Spin Models, Dynamics, and Criticality with Atoms in Tilted Optical Superlattices.

We show that atoms in tilted optical superlattices provide a platform for exploring coupled spin chains of forms that are not present in other systems. In particular, using a period-2 superlattice in one dimension, we show that coupled Ising spin chains with XZ and ZZ spin coupling terms can be engineered. We use optimized tensor network techniques to explore the criticality and nonequilibrium dynamics in these models, finding a tricritical Ising point in regimes that are accessible in current experiments. These setups are ideal for studying low-entropy physics, as initial entropy is "frozen-out" in realizing the spin models, and provide an example of the complex critical behavior that can arise from interaction-projected models.

Nontopological Majorana Zero Modes in Inhomogeneous Spin Ladders.

We show that the coupling of homogeneous Heisenberg spin-1/2 ladders in different phases leads to the formation of interfacial zero energy Majorana bound states. Unlike Majorana bound states at the interfaces of topological quantum wires, these states are void of topological protection and generally susceptible to local perturbations of the host spin system. However, a key message of our Letter is that, in practice, they show a high degree of resilience over wide parameter ranges which may make them interesting candidates for applications.

Integrability-based analysis of the hyperfine-interaction-induced decoherence in quantum dots.

Using the algebraic Bethe ansatz in conjunction with a simple Monte Carlo sampling technique, we study the problem of the decoherence of a central spin coupled to a nuclear spin bath. We describe in detail the full crossover from strong to weak external magnetic field, a limit where a large nondecaying coherence factor is found. This feature is explained by Bose-Einstein-condensate-like physics which also allows us to argue that the corresponding zero frequency peak would not be broadened by statistical or ensemble averaging.

Relaxation versus decoherence: spin and current dynamics in the anisotropic Kondo model at finite bias and magnetic field.

Using a nonequilibrium renormalization group method we study the real-time evolution of spin and current in the anisotropic Kondo model (both antiferromagnetic and ferromagnetic) at a finite magnetic field h(0) and bias voltage V. We derive analytic expressions for all times in the weak-coupling regime max{V, h(0),1/t} >> T(c) (T(c) is the strong-coupling scale). We find that all observables decay both with the spin relaxation and decoherence rates Gamma(1/2). Various V-dependent logarithmic, oscillatory, and power-law contributions are predicted. The low-energy cutoff of logarithmic terms is generically identified by the difference of transport decay rates. For small times t << max{V, h(0)}(-1), we obtain universal dynamics for spin and current.

Local density of states of one-dimensional Mott insulators and charge-density wave states with a boundary.

We determine the local density of states of one-dimensional incommensurate charge-density wave states in the presence of a strong impurity potential, which is modeled by a boundary. We find that the charge-density wave gets pinned at the impurity, which results in a singularity in the Fourier transform of the local density of states at momentum 2k_{F}. At energies above the spin gap we observe dispersing features associated with the spin and charge degrees of freedom, respectively. In the presence of an impurity magnetic field we observe the formation of a bound state localized at the impurity. All of our results carry over to the case of 1D Mott insulators by exchanging the roles of spin and charge degrees of freedom. We discuss the implications of our result for scanning tunneling microscopy experiments on spin-gap systems such as two-leg ladder cuprates.

Many-spinon states and the secret significance of Young tableaux.

We establish a one-to-one correspondence between the Young tableaux classifying the total spin representations of N spins and the exact eigenstates of the Haldane-Shastry model for a chain with N sites classified by the total spins and the fractionally spaced single-particle momenta of the spinons.