Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions

Abstract

We investigate the magnetic susceptibility $\chi (T)$ of quantum spin chains of $N=1280$ spins with power-law long-range antiferromagnetic coupling as a function of their spatial decay exponent $\alpha$ and cutoff length $\xi$. The calculations are based on the strong disorder renormalization method which is used to obtain the temperature dependence of $\chi (T)$ and distribution functions of couplings at each renormalization step. For the case with only algebraic decay ($\xi =\infty$) we find a crossover at ${\alpha }^{\ast }=1.066$ between a phase with a divergent low-temperature susceptibility $\chi (T\to 0)$ for $\alpha >{\alpha }^{\ast }$ to a phase with a vanishing $\chi (T\to 0)$ for $\alpha <{\alpha }^{\ast }$. For finite cutoff lengths $\xi$, this crossover occurs at a smaller ${\alpha }^{\ast }(\xi )$. Additionally we study the localization of spin excitations for $\xi =\infty$ by evaluating the distribution function of excitation energies and we find a delocalization transition that coincides with the opening of the pseudo-gap at ${\alpha }_c={\alpha }^{\ast }$.

arXiv comment6 pages, 7 figures

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• Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random Long-Range Interactions
• Simulating realistic screening clouds around quantum impurities: role of spatial anisotropy and disorder
• Thermal Properties of Rung Disordered Two-leg Quantum Spin Ladders: Quantum Monte Carlo Study
• Effect of Hilbert space truncation on Anderson localization
• Testing the validity of random-singlet state for long-range hopping models through the scaling of entanglement entropy
• Thermodynamic properties of disordered quantum spin ladders
• Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Ground State Properties
• Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Excited States and Finite Temperature Properties