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arXiv:1806.01717 · Physical Review Letters

Dynamic Structure Factor of Disordered Quantum Spin Ladders

Max Hörmann, Paul Wunderlich, Kai Phillip Schmidt

Published Oct 16, 2018• 13 citations
arXivHTMLPDF

Abstract

We investigate the impact of quenched disorder on the zero-temperature dynamic structure factor of two-leg quantum spin ladders. Using linked-cluster expansions and bond-operator mean-field theory, huge effects on individual quasiparticles but also on composite bound states and two-quasiparticle continua are observed. This leads to intriguing quantum structures in dynamical correlation functions well observable in spectroscopic experiments.

DOI
10.1103/physrevlett.121.167201

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We investigate the impact of quenched disorder on the zero-temperature dynamic structure factor of two-leg quantum spin ladders. Using linked-cluster expansions and bond-operator mean-field theory, huge effects on individual quasiparticles but also on composite bound states and two-quasiparticle continua are observed. This leads to intriguing quantum structures in dynamical correlation functions well observable in spectroscopic experiments.
We determine the dynamical structure factors of two gapped correlated electron systems, namely the Ising model in a strong transverse field and the two-leg spin-1/2 Heisenberg ladder in the limit of strong rung coupling. We consider the low-temperature limit, employing a variety of analytical and numerical techniques. The coherent modes of single-particle excitations, which are delta functions at zero temperature, are shown to broaden asymmetrically in energy with increasing temperature. Firstly, we apply a low-temperature “resummation” inspired by the Dyson equation to a linked-cluster expansion of the two-leg Heisenberg ladder. We include matrix elements to second order in the interaction between states containing up to two particles. A low-frequency response similar to the “Villain mode” is also observed. Next, we apply a cumulant expansion technique to the transverse field Ising model. We resolve the issue of negative spectral weight caused by double pole in the leading self-energy diagram by including a resummation of terms obtained from the six-point function, demonstrating that the perturbation series in 2n-spin correlation functions can be extended to higher orders. The result generalises to higher dimensions and the analytic calculation is compared to a numerical Pade approximant. We outline the extension of this method to the strong coupling ladder. Finally, we compare the previous results to numerical data obtained by full diagonalisation of finite chains and numerical evaluation of the Pfaffian, a method specific to the transverse field Ising chain. The latter method is used for a phenomenological study of the asymmetric broadening as well as an evaluation of fitting functions for the broadened lineshapes.
A two-leg quenched random bond disordered antiferromagnetic spin-1/2 Heisenberg ladder system is investigated by means of stochastic series expansion quantum Monte Carlo (QMC) method. Thermal properties of the uniform and staggered susceptibilities, the structure factor, the specific heat, and the spin gap are calculated over a large number of random realizations in a wide range of disorder strength. According to our QMC simulation results, the considered system has a special temperature point at which the specific heat takes the same value regardless of the strength of the disorder. Moreover, the uniform susceptibility is shown to display the same character except for a small difference in the location of the special point. Finally, the spin gap values are found to decrease with increasing disorder parameter and the smallest gap value found in this study is well above the weak coupling limit of the clean case.
This PhD thesis concerns the physics of low-dimensional quantum systems and especially quantum spin ladders. Novel metal-organic compounds (C5H12N)2CuBr4 and (C5H12N)2CuCl4 are investigated as model materials for low-dimensional quantum behavior by neutron scattering experiments and by measurements of magnetic and thermodynamic properties. The experimental results are compared quantitatively to calculations using a variety of theoretical and numerical methods (DMRG, ED) of the ground state and excitations of such systems. Key results are the determination of the Hamiltonian and its exchange parameters of (C5H12N)2CuCl4 studied here for the first time from quantitative modelling of magnetic susceptibility and neutron spectroscopy data. When a magnetic field is applied two quantum critical points occur at which fractionalization of the elementary quasi-particle excitations is ob- served. The characteristic excitation continua are explained by effective spin-chain and t-J models and are observed systematically as a function of magnetic field and temperature. Coherent and incoherent spin Luttinger-liquid physics is observed and for the first time modelled fully quantitatively. The chemical flexibility of the these metal-organic compounds allows continuous solid-state mixtures of Br and Cl resulting in systems with quenched disorder. The rung and leg exchange parameters assume discrete values given by the specific chemical composition of the exchange pathways. The influence of such quenched disorder on the excitations of quantum spin ladders has been studied experimentally. The observed spectra with damped excitations of the unperturbed ladder and more localized modes provide detailed insights into the physics that may be observed in such systems if a magnetic field is applied and so called Bose glass phases are induced.
Random bond disorder in antiferromagnetic spin-1/2 Heisenberg ladders is investigated using the stochastic series expansion quantum Monte Carlo method. We find that the effects of individual bond impurities vary strongly, depending on their positions on legs and rungs. We initially focus on how the distribution of local bond energies depends on the impurity concentration. Then we study how the phase diagram of even-leg ladders is affected by random bond doping. We observe Bose glass phases in two regimes (${h}^{\ensuremath{'}}<h\ensuremath{\lesssim}{h}_{c1}$ and ${h}^{\ensuremath{'}\ensuremath{'}}<h<{h}_{c2}$) and a Bose-Einstein Condensate in between. Their presence is discussed in relation to the local bond energies.
Weakly coupled Ising chains provide a condensed-matter realization of confinement. In these systems, kinks and antikinks bind into mesons due to an attractive interaction potential that increases linearly with the distance between the particles. While single mesons have been directly observed in experiments, the role of the multiparticle continuum and bound states of mesons in the excitation spectrum is far less clear. Using time-dependent density-matrix renormalization group methods, we study the dynamical structure factors of one- and two-spin operators in a transverse-field two-leg Ising ladder in the ferromagnetic phase. The propagation of time-dependent correlations and the two-spin excitation spectrum reveal the existence of interchain bound states, which are absent in the one-spin dynamical structure factor. We also identify two-meson bound states that appear at higher energies, above the thresholds of several two-meson continua.
The zero-temperature dynamical spin-spin correlation functions are calculated for the spin-12\frac{1}{2}21​ two-leg antiferromagnetic Heisenberg ladder in a magnetic field above the lower critical field Hc1{H}_{c1}Hc1​. The dynamical structure factors are calculated, which exhibit both massless modes and massive excitations. These modes appear in different sectors characterized by the parity in the rung direction and by the momentum in the direction of the chains. The structure factors have power-law singularities at the lower edges of their support. The results are also applicable to the spin-1 Heisenberg chain. The implications are briefly discussed for the various correlation functions and the $\ensuremath{\pi}$ resonance in the SO(5) symmetric ladder model.