Statistical properties of eigenstates in three-dimensional quantum disordered systems

W. D. Heiss, A. A. Kotz�

Kyungmin Lee, Ronald Melendrez, Arijeet Pal +1 more

Nonequilibrium properties of quantum materials present many intriguing properties, among them athermal behavior, which violates the eigenstate thermalization hypothesis. Such behavior has primarily been observed in disordered systems. More recently, experimental and theoretical evidence for athermal eigenstates, known as ``quantum scars,'' has emerged in nonintegrable disorder-free models in one dimension with constrained dynamics. In this Rapid Communication, we show the existence of quantum scar eigenstates and investigate their dynamical properties in many simple two-body Hamiltonians with ``staggered'' interactions, involving ferromagnetic and antiferromagnetic motifs, in arbitrary dimensions. These magnetic models include simple modifications of widely studied ones (e.g., the XXZ model) on a variety of frustrated and unfrustrated lattices. We demonstrate our ideas by focusing on the two-dimensional frustrated spin-1/2 kagome antiferromagnet, which was previously shown to harbor a special exactly solvable point with ``three-coloring'' ground states in its phase diagram. For appropriately chosen initial product states---for example, those which correspond to any state of valid three-colors---we show the presence of robust quantum revivals, which survive the addition of anisotropic terms. We also suggest avenues for future experiments which may see this effect in real materials.

Jinghu Liu, Zhihao Xu

Recent studies on disorder-induced many-body localization (MBL) in non-Hermitian quantum systems have attracted great interest. However, the non-Hermitian disorder-free MBL still needs to be clarified. We consider a one-dimensional interacting Stark model with nonreciprocal hoppings having time-reversal symmetry, the properties of which are boundary dependent. Under periodic boundary conditions (PBCs), such a model exhibits three types of phase transitions: the real-complex transition of eigenenergies, the topological phase transition, and the non-Hermitian Stark MBL transition. The real-complex and topological phase transitions occur at the same point in the thermodynamic limit but do not coincide with the non-Hermitian Stark MBL transition, which is quite different from the non-Hermitian disordered cases. By the level statistics, the system transitions from the Ginibre ensemble (GE) to the Gaussian orthogonal ensemble (GOE) to the Possion ensemble with the increase of the linear tilt potential's strength. The real-complex transition of the eigenvalues is accompanied by the GE-to-GOE transition in the ergodic regime. Moreover, the second transition of the level statistics corresponds to the occurrence of non-Hermitian Stark MBL. We demonstrate that the non-Hermitian Stark MBL is robust and shares many similarities with disorder-induced MBL, which several existing characteristic quantities of the spectral statistics and eigenstate properties can confirm. The dynamical evolutions of the entanglement entropy and the density imbalance can distinguish the real-complex and Stark MBL transitions. Finally, we find that our system under open boundary conditions lacks a real-complex transition, and the transition of non-Hermitian Stark MBL is the same as that under PBCs.

David A. Evensky

Jan Philipp Klinger, Martin Gärttner

We study excitation transport in a two-dimensional system of randomly assembled spins with power-law hopping in two dimensions. This model can be realized in cold atom quantum simulators with Rydberg atoms. In these experiments, due to the Rydberg blockade effect, the degree of disorder in the system is effectively tunable by varying the spin density. We study dynamics and eigenstate properties of the model as a function of disorder strength and system size and discuss potential limitations for experiments. At strong disorder we predominantly observe localized eigenstates with power-law tails. In this regime the spectral and eigenstate properties can be understood in a perturbative picture of states localized on small clusters of spins. As the disorder strength is weakened eigenstates become increasingly delocalized and a set of seemingly multifractal states appears in the low-energy tail of the spectrum. A detailed study of the system-size scaling of the eigenstate properties indicates that in the infinite-size limit all states eventually become localized. We discuss the feasibility of observing localization effects experimentally in the spatial spreading of an initially localized excitation and identify limited system sizes and finite decoherence rates as major challenges. Our study paves the way towards an experimental observation of localization effects in Rydberg spin systems with tunable disorder.

Yong-Shi Wu