitions. Electron exchange scattering gives rise to the spin density wave and charge density wave transitions. Calculation is made by the use of the one-dimensional dispersion. Following Menyhárd's method (Ref. 1) for the model with interchain backward scattering only, the change of the fluctuation from the one-dimensional region to the three-dimensional region is described. The transition temperatures are given by the bare couplings at high temperatures.Phase transitions of a quasi-one-dimensional Fermi gas are studied by the use of the renormalization group method for the fermion system without the bosonization. Intrachain backward and forward scatterings, pair electron hopping between different chains and exchange scattering of electrons in different chains are taken account of. Pair electron hopping gives rise to the singlet and triplet superconductor phase transitions. Electron exchange scattering gives rise to the spin density wave and charge density wave transitions. Calculation is made by the use of the one-dimensional dispersion. Following Menyhárd's method (Ref. 1) for the model with interchain backward scattering only, the change of the fluctuation from the one-dimensional region to the three-dimensional region is described. The transition temperatures are given by the bare couplings at high temperatures.

Molecular crystals and liquid crystalsJan 1, 19821 citation

Influence of the modulated hopping on the one-dimensional interacting electron system

Hanqin Ding, Jun Zhang

Physics Letters AMay 19, 20153 citations

Phase transition in a U(1)-lattice-gauge system derived from a weakly three-dimensionalt-Jmodel

Yasuko Munehisa

We numerically study a U(1)-lattice-gauge system, which is an effective model of the Ginzburg-Landau-type obtained from the t-J model of electrons. The model, which we call the ``GL'' model for short, is composed of link variables interpreted as a nearest-neighbor hole-pair field bounded by the singlet spin pairs. We concentrate our attention on the weakly three-dimensional case in which the electron hopping in the third direction is suppressed compared to other directions. When we simulate the model on an ${\mathit{L}}^{3}$ lattice, we therefore actually treat a system of L loosely coupled layers each of which is of size ${\mathit{L}}^{2}$ . Monte Carlo simulations are done on ${12}^{3}$ , ${20}^{3}$ , and ${30}^{3}$ lattices with the electron density slightly less than the half-filled one (the doping parameter \ensuremath{\delta} is mostly 0.06) and with the ratio of the interlayer-to-intralayer hopping parameter ranging between 0.1 and 0.9. We observe cusplike behavior of the specific heat, which indicates a phase transition due to the spontaneous breaking of a global symmetry of the GL model. An average link variable in one direction within the layers turns out to serve as a nice order parameter of the transition. The transition temperature ${\mathit{T}}_{\mathit{c}}$ decreases as the interlayer hopping of the electrons increases. Results on some expectation values, which indicate strong correlations between link variables below ${\mathit{T}}_{\mathit{c}}$ , are also presented.We numerically study a U(1)-lattice-gauge system, which is an effective model of the Ginzburg-Landau-type obtained from the t-J model of electrons. The model, which we call the ``GL'' model for short, is composed of link variables interpreted as a nearest-neighbor hole-pair field bounded by the singlet spin pairs. We concentrate our attention on the weakly three-dimensional case in which the electron hopping in the third direction is suppressed compared to other directions. When we simulate the model on an ${\mathit{L}}^{3}$ lattice, we therefore actually treat a system of L loosely coupled layers each of which is of size ${\mathit{L}}^{2}$. Monte Carlo simulations are done on ${12}^{3}$, ${20}^{3}$, and ${30}^{3}$ lattices with the electron density slightly less than the half-filled one (the doping parameter \ensuremath{\delta} is mostly 0.06) and with the ratio of the interlayer-to-intralayer hopping parameter ranging between 0.1 and 0.9. We observe cusplike behavior of the specific heat, which indicates a phase transition due to the spontaneous breaking of a global symmetry of the GL model. An average link variable in one direction within the layers turns out to serve as a nice order parameter of the transition. The transition temperature ${\mathit{T}}_{\mathit{c}}$ decreases as the interlayer hopping of the electrons increases. Results on some expectation values, which indicate strong correlations between link variables below ${\mathit{T}}_{\mathit{c}}$, are also presented.

Physical review. B, Condensed matterJul 1, 19920 citations

Phase transitions in the one-dimensional ionic Hubbard model

Myung-Hoon Chung

arXiv:2011.05592Journal of the Korean Physical SocietyFeb 10, 20214 citations

Phase transitions in the one-dimensional modified Penson-Kolb model with density-dependent hopping

Xin Sun, Hanqin Ding

By relaxing the conventional assumption of the equal one-electron hopping amplitude, we modify the one-dimensional half-filled Penson-Kolb (PK) model to obey the density-dependent hopping (DDH). For positive small modulation parameter [Formula: see text] and pair hopping [Formula: see text], we use bosonization and renormalization-group analysis to determine the ground state phase diagram. In the attractive case([Formula: see text]), the existence of the DDH leads to a gap transition in the spin sector and produces a fully gapless phase where a Luttinger liquid metal phase with dominant triplet superconducting correlations is realized for [Formula: see text], with the charge transition point [Formula: see text] and the spin transition point [Formula: see text]. Besides, there is a Luther-Emery matal phase with dominant singlet-superconducting correlations for [Formula: see text] and a Haldane insulator phase characterized by dominant bond-spin-density-wave correlations for [Formula: see text] in the repulsive regime ([Formula: see text]).By relaxing the conventional assumption of the equal one-electron hopping amplitude, we modify the one-dimensional half-filled Penson-Kolb (PK) model to obey the density-dependent hopping (DDH). For positive small modulation parameter [Formula: see text] and pair hopping [Formula: see text], we use bosonization and renormalization-group analysis to determine the ground state phase diagram. In the attractive case([Formula: see text]), the existence of the DDH leads to a gap transition in the spin sector and produces a fully gapless phase where a Luttinger liquid metal phase with dominant triplet superconducting correlations is realized for [Formula: see text], with the charge transition point [Formula: see text] and the spin transition point [Formula: see text]. Besides, there is a Luther-Emery matal phase with dominant singlet-superconducting correlations for [Formula: see text] and a Haldane insulator phase characterized by dominant bond-spin-density-wave correlations for [Formula: see text] in the repulsive regime ([Formula: see text]).

Modern Physics Letters BOct 13, 20260 citations

A quantum phase transition in a model with boson-controlled hopping

David M. Edwards

Physica B Condensed MatterFeb 21, 200631 citations

{\mathit{L}}^{3}

lattice, we therefore actually treat a system of L loosely coupled layers each of which is of size

{\mathit{L}}^{2}

. Monte Carlo simulations are done on

{12}^{3}

{20}^{3}

, and

{30}^{3}

lattices with the electron density slightly less than the half-filled one (the doping parameter \ensuremath{\delta} is mostly 0.06) and with the ratio of the interlayer-to-intralayer hopping parameter ranging between 0.1 and 0.9. We observe cusplike behavior of the specific heat, which indicates a phase transition due to the spontaneous breaking of a global symmetry of the GL model. An average link variable in one direction within the layers turns out to serve as a nice order parameter of the transition. The transition temperature

{\mathit{T}}_{\mathit{c}}

decreases as the interlayer hopping of the electrons increases. Results on some expectation values, which indicate strong correlations between link variables below

{\mathit{T}}_{\mathit{c}}

, are also presented.