arXiv:cond-mat/9601027 · Journal of the Physical Society of Japan

Possible Phase Diagram of at-J Ladder Model

Kazuhiro Sano

Published May 15, 1996• 21 citations

Abstract

We investigate a t-J ladder model by numerical diagonalization method. By calculating correlation functions and assuming the Luttinger liquid relation, we obtained a possible phase diagram of the ground state as a function of J/t and electron density $n$. We also found that behavior of correlation functions seems to consist with the prediction of Luttinger liquid relation. The result suggests that the superconducting phase appear in the region of $J/t \displaystyle{ \mathop{>}_{\sim}} 0.5$ for high electron density and $J/t \displaystyle{ \mathop{>}_{\sim}} 2.0$ for low electron density.

DOI: 10.1143/jpsj.65.1146

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arXiv:cond-mat/9601027 · Journal of the Physical Society of Japan

Possible Phase Diagram of at-J Ladder Model

Kazuhiro Sano

Published May 15, 1996• 21 citations

arXiv HTML PDF

Abstract

n

. We also found that behavior of correlation functions seems to consist with the prediction of Luttinger liquid relation. The result suggests that the superconducting phase appear in the region of

J/t \displaystyle{ \mathop{>}_{\sim}} 0.5

for high electron density and

J/t \displaystyle{ \mathop{>}_{\sim}} 2.0

for low electron density.

DOI: 10.1143/jpsj.65.1146

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Masao Ogata, Marco U. Luchini, Sandro Sorella +1 more

The phase diagram of the one-dimensional t-J model is investigated by analyzing the results of exact diagonalization and the exact solutions at J/t=0 and 2. Phase separation takes place above a critical value of J around ${\mathit{J}}_{\mathit{c}}$ /t=2.5--3.5 depending on the electron density. In the small-J region, Tomonaga-Luttinger liquid theory holds and its correlation exponents are calculated as a function of J/t and the electron density. Superconducting correlations become dominant in a region between the solvable case (J/t=2) and phase separation. A spin-gap region is also found at low density.The phase diagram of the one-dimensional t-J model is investigated by analyzing the results of exact diagonalization and the exact solutions at J/t=0 and 2. Phase separation takes place above a critical value of J around ${\mathit{J}}_{\mathit{c}}$/t=2.5--3.5 depending on the electron density. In the small-J region, Tomonaga-Luttinger liquid theory holds and its correlation exponents are calculated as a function of J/t and the electron density. Superconducting correlations become dominant in a region between the solvable case (J/t=2) and phase separation. A spin-gap region is also found at low density.

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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.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.

arXiv:1012.4028Physical Review BMay 18, 201158 citations

n

. We also found that behavior of correlation functions seems to consist with the prediction of Luttinger liquid relation. The result suggests that the superconducting phase appear in the region of

J/t \displaystyle{ \mathop{>}_{\sim}} 0.5

for high electron density and

J/t \displaystyle{ \mathop{>}_{\sim}} 2.0

for low electron density.

{\mathit{J}}_{\mathit{c}}

/t=2.5--3.5 depending on the electron density. In the small-J region, Tomonaga-Luttinger liquid theory holds and its correlation exponents are calculated as a function of J/t and the electron density. Superconducting correlations become dominant in a region between the solvable case (J/t=2) and phase separation. A spin-gap region is also found at low density.

{V=V}_{\mathrm{PS}}.

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<{V}_{\mathrm{PS}},

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 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.