We investigate magnetization reversal processes of magnetic nanorings. Exploring extensive parameter sets using Monte Carlo technique combined with scaling method, we constructed magnetization switching phase diagrams for such structures. The dominant switching mechanisms are found to strongly depend on the relative spatial dimensions of the rings, i.e., height, width, and radius. Furthermore, they are shown to depend on a characteristic exchange length scale, which is determined by the competing short-range ferromagnetic and long-range dipolar interactions in these systems. Detailed simulations allow us to identify three switching mechanisms, which should be useful for building high-density storage systems.

Entanglement measures are useful tools in characterizing otherwise unknown quantum phases and indicating transitions between them. Here we examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $\alpha$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $\alpha >\frac{1}{2}$. A numerical implementation of the SDRG method yields a power-law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading-order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $\alpha$, corresponding to a critical behavior with an effective central charge $c=\ln \left(2\right)$, independent of $\alpha$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $\alpha$. For a wide range of partition size $l$, the EE fits a critical behavior with a central charge close to $c=1$, which is the same as for the clean Haldane-Shastry model with a power-law-decaying interaction with $\alpha =2$. Only for small $l\ll L$, in a range which increases with the number of spins $N$, we find deviations which are rather consistent with the strong disorder fixed point central charge $c=\ln \left(2\right)$. Furthermore, we find using ED that the concurrence shows power-law decay, albeit with smaller power exponents than obtained by SDRG. We also present results obtained with DMRG and find agreement with ED for sufficiently small $\alpha <2$, whereas for larger $\alpha$ DMRG tends to underestimate the entanglement entropy and finds a faster decaying concurrence.

We apply a generalized version of the Lieb-Schultz-Mattis theorem to fermionic ladder systems to show the existence of a low-lying excited state (except for some special fillings). This can be regarded as a nonperturbative proof for the conservation under interaction of the sum of the Fermi wave vectors of the individual channels, corresponding to a generalized version of the Luttinger theorem to fermionic ladder systems. We conclude by noticing that the Lieb-Schultz-Mattis theorem is not applicable in this form to show the existence of low-lying excitations in the limit that the number of legs goes to infinity, e.g., in the limit of a 2D plane.

We investigate the magnetic susceptibility $\chi \left(T\right)$ of quantum spin chains of $N=1280$ spins with power-law long-range antiferromagnetic couplings 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 $\chi \left(T\right)$ and distribution functions of couplings at each renormalization step. For the case with only algebraic decay $\left(\xi =\infty \right)$ we find a crossover at ${\alpha }^{*}=1.066$ between a phase with a divergent low-temperature susceptibility $\chi (T\to 0)$ for $\alpha >{\alpha }^{*}$ to a phase with a vanishing $\chi (T\to 0)$ for $\alpha <{\alpha }^{*}$. For finite cutoff lengths $\xi$, this crossover occurs at a smaller ${\alpha }^{*}\left(\xi \right)$. 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 pseudogap at ${\alpha }_c={\alpha }^{*}$.

We study the equilibration behavior following local quenches, using frustrated quantum spin chains as an example of interacting closed quantum systems. Specifically, we examine the statistics of the time series of the Loschmidt echo, the trace distance of the time-evolved local density matrix to its average state, and the local magnetization. Depending on the quench parameters, the equilibration statistics of these quantities show features of good or poor equilibration, indicated by Gaussian, exponential, or bistable distribution functions. These universal functions provide valuable tools to characterize the various time-evolution responses and give insight into the plethora of equilibration phenomena in complex quantum systems.

Adaptive quantum design is used to identify broken-symmetry quantum-well potential profiles with optical response properties superior to previous ad hoc solutions. This technique performs an unbiased stochastic search of configuration space. It allows us to engineer many-body excitonic wave functions and thus provides a new methodology to efficiently develop optimized quantum-confined Stark effect device structures.