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arXiv:cond-mat/0406430 · Physical Review B

Magnetic response and quantum critical behavior in the doped two-leg extended Hubbard ladder

Masahisa Tsuchiizu, Yoshikazu Suzumura

Published Aug 16, 2005• 14 citations
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Abstract

We have investigated quantum critical behavior in the doped two-leg extended Hubbard ladder, by using a weak-coupling bosonization method. In the ground state, the dominant fluctuation changes from the conventional $d$-wave-like superconducting $(\mathrm{SC}d)$ state into density-wave states, with increasing nearest-neighbor repulsions and/or decreasing doping rate. The competition between the $\mathrm{SC}d$ state and the charge-density-wave state coexisting with the $p$-density-wave state becomes noticeable on the critical point, at which the gap for magnetic excitations vanishes. Based on the Majorana-fermion description of the effective theory, we calculate the temperature dependence of the magnetic response such as the spin susceptibility and the NMR relaxation rate, which exhibit unusual properties due to two kinds of spin excitation modes. On the quantum critical point, the spin susceptibility shows paramagnetic behavior with logarithmic corrections and the NMR relaxation rate also exhibits anomalous power-law behavior. We discuss the commensurability effect due to the umklapp scattering and relevance to the two-leg ladder compounds ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$.

DOI
10.1103/physrevb.72.075121

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We have investigated quantum critical behavior in the doped two-leg extended Hubbard ladder, by using a weak-coupling bosonization method. In the ground state, the dominant fluctuation changes from the conventional ddd-wave-like superconducting (SCd)(\mathrm{SC}d)(SCd) state into density-wave states, with increasing nearest-neighbor repulsions and/or decreasing doping rate. The competition between the SCd\mathrm{SC}dSCd state and the charge-density-wave state coexisting with the ppp-density-wave state becomes noticeable on the critical point, at which the gap for magnetic excitations vanishes. Based on the Majorana-fermion description of the effective theory, we calculate the temperature dependence of the magnetic response such as the spin susceptibility and the NMR relaxation rate, which exhibit unusual properties due to two kinds of spin excitation modes. On the quantum critical point, the spin susceptibility shows paramagnetic behavior with logarithmic corrections and the NMR relaxation rate also exhibits anomalous power-law behavior. We discuss the commensurability effect due to the umklapp scattering and relevance to the two-leg ladder compounds Sr14\ensuremath−xCaxCu24O41{\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14\ensuremath−x​Cax​Cu24​O41​.
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 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 ($t\text{\ensuremath{-}}J$ 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 4kF4{k}_{F}4kF​ density correlations. In addition, we have computed the zero-field orbital susceptibility for a large range of doping and interaction ratio J∕tJ∕tJ∕t: we found strong anomalies at low J∕tJ∕tJ∕t only in the vicinity of the commensurate fillings corresponding to $\ensuremath{\delta}=1∕4$ and 1∕21∕21∕2. Furthermore, the behavior of the orbital susceptibility reveals that the nature of these insulating phases is different: while for $\ensuremath{\delta}=1∕4$ a 4kF4{k}_{F}4kF​ charge density wave is confirmed, the $\ensuremath{\delta}=1∕2$ phase is shown to be a bond order wave.
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 (FLEX). Our calculations reveal that 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 FLEX approximation. For the charge response, 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 FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard UUU 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.
We study magnetic-field-induced critical singularities in the superconducting phase of the hole-doped Hubbard model of repulsively interacting electrons, defined on a two-leg ladder. We argue that, provided the low-energy spin excitations in doped ladders carry electric charge, the low-temperature thermodynamic quantities, such as the specific-heat coefficient and magnetic susceptibility, will show logarithmic singularities in the quantum critical regime. This behavior is in drastic contrast to the magnetic-field-induced criticality in undoped Mott insulator ladders, which is governed by the zero-scale-factor universality with its hallmark square-root singularities.
Magnetic interactions are widely believed to play a crucial role in the microscopic mechanism leading to high critical temperature superconductivity. It is therefore important to study the signatures of pairing in the magnetic excitation spectrum of simple models known to show unconventional superconducting tendencies. Using the density matrix renormalization group technique, we calculate the dynamical spin structure factor $S(\mathbf{k},\ensuremath{\omega})$ of a generalized $t\ensuremath{-}U\ensuremath{-}J$ Hubbard model away from half filling in a two-leg ladder geometry. The addition of JJJ enhances pairing tendencies. We analyze quantitatively the signatures of pairing in the magnetic excitation spectra. We found that the superconducting pair-correlation strength, that can be estimated independently from ground state properties, is closely correlated with the integrated low-energy magnetic spectral weight in the vicinity of $(\ensuremath{\pi},\ensuremath{\pi})$. In this wave-vector region, robust spin incommensurate features develop with increasing doping. The branch of the spectrum with rung direction wave vector krung=0{k}_{\mathrm{rung}}=0krung​=0 does not change substantially with doping where pairing dominates and thus plays a minor role. We discuss the implications of our results for neutron scattering experiments, where the spin excitation dynamics of hole-doped quasi-one-dimensional magnetic materials can be measured and also address implications for recent resonant inelastic x-ray scattering experiments.
Magnetic interactions are widely believed to play a crucial role in the microscopic mechanism leading to high critical temperature superconductivity. It is therefore important to study the signatures of pairing in the magnetic excitation spectrum of simple models known to show unconventional superconducting tendencies. Using the density matrix renormalization group technique, we calculate the dynamical spin structure factor $S(\mathbf{k},\ensuremath{\omega})$ of a generalized $t\ensuremath{-}U\ensuremath{-}J$ Hubbard model away from half filling in a two-leg ladder geometry. The addition of JJJ enhances pairing tendencies. We analyze quantitatively the signatures of pairing in the magnetic excitation spectra. We found that the superconducting pair-correlation strength, that can be estimated independently from ground state properties, is closely correlated with the integrated low-energy magnetic spectral weight in the vicinity of $(\ensuremath{\pi},\ensuremath{\pi})$. In this wave-vector region, robust spin incommensurate features develop with increasing doping. The branch of the spectrum with rung direction wave vector krung=0{k}_{\mathrm{rung}}=0krung​=0 does not change substantially with doping where pairing dominates and thus plays a minor role. We discuss the implications of our results for neutron scattering experiments, where the spin excitation dynamics of hole-doped quasi-one-dimensional magnetic materials can be measured and also address implications for recent resonant inelastic x-ray scattering experiments.