Many-body localization (MBL) is an intriguing physical phenomenon that arises from the interplay of interaction and disorder, allowing quantum systems to prevent thermalization. In this study, we investigate the MBL properties of the fully frustrated Heisenberg spin-1/2 ladder model with next-nearest-neighbor hopping interaction along the leg direction and compare it with the Heisenberg spin-1/2 single-chain model with next-nearest-neighbor hopping interaction. We explore the MBL transition using random matrix theory and study the characteristics of entanglement entropy and its variance. Our results show that for the single-chain model, the critical point
w1∼ 7.5
± 0.5, whereas for the frustrated ladder model,
w2∼ 10.5
± 0.5. Moreover, we observe the existence of a many-body mobility edge in the frustrated ladder model. We also investigate the dynamical properties of the frustrated ladder model and identify the logarithmic growth of entanglement entropy, high fidelity of initial information, and magnetic localization phenomenon in the localized phase. Finally, we explore the finite-size scaling of the two models. Our findings suggest that interpreting MBL transition as a continuous second-order phase transition yields a better scaling solution than the Kosterlitz-Thouless type transition for our two models, and this difference is more pronounced in the frustrated ladder model compared with the single-chain model.
Low-dimensional quantum magnets at finite temperatures present a complex interplay of quantum and thermal fluctuation effects in a restricted phase space. While some information about dynamical response functions is available from theoretical studies of the one-triplet dispersion in unfrustrated chains and ladders, little is known about the finite-temperature dynamics of frustrated systems. Experimentally, inelastic neutron scattering studies of the highly frustrated two-dimensional material
SrCu2(BO3)2 show an almost complete destruction of the one-triplet excitation band at a temperature only 1/3 of its gap energy, accompanied by strong scattering intensities for apparent multi-triplet excitations. We investigate these questions in the frustrated spin ladder and present numerical results from exact diagonalization for the dynamical structure factor as a function of temperature. We find anomalously rapid transfer of spectral weight out of the one-triplet band and into both broad and sharp spectral features at a wide range of energies, including below the zero-temperature gap of this excitation. These features are multi-triplet bound states, which develop particularly strongly near the quantum phase transition, fall to particularly low energies there, and persist all the way to infinite temperature. Our results offer valuable insight into the physics of finite-temperature spectral functions in
SrCu2(BO3)2 and many other highly frustrated spin systems.
The spin ladder systems have attracted a lot of interest in the field of low-dimensional physics. It is well known that the S = 1/2 two-leg spin ladder has a spin gap, while the three-leg one has a gapless spin liquid ground state. Some spin liquid behaviors were observed in the recent experiments of some frustrated systems; the distorted triangular lattice and kagome lattice antiferromagnets etc. Thus we consider the S = 1/2 three-leg spin ladder system with the next-nearest-neighbor interaction to investigate the effect of frustration on the spin liquids. Using the exact numerical diagonalization of finite-cluster systems, we study the ground state of this system. The phase diagram with respect to some exchange interaction constants is presented. It is revealed that sufficiently large next-nearest-neighbor coupling leads to a ferrimagnetic phase, which has a frustration-induced spontaneous magnetization. In addition we find two spin liquid phases, one of which corresponds to a Néel-like spin configuration and the other a collinear spin configuration. As a result of the numerical study, we find a new phase which is different from three phases.