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Journal of the Physical Society of Japan

Superconductivity and Spin Gap in the Zigzag-Chaint–JModel Simulating a CuO Double Chain in Pr2Ba4Cu7O15-δ

Kazuhiro Sano, Yoshiaki Ōno

Published Oct 24, 2007• 6 citations
Publisher

Abstract

Using the numerical diagonalization method, we examine the one-dimensional t1–t2–J1–J2 model (zigzag-chain t–J model) which is an effective model for metallic CuO double chains in the superconductor Pr2Ba4Cu7O15-δ. Based on the Tomonaga–Luttinger liquid theory, we calculate the Luttinger liquid parameter Kρ as a function of the electron density n. It is found that superconductivity is realized in the parameter region, which is in accordance with experimental results. We show the phase diagram of a spin gap in the t2/|t1|–n plane by analyzing the expectation value of the twist operator Zσ in the spin sector. The spin gap appears in the region with a large t2/|t1|, where the phase boundary at half filling is consistent with that of the known frustrated quantum spin system. The analysis also suggests that the estimated value of the spin gap reaches ∼100 K in the realistic parameter region of Pr2Ba4Cu7O15-δ.

DOI
10.1143/jpsj.76.113701

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Using the numerical diagonalization method, we examine the one-dimensional t1–t2–J1–J2 model (zigzag-chain t–J model) which is an effective model for metallic CuO double chains in the superconductor Pr2Ba4Cu7O15-δ. Based on the Tomonaga–Luttinger liquid theory, we calculate the Luttinger liquid parameter Kρ as a function of the electron density n. It is found that superconductivity is realized in the parameter region, which is in accordance with experimental results. We show the phase diagram of a spin gap in the t2/|t1|–n plane by analyzing the expectation value of the twist operator Zσ in the spin sector. The spin gap appears in the region with a large t2/|t1|, where the phase boundary at half filling is consistent with that of the known frustrated quantum spin system. The analysis also suggests that the estimated value of the spin gap reaches ∼100 K in the realistic parameter region of Pr2Ba4Cu7O15-δ.
Using the numerical diagonalization method, we examine the one-dimensional t_1-t_2-J_1-J_2 model (zigzag chain t-J model) which represents an effective model for metallic CuO double chain in the superconductor Pr_2Ba_4Cu_7O_15-δ. Based on the Tomonaga-Luttinger liquid theory, we calculate the Luttinger-liquid parameter K_ρas a function of electron density n. It is found that superconductivity is realized in parameter region corresponding to the experimental result. We show phase diagram of spin gap on the t_2/|t_1|-n plane by analyzing the expectation value of twist-operator Z_σin the spin sector. The spin gap appears in the region with large t_2/|t_1|, where the phase boundary at half-filling is consistent with that of the known frustrated quantum spin system. The analysis also suggests that the estimated value of the spin gap reaches 100K in the realistic parameter region of Pr_2Ba_4Cu_7O_15-delta.
An effective Hamiltonian for the Kohn-Luttinger superconductor is constructed and solved in the BCS approximation. The method is applied to the $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model in two dimensions with the following results: (i) The superconducting phase diagram at half filling is shown to provide a weak-coupling analog of the recently proposed spin liquid state in the ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model. (ii) In the parameter region relevant for the cuprates, we have found a nontrivial energy dependence of the gap function in the dominant d-wave pairing sector. The hot spot effect in the angular dependence of the superconducting gap is shown to be quite weak.
A two-band Hubbard model describing a CuO chain is studied using quantum Monte Carlo simulation. The Luttinger-liquid exponent K ρ is extracted as a function of the nearest-neighbor repulsion V , at hole fillings ⟨ n ⟩ between 1 (half-filled lower band) and 2. Evidence is presented for the existence of a regime with dominant singlet superconducting fluctuations and a gap in the spin excitation spectrum at ⟨ n ⟩ = 1.75, in the neighborhood of the V for which the system phase separates. Closer to half-filling (⟨ n ⟩≲1.6), spin-density-wave fluctuations always dominate.
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 Jc{\mathit{J}}_{\mathit{c}}Jc​/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 one-dimensional dimerized t-J model is investigated by exact-diagonalization, quantum tranfer-matrix, and quantum Monte Carlo methods. The spin gap persists near but away from half-filling as well as in a strongly dimerized region, while the charge can be described as a Tomonaga-Luttinger liquid in the entire region. The spin-gap region extends to the weak-dimerization region as well as to the Haldane-gap region. Critical exponents of various correlation functions are discussed. The pairing correlation shows remarkable enhancement and by far dominates over other correlations near half-filling. At quarter filling, charge-gap formation is observed.
We investigated the one-dimensional extended Hubbard model with the on-site interaction U and the nearest-neighbor interaction V by using the numerical diagonalization method. Assuming the Luttinger liquid relations, we obtained the phase diagram of the ground state on the U - V plane. In the weak coupling region, the phase diagram agrees with the result of g -ology. On the other hand, in the strong coupling region for V ≫∣ t ∣, a novel superconducting phase appears both for positive and negative U . We also investigated the charge gap and the spin gap. The results suggest that the superconducting phase extends over the Tomonaga-Luttinger region (without spin gap) and the Luther-Emery region (with spin gap).