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Register a new userDoping evolution of charge and spin excitations in two-leg Hubbard ladders: comparing DMRG and RPA+FLEX results
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We study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (RPA+FLEX). Our calculations reveal that RPA+FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly-interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gapped spin excitations at large momentum transfer that remain gapless within the RPA+FLEX approximation. For the charge response, RPA+FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that RPA+FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard $U$ values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.
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To shed light on how electronic correlations vary across the phase diagram of the cuprate superconductors, we examine the doping evolution of spin and charge excitations in the single-band Hubbard model using determinant quantum Monte Carlo (DQMC). In the single-particle response, we observe that the effects of correlations weaken rapidly with doping, such that one may expect the random phase approximation (RPA) to provide an adequate description of the two-particle response. In contrast, when compared to RPA, we find that significant residual correlations in the two-particle excitations persist up to $40%$ hole and $15%$ electron doping (the range of dopings achieved in the cuprates). These fundamental differences between the doping evolution of single- and multi-particle renormalizations show that conclusions drawn from single-particle processes cannot necessarily be applied to multi-particle excitations. Eventually, the system smoothly transitions via a momentum-dependent crossover into a weakly correlated metallic state where the spin and charge excitation spectra exhibit similar behavior and where RPA provides an adequate description.
Magnetic excitations in two-leg S=1/2 ladders are studied both experimentally and theoretically. Experimentally, we report on the reflectivity, the transmission and the optical conductivity sigma(omega) of undoped La_x Ca_14-x Cu_24 O_41 for x=4, 5, and 5.2. Using two different theoretical approaches (Jordan-Wigner fermions and perturbation theory), we calculate the dispersion of the elementary triplets, the optical conductivity and the momentum-resolved spectral density of two-triplet excitations for 0.2 <= J_parallel/J_perpendicular <= 1.2. We discuss phonon-assisted two-triplet absorption, the existence of two-triplet bound states, the two-triplet continuum, and the size of the exchange parameters.
We study the dynamical spin response of doped two-leg Hubbard-like ladders in the framework of a low-energy effective field theory description given by the SO(6) Gross Neveu model. Using the integrability of the SO(6) Gross-Neveu model, we derive the low energy dynamical magnetic susceptibility. The susceptibility is characterized by an incommensurate coherent mode near $(pi,pi)$ and by broad two excitation scattering continua at other $k$-points. In our computation we are able to estimate the relative weights of these contributions. All calculations are performed using form-factor expansions which yield exact low energy results in the context of the SO(6) Gross-Neveu model. To employ this expansion, a number of hitherto undetermined form factors were computed. To do so, we developed a general approach for the computation of matrix elements of semi-local SO(6) Gross-Neveu operators. While our computation takes place in the context of SO(6) Gross-Neveu, we also consider the effects of perturbations away from an SO(6) symmetric model, showing that small perturbations at best quantitatively change the physics.
We consider the effects of Umklapp processes in doped two-leg fermionic ladders. These may emerge either at special band fillings or as a result of the presence of external periodic potentials. We show that such Umklapp processes can lead to profound changes of physical properties and in particular stabilize pair-density wave phases.
We study the magnetic orbital effect of a doped two-leg ladder in the presence of a magnetic field component perpendicular to the ladder plane. Combining both low-energy approach (bosonization) and numerical simulations (density-matrix renormalization group) on the strong coupling limit (t-J model), a rich phase diagram is established as a function of hole doping and magnetic flux. Above a critical flux, the spin gap is destroyed and a Luttinger liquid phase is stabilized. Above a second critical flux, a reentrance of the spin gap at high magnetic flux is found. Interestingly, the phase transitions are associated with a change of sign of the orbital susceptibility. Focusing on the small magnetic field regime, the spin-gapped superconducting phase is robust but immediately acquires algebraic transverse (i.e. along rungs) current correlations which are commensurate with the 4k_F density correlations. In addition, we have computed the zero-field orbital susceptibility for a large range of doping and interactions ratio J/t : we found strong anomalies at low J/t only in the vicinity of the commensurate fillings corresponding to delta = 1/4 and 1/2. Furthermore, the behavior of the orbital susceptibility reveals that the nature of these insulating phases is different: while for delta = 1/4 a 4k_F charge density wave is confirmed, the delta = 1/2 phase is shown to be a bond order wave.
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