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arXiv:cond-mat/9803363 · Physical review. B, Condensed matter

Low-energy effective action of lightly doped two-leg t−J ladders

Yu-Wen Lee, Yu-Li Lee

Published Jan 1, 1999• 1 citation
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Abstract

We propose a low-energy effective theory of lightly doped two-leg $t\ensuremath{-}J$ ladders with the help of slave fermion technique. The continuum limit of this model consists of two kinds of Dirac fermions, which are coupled to the O(3) nonlinear sigma model in terms of the gauge coupling with opposite sign of ``charges.'' In addition to the gauge interaction, there is another kind of attractive force between these Dirac fermions, which arises from the short-ranged antiferromagnetic order. We show that the latter is essential to determine the low energy properties of lightly doped two-leg $t\ensuremath{-}J$ ladders. The effective Hamiltonian we obtain is a bosonic Gaussian model and the boson field basically describes the particle-density fluctuation. We also find two types of gapped spin excitations. Finally, we discuss the possible instabilities: charge density wave and singlet superconductivity (SC). We find that the SC instability dominates in our approximation. Our results indicate that lightly doped ladders fall into the universality class of Luther-Emery model.

DOI
10.1103/physrevb.59.1290

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We propose a low-energy effective theory of lightly doped two-leg t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J ladders with the help of slave fermion technique. The continuum limit of this model consists of two kinds of Dirac fermions, which are coupled to the O(3) nonlinear sigma model in terms of the gauge coupling with opposite sign of ``charges.'' In addition to the gauge interaction, there is another kind of attractive force between these Dirac fermions, which arises from the short-ranged antiferromagnetic order. We show that the latter is essential to determine the low energy properties of lightly doped two-leg t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J ladders. The effective Hamiltonian we obtain is a bosonic Gaussian model and the boson field basically describes the particle-density fluctuation. We also find two types of gapped spin excitations. Finally, we discuss the possible instabilities: charge density wave and singlet superconductivity (SC). We find that the SC instability dominates in our approximation. Our results indicate that lightly doped ladders fall into the universality class of Luther-Emery model.
We study the $t\ensuremath{-}J$ model on a ladder using the slave-fermion-CP1{\mathrm{CP}}^{1}CP1 formalism that has been used successfully in studying lightly-doped high-Tc{T}_{c}Tc​ cuprates. We obtain a low-energy effective model assuming a short-range antiferromagnetic order (SRAFO), which includes gauge-field degrees of freedom because of the use of the slave-particle picture. We give a systematic study on the dynamics of composite gauge bosons to show that the confinement phase is realized in a two-leg system whereas the deconfinement phase is realized in a chain system. This explains why quasiexcitations are so different in the chain and ladder systems. The effective model also reveals attractive forces between holes, which generate ddd-wave-type superconductive correlations in SRAFO. The low-energy excitations on a ladder are consistently described by the universality class of the Luther-Emery liquid.
We present a low-energy effective model for the charge degrees of freedom in two-leg $t\ensuremath{-}J$ ladders. Starting from SU(2)\mathrm{SU}(2)SU(2) mean-field theory, we exclude the spin degrees of freedom that have an energy gap. At low temperatures, the mean-field solution is the staggered-flux phase. For gapless charge excitations the effective theory is the Luther-Emery liquid. Our analysis is applicable at low doping and in the ``physical'' range of parameters $t/J\ensuremath{\sim}3$ where there is only one massless mode in the charge sector and no massless modes in the spin sector. Within our model we make predictions about correlation exponents and the superconductivity order parameter, and discuss the comparison with the existing numerical results.
We investigate electronic properties of the doped two-leg Hubbard ladder with both the onsite and the nearest-neighbor Coulomb repulsions, by using the the weak-coupling renormalization-group method. It is shown that, for strong nearest-neighbor repulsions, the charge-density-wave state coexisting with the p-density-wave state becomes dominant fluctuation where spins form intrachain singlets. By increasing doping rate, we have also shown that the effects of the nearest-neighbor repulsions are reduced and the system exhibits a quantum phase transition into the d-wave-like (or rung-singlet) superconducting state. We derive the effective fermion theory which describes the critical properties of the transition point with the gapless excitation of magnon. The phase diagram of the two-leg ladder compound, Sr_{14-x}Ca_xCu_{24}O_{41}, is discussed.
We study low-energy magnetic excitations of doped spin-ladders, based on an effective Hamiltonian describing interactions of mobile spin and background spins. The helicity modulus against fluctuations in the ladder plane as well as out-of-the-plane are calculated in terms of the doping concentration, the leg number and interaction strengths in the ladder. The doping range for spiral phase is computed and its relation to spin gap structure is discussed. The spiral order can enhance existing antiferromagnetic order at certain doping or reduce it at very low density of holes. For odd-legged ladders, formation of spin gap at certain narrow doping range becomes possible via coupling of spirals and background spins. Our results of the doping range for gapped mode in odd-ladders agree well with those existing numerical studies.
A proper theoretical description of doped antiferromagnets is until now an unresolved issue. In this work we study chain and ladder systems, and in particularly we focus on the physically most interesting two leg ladder. Our starting point is the Spin Fermion model in which an antiferromagnetic background of localized spins interacts with mobile holes via a rotation invariant Kondo-like term. The interesting region of the phase diagram is that close to the Mott-insulator transition where the doping delta is zero. At zero doping in fact the system is an insulator and the spins organize themselves in a spin liquid, a rotational invariant state characterized by a finite correlation length and an energy gap (a spin gap) above the ground state. Such a state is also the ground state of a field theory, the non linear sigma model (NLsigmaM) which is recognized as the low energy effective theory for antiferromagnetic spin ladder. The first question we answer is how such a spin state evolves as one moves off from the Mott phase by increasing the doping. Integrating out the fermions in our model we obtain an effective theory for the spins which we are able to evaluate in the continuum limit. The effective theory is again a NLsigmaM with coupling constants which depend on the concentration of dopant holes. In contrast to existing mean field calculation our theory predicts a lowering of the spin gap with doping and a consequent increase in the correlation length. Indeed a lowering of the spin gap due to doping is also observed in numerical simulation and on NMR experiments on $Sr14-xCaxCu24O41 with which we obtain very good agreement. Secondly we concentrated on the behavior of the fermions. The general paradigm of interacting fermions in one dimension is that of the Luttinger Liquid characterized by bosonic excitations and spin charge separation. By generalizing our approach we are able to access the one particle fermion propagator as a quantity averaged over the NLsigmaM which controls the spin background. We see that in the limit of zero doping the quasiparticle weight Z is non-zero in a neighborhood of the Fermi energy. This in turn implies that the Luttinger liquid parameter Krho goes to one as the doping delta goes to zero as was first argued by Schulz. Our stronger result allows us to assert that in the very low doping regime the fermions constitute a Fermi liquid.
We study a model of the stripe state in strongly correlated systems consisting of an array of antiferromagnetic spin ladders, each with n(leg) legs, coupled to each other through the spin-exchange interaction to charged stripes in between each pair of ladders. The charged stripes are assumed to be Luttinger liquids in a spin-gap regime. An effective interaction for a pair of neighboring ladders is calculated by integrating out the gapped spin degrees of freedom in the charged stripes. The low energy effective theory of each ladder is a nonlinear sigma model with additional cross couplings of neighboring ladders, which favor either in-phase or antiphase short-range spin orderings depending on the physical parameters of the charged stripe.