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arXiv:2403.17412 · Journal of the Physical Society of Japan

Multi-Triplon Excitations of Hubbard Ladders with Site-Dependent Potentials

Nobuya Maeshima, Ken-ichi Hino

Published Apr 22, 2024• 1 citation
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Abstract

We study low-lying spin-singlet excitations of two-leg Hubbard ladders with site-dependent potentials. Using general formulas of the charge disproportionation induced by the site-dependent potentials, we derive the contributions of spin degrees of freedom to the spectral functions such as the dynamical charge structure factor $N(\boldsymbol{k},ω)$ and the optical conductivity $σ_γ(ω)$ along the $γ(=x,y)$-direction of the two-leg ladders. Numerical results obtained by the Lanczos diagonalization method have clarified that the multi-triplon singlet states, including two- and three-triplon excitations, can be detected by observing these quantities. Furthermore, we have found that ladders with random potentials also have non-negligible contributions of these excitations to $σ_x(ω)$.

DOI
10.7566/jpsj.93.054707

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We study low-lying spin-singlet excitations of two-leg Hubbard ladders with site-dependent potentials. Using general formulas of the charge disproportionation induced by the site-dependent potentials, we derive the contributions of spin degrees of freedom to the spectral functions such as the dynamical charge structure factor N(k,ω)N(\boldsymbol{k},ω)N(k,ω) and the optical conductivity σγ(ω)σ_γ(ω)σγ​(ω) along the γ(=x,y)γ(=x,y)γ(=x,y)-direction of the two-leg ladders. Numerical results obtained by the Lanczos diagonalization method have clarified that the multi-triplon singlet states, including two- and three-triplon excitations, can be detected by observing these quantities. Furthermore, we have found that ladders with random potentials also have non-negligible contributions of these excitations to σx(ω)σ_x(ω)σx​(ω).
We study the spectral function of two-leg Hubbard ladders with the time-dependent density matrix renormalization group method (tDMRG). The high-resolution spectrum displays features of spin-charge separation and a scattering continuum of excitations with coherent bands of bound states ``leaking'' from it. As the interleg hopping is increased, the continuum in the bonding channel moves to higher energies and spinon and holon branches merge into a single coherent quasiparticle band. Simultaneously, the spectrum undergoes a crossover from a regime with two minima at incommensurate values of kx{k}_{x}kx​ (a Mott insulator), to one with a single minimum at ${k}_{x}=\ensuremath{\pi}$ (a band insulator). We identify the presence of a continuum of scattering states consisting of a triplon and a polaron. We analyze the processes leading to quasiparticle formation by studying the time evolution of charge and spin degrees of freedom in real space after the hole is created. At short times, incoherent holons and spinons are emitted but after a characteristic time $\ensuremath{\tau}$ charge and spin form polarons that propagate coherently.
The charge carrier dynamics of doped electronic correlated systems on ladders and chains, subject to ultrafast photoirradiation, is investigated using the time-dependent Lanczos method. The time-resolved optical conductivity and the temporal profiles of other relevant quantities, including the doublon number, the kinetic energy, and the interaction energy, are calculated. Two competitive factors that can influence the transient charge carrier dynamics are identified as the thermal effect and the charge effect. We demonstrate that the analysis of their interplay can provide an intuitive way to understand the numerical results and the recent optical pump-probe experiment on a two-leg ladder cuprate.
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.
Resonant inelastic x-ray scattering (RIXS) has become an important tool for studying elementary excitations in correlated materials. Here, we present a systematic theoretical investigation of the Cu LLL-edge RIXS spectra of undoped and doped cuprate two-leg spin-ladders in both the non-spin-conserving (NSC) and spin-conserving (SC) channels. The spectra are rich and host many exotic excitations. In the NSC channel of the undoped case, we identify one-triplon and bound triplet two-triplon excitations in the strong rung coupling limit, as well as confined spinons in the weak rung coupling limit. In the doped case, we observe a quasiparticle excitation formed from a bound charge and spin-1/21/21/2 in the strong rung coupling limit. In the SC channel, we also identify several new features, including bound singlet two-triplon excitations and confined spinons in the undoped ladders in the strong and weak rung coupling limits, respectively. Conversely, in the doped case, the SC channel primarily probes both gapless and gapped charge excitations. Finally, we revisit the available data for the ladder compound Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​ in the context of our results.
We study the ground state and low-lying excited states of the Kitaev-Heisenberg model on a two-leg ladder geometry using the density-matrix renormalization-group and Lanczos exact diagonalization methods. The Kitaev and Heisenberg interactions are parametrized as $K=sin\ensuremath{\phi}$ and $J=cos\ensuremath{\phi}$ with an angle parameter $\ensuremath{\phi}$. Based on the results for several types of order parameters, excitation gaps, string order parameter, and entanglement spectra, the $\ensuremath{\phi}$-dependent ground state phase diagram is determined. Remarkably, the phase diagram is quite similar to that of the Kitaev-Heisenberg model on a honeycomb lattice, exhibiting the same long-range-ordered states, namely rung singlet (analog to N\'eel in three dimensions), zigzag, ferromagnetic, and stripy, and the presence of gapped spin liquids around the exactly solvable Kitaev points $\ensuremath{\phi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. We also calculate the expectation value of a plaquette operator corresponding to a $\ensuremath{\pi}$-flux state in order to establish how the gapped Kitaev spin liquid extends away from the $\ensuremath{\phi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. Furthermore, we determine the dynamical spin structure factor and discuss the effect of the Kitaev interaction on the spin-triplet dispersion.
This article summarizes and extends the recent developments in the microscopic modeling of the magnetic excitations in cuprate two-leg ladder systems. The microscopic Hamiltonian comprises dominant Heisenberg exchange terms plus an additional four-spin interaction which is about five times smaller. We give an overview over the relevant energies like the one-triplon dispersion, the energies of two-triplon bound states and the positions of multi-triplon continua and over relevant spectral properties like spectral weights and spectral densities in the parameter regime appropriate for cuprate systems. It is concluded that an almost complete understanding of the magnetic excitations in undoped cuprate ladders has been obtained as measured by inelastic neutron scattering, inelastic light (Raman) scattering and infrared absorption.