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arXiv:cond-mat/9709199 · Physical review. B, Condensed matter

Mean-field theory for the spin-ladder system

Xi Dai, Zhao-Bin Su

Published Jan 1, 1998• 40 citations
arXivHTMLPDF

Abstract

In the present paper, we propose a mean-field approach for spin ladders based upon the Jordan-Wigner transformation along an elaborately ordered path. We show on the mean-field level that ladders with even-numbered legs open an energy gap in their low-energy excitation with a magnitude close to the corresponding experimental values, whereas the low-energy excitation of the odd-numbered-leg ladders are gapless. It supports the validity of our approach. We then calculate the gap size and the excitation spectra of a two-leg-ladder system. Our result is in good agreement with both the experimental data and the numerical results.

DOI
10.1103/physrevb.57.964

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In the present paper, we propose a mean-field approach for spin ladders based upon the Jordan-Wigner transformation along an elaborately ordered path. We show on the mean-field level that ladders with even-numbered legs open an energy gap in their low-energy excitation with a magnitude close to the corresponding experimental values, whereas the low-energy excitation of the odd-numbered-leg ladders are gapless. It supports the validity of our approach. We then calculate the gap size and the excitation spectra of a two-leg-ladder system. Our result is in good agreement with both the experimental data and the numerical results.
We study the low-lying excitations and thermodynamic properties of a ferrimagnetic Heisenberg two-leg ladder, which is composed of alternating-spin (1/2, 1) double chains with antiferromagnetic coupling between the chains. The spin excitation spectra as well as the corresponding energy gaps are calculated by means of the Schwinger-boson mean-field theory. The two interactions between the chains and along the chains play an important role in determining the two branches of the spectrum, not only regarding the size of the low-lying excitation energy gap but also the bandgap between the optical spectrum and the acoustic spectrum. In addition, the two energy gaps and the specific heat have also been calculated at low temperatures.
Two-leg t-J ladders are investigated in the framework of a combination of the phass string formulation and bond-operator representation. We develope a mean-field theory in the strong rung interaction regime, i.e. J┴ ＞＞ J, t, which provides a unified description of the undoped insulating phase and the low doping spin gap phase. The ground state of the doped phase is intrinsically a superconductor with a d-wave symmetry gap driven by the t- term. The ground-state energy is in good agreement with numerical results. Phase separation is shown to occur beyond some critical value of J/t for given doping concentration. The local structure of hole pairs as well as the spectra of various spin and charge modes are also analyzed.
We present a method for studying the excitations of low-dimensional quantum spin systems based on the Jordan-Wigner transformation. Using an extended random-phase approximation (RPA) scheme we calculate the correlation function of neighboring spin flips for the one-dimensional spin-1/2 chain which well approximates the optical conductivity of Sr2CuO3.{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.Sr2​CuO3​. We analyze several possible generalizations of the Jordan-Wigner approach to the two-leg spin-1/2 ladder. On the mean-field level the most accurate results are obtained when the spin operators are numbered in a meanderlike sequence. Calculation of the optical conductivity based on an extended RPA scheme for the meander-path approach yields very good agreement with a previous density matrix renormalization group evaluation. For polarization along the legs higher-order correlations are important to explain the weight of high-energy continuum excitations and we estimate the contribution of 4- and 6-fermion processes.
Two-leg $t\ensuremath{-}J$ ladders are investigated in the framework of a combination of the phase string formulation and bond-operator representation. We develop a mean-field theory in the strong rung interaction regime, i.e., ${J}_{\ensuremath{\perp}}\ensuremath{\gg}J,t,$ which provides a unified description of the undoped insulating phase and the low-doping phase---the so-called C1S0C1S0C1S0 phase. Both of them are characterized by the resonating-valence-bond (RVB) order parameter, with gap opened up in all spin excitations. The ground state of the doped phase is intrinsically a superconductor with a d-wave symmetry, which is driven by the RVB correlations. The ground-state energy is in good agreement with numerical results. Phase separation is shown to occur beyond some critical value of J/tJ/tJ/t for given doping concentration. The local structure of hole pairs as well as the spectra of various spin and charge modes are analyzed in comparison with other approaches.
We investigate the NNN-leg spin-SSS Heisenberg ladders by using the density matrix renormalization group method. We present estimates of the spin gap ${\ensuremath{\Delta}}_{s}$ and of the ground-state energy per site ${e}_{\ensuremath{\infty}}^{N}$ in the thermodynamic limit for ladders with widths up to six legs and spin $S\ensuremath{\le}\frac{5}{2}$. We also estimate the ground-state energy per site ${e}_{\ensuremath{\infty}}^{2\mathrm{D}}$ for the infinite two-dimensional spin-SSS Heisenberg model. Our results support that for ladders with semi-integer spins the spin excitation is gapless for NNN odd and gapped for NNN even, whereas for integer spin ladders the spin gap is nonzero, independent of the number of legs. Those results agree with the well-known conjectures of Haldane and S\'en\'echal-Sierra for chains and ladders, respectively. We also observe edge states for ladders with NNN odd, similar to what happens in spin chains.