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arXiv:2012.06935 · Physical review. B./Physical review. B

Ground-state phase diagram of the one-dimensional t−Js−Jτ model at quarter filling

Yuya Kurebayashi, Hiroki Oshiyama, Naokazu Shibata

Published Apr 14, 2021• 0 citations
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Abstract

We study the ground state of the one-dimensional ``$t\text{\ensuremath{-}}{J}_{s}\text{\ensuremath{-}}{J}_{\ensuremath{\tau}}$ model,'' which is a variant of the $t\text{\ensuremath{-}}J$ model with an additional channel degree of freedom. The model is not only a generalization of the $t\text{\ensuremath{-}}J$ model but also an effective model of the two-channel Kondo lattice model in the strong-coupling region. The low-energy excitations and correlation functions are systematically calculated by the density matrix renormalization group method, and the ground-state phase diagram at quarter filling consisting of a Tomonaga-Luttinger liquid, spin-gap state, channel-gap state, insulator, and phase separation is determined. We find that weak channel fluctuations stabilize the spin-gap state, while strong channel fluctuations lead to the transition to the insulator.

DOI
10.1103/physrevb.103.165115

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We study the ground state of the one-dimensional ``t\ensuremath-Js\ensuremath-J\ensuremathτt\text{\ensuremath{-}}{J}_{s}\text{\ensuremath{-}}{J}_{\ensuremath{\tau}}t\ensuremath-Js​\ensuremath-J\ensuremathτ​ model,'' which is a variant of the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model with an additional channel degree of freedom. The model is not only a generalization of the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model but also an effective model of the two-channel Kondo lattice model in the strong-coupling region. The low-energy excitations and correlation functions are systematically calculated by the density matrix renormalization group method, and the ground-state phase diagram at quarter filling consisting of a Tomonaga-Luttinger liquid, spin-gap state, channel-gap state, insulator, and phase separation is determined. We find that weak channel fluctuations stabilize the spin-gap state, while strong channel fluctuations lead to the transition to the insulator.
We examine the ground-state phase diagram of the ttt-JJJ model in one dimension by means of the density matrix renormalization group. This model is characterized by a rich phase diagram as a function of the exchange interaction JJJ and the density nnn, displaying Luttinger-liquid (LL) behavior both of repulsive and attractive (i.e., superconducting) natures, a spin-gap phase, and phase separation. The phase boundaries separating the repulsive from the attractive LL phase as JJJ is increased, and also the boundaries of the spin-gap region at low densities, and phase separation at even larger JJJ, are determined on the basis of correlation functions and energy gaps. In particular, we shed light on a contradiction between variational and renormalization-group (RG) results about the extent of the spin-gap phase, which results larger than the variational but smaller than the RG one. Furthermore, we show that the spin gap can reach a sizable value ( 0.1t~0.1t 0.1t) at low enough filling, such that preformed pairs should be observable at temperatures below these energy scales. No evidence for a phase with clustering of more than two particles is found on approaching phase separation.
We study the one-dimensional Hubbard model with nearest-neighbor and next-nearest-neighbor hopping integrals by using the density-matrix renormalization group method and Hartree-Fock approximation. Based on the calculated results for the spin gap, total-spin quantum number, and Tomonaga-Luttinger-liquid parameter, we determine the ground-state phase diagram of the model in the entire filling and wide parameter region. We show that, in contrast to the weak-coupling regime where a spin-gapped liquid phase is predicted in the region with four Fermi points, the spin gap vanishes in a substantial region in the strong-coupling regime. It is remarkable that a large variety of phases, such as the paramagnetic metallic phase, spin-gapped liquid phase, singlet and triplet superconducting phases, and fully polarized ferromagnetic phase, appear in such a simple model in the strong-coupling regime.
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Inspired by the observation of a robust ddd-wave superconducting phase driven by tuning the next-nearest-neighbor (NNN) electron hopping in recent density matrix renormalization group (DMRG) studies of six- and eight-leg $t\text{\ensuremath{-}}J$ model, we systematically study the phase diagram of the two-leg $t\text{\ensuremath{-}}J$ ladder with the NNN couplings (including NNN hopping and spin interaction) in a large region of doping level, by means of the DMRG calculations. Upon doping from half filling, we identify the Luther-Emery liquid (LEL) phase, which can be distinguished as the pairing-dominant and charge density-dominant regime by comparing the Luttinger parameter ${K}_{\ensuremath{\rho}}$. With the growing NNN couplings, pairing correlations are enhanced and correspondingly ${K}_{\ensuremath{\rho}}$ increases, driving the system from the density-dominant to the pairing-dominant regime. In the Tomonaga-Luttinger liquid (TLL) phase in the larger doping region, we identify two TLL regimes with different features of charge density correlation. At the quarter filling (1/21/21/2 doping level), we find that the strong dimer orders of bond energy in the open system actually decay algebraically and thus do not indicate a spontaneous translational symmetry breaking. Our results show that in the LEL phase of the two-leg ladder, the NNN couplings seem to play the similar role as that on the wider $t\text{\ensuremath{-}}J$ cylinder, and studies on this more accessible system can be helpful toward understanding the emergence of the remarkable ddd-wave superconducting phase on the wider system.
We study the one-dimensional spin-12\frac{1}{2}21​ Heisenberg model with antiferromagnetic nearest-neighbor J1{J}_{1}J1​ and next-nearest-neighbor J2{J}_{2}J2​ exchange couplings in magnetic field hhh. With varying dimensionless parameters J2/J1{J}_{2}/{J}_{1}J2​/J1​ and h/J1h/{J}_{1}h/J1​, the ground state of the model exhibits several phases including three gapped phases (dimer, 1/3-magnetization plateau, and fully polarized phases) and four types of gapless Tomonaga-Luttinger liquid (TLL) phases which we dub TLL1, TLL2, spin-density-wave (SDW2)({\text{SDW}}_{2})(SDW2​), and vector chiral phases. From extensive numerical calculations using the density-matrix renormalization-group method, we investigate various (multiple-)spin-correlation functions in detail and determine dominant and subleading correlations in each phase. For the one-component TLLs, i.e., the TLL1, SDW2{\text{SDW}}_{2}SDW2​, and vector chiral phases, we fit the numerically obtained correlation functions to those calculated from effective low-energy theories of TLLs and find good agreement between them. The low-energy theory for each critical TLL phase is thus identified, together with TLL parameters which control the exponents of power-law decaying correlation functions. For the TLL2 phase, we develop an effective low-energy theory of two-component TLL consisting of two free bosons (central charge c=1+1c=1+1c=1+1), which explains numerical results of entanglement entropy and Friedel oscillations of local magnetization. Implications of our results to possible magnetic phase transitions in real quasi-one-dimensional compounds are also discussed.