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arXiv:1012.4028 · Physical Review B

Ground-state phase diagram of the one-dimensional t - J model

Alexander Moreno, Alejandro Muramatsu, Salvatore R. Manmana

Published May 18, 2011• 58 citations
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Abstract

We examine the ground-state phase diagram of the $t$-$J$ 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 $J$ and the density $n$, 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 $J$ is increased, and also the boundaries of the spin-gap region at low densities, and phase separation at even larger $J$, 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 ($~0.1t$) 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.

DOI
10.1103/physrevb.83.205113

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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 systematically the effect of long-range dipolar interactions on the ground-state phase diagram of the one-dimensional model by means of the density matrix renormalization group. While the basic phases described by the Luttinger parameter , namely, the repulsive Luttinger liquid (metallic phase, ), attractive Luttinger liquid (superconducting phase, ), and the phase separation , are similar to those of the conventional model, the presence of the long-range dipolar interactions leads to significant differences. i) At high-density regime, the phase boundaries of these three phases are even pushed to the large- J region; ii) at low-density regime, these phase boundaries shift toward the small- J region and, most importantly, iii) the spin-gap region spreads across the boundary of , suggesting an exotic metallic phase with spin-gap, which is absent in the conventional model. The result indicates that the long-range dipolar interactions have a significant influence on the ground-state properties of the one-dimensional model. Its implication on the pseudogap phenomenon of the hole-doped cuprates is briefly discussed.
We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on-site interaction U and a nearest-neighbor interaction V. We focus on the ground state phases of the model in the $V\ensuremath{\gg}U$ region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=VPS.{V=V}_{\mathrm{PS}}.V=VPS​. Using quantum Monte Carlo methods on lattices much larger than in previous Lancz\"os diagonalization studies, we determine the boundary of phase separation, the Luttinger-liquid correlation exponent ${K}_{\ensuremath{\rho}},$ and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state reenters from phase separation as the electron density is increased towards half filling. For V<VPS,V<{V}_{\mathrm{PS}},V<VPS​, our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger liquid with ${K}_{\ensuremath{\rho}}<1,$ but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger liquid.
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.
Distinct from the SU(2)\text{SU}(2)SU(2) case, the fermionic systems with SU(N)\text{SU}(N)SU(N) symmetry are expected to exhibit novel physics, such as exotic singlet formation. Using the density matrix renormalization group technique, we obtain the ground-state phase diagram of the SU(3)\text{SU}(3)SU(3) $t\text{\ensuremath{-}}J$ chain for density n<1n<1n<1. The ground-state phase diagram includes the Luttinger liquid, the extended Luther-Emery liquid characterized by a spin gap, and the phase separation state. We quantitatively assess the characteristics of the three phases by measuring spin gap, compressibility, various correlation functions, and structure factors. We further study the extended Luther-Emery liquid phase and discover molecular superfluid quasi-long-range order. The mechanism of the molecular superfluid is the combination of three SU(3)\text{SU}(3)SU(3) fermions on sites that are not entirely connected. Accordingly, we can speculate the behavior of the SU(N)\text{SU}(N)SU(N) $t\text{\ensuremath{-}}J$ chain model with larger NNN values, operating within the same filling regime.
We study the phase diagram of the one-dimensional U-V model at quarter filling in the most general case where the on-site and first-neighbor interactions U and V can be both attractive and repulsive. The results have been obtained using exact diagonalization of small clusters and variational techniques, as well as exact results in various limits. We have analyzed four properties of the ground state: (i) whether it is insulating or metallic; (ii) whether it is homogeneous or phase separated; (iii) whether it has a spin gap; (iv) whether it has dominant superconducting fluctuations. With eight phases, the resulting phase diagram is unexpectedly rich. The four phases not found in the weak coupling limit are: (i) an insulating phase when U and V are large enough; (ii) a region of phase separation when V is attractive; (iii) another region of phase separation when V is large enough and U small; (iv) a region with dominant superconducting fluctuations when V is intermediate and U small. The actual nature of this last plase, which has pairs but no spin gap, is not fully clear yet.