Quantum scars in spin-1/2 isotropic Heisenberg clusters

We investigate the influence of the external fields on the statistics of energy levels and towers of eigenstates in spin-1/2 isotropic Heisenberg clusters, including chain, ladder, square and triangular lattices. In the presence of uniform field in one direction, the SU(2) symmetry of the system allows that almost whole spectrum consists of a large number of towers with identical level spacing. Exact diagonalization on finite clusters shows that random transverse fields in other two directions drive the level statistics from Poisson to Wigner-Dyson distributions with different values of mean level spacing ratio, indicating the transition from integrability to non-integrability. However, for the three types of clusters, it is found that the largest tower still hold approximately even the symmetry is broken, resulting to a quantum scar. Remarkably, the non-thermalized states cover the Greenberger-Horn-Zeilinger and W states, which maintain the feature of revival while a Neel state decays fast in the dynamic processes. In addition, some dynamic schemes for experimental detection are proposed. Our finding reveals the possibility of quantum information processing that is immune to the thermalization in finite size quantum spin clusters.

Automated summary

We studied the impact of external fields on the energy level statistics and towers of eigenstates in spin-1/2 isotropic Heisenberg clusters. Different lattice structures were considered, including chain, ladder, square and triangular lattices. The presence of a uniform field in one direction allowed for a spectrum consisting mostly of towers with identical level spacing, thanks to the SU(2) symmetry. However, introducing random transverse fields in the other directions caused a transition from integrability to non-integrability, as evidenced by the change in level statistics from Poisson to Wigner-Dyson distributions. The largest tower still remained approximately intact even when the symmetry was broken, resulting in a quantum scar. Additionally, non-thermalized states, such as the Greenberger-Horn-Zeilinger and W states, were found to exhibit revival features while a Neel state decayed rapidly in dynamic processes. Several dynamic schemes for experimental detection were also proposed. Our findings suggest the potential for thermalization-immune quantum information processing in finite-sized spin clusters.