Inverse participation ratios in the XXZ spin chain

Grégoire Misguich (1) , Vincent Pasquier (1) , Jean-Marc Luck (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We investigate numerically the inverse participation ratios in a spin-1/2 XXZ chain, computed in the “Ising” basis (i.e., eigenstates of σ$^z_i$). We consider in particular a quantity $T$, defined by summing the inverse participation ratios of all the eigenstates in the zero-magnetization sector of a finite chain of length N, with open boundary conditions. From a dynamical point of view, T is proportional to the stationary return probability to an initial basis state, averaged over all the basis states (initial conditions). We find that T exhibits an exponential growth, T∼exp($aN$), in the gapped phase of the model and a linear scaling, T∼N, in the gapless phase. These two different behaviors are analyzed in terms of the distribution of the participation ratios of individual eigenstates. We also investigate the effect of next-nearest-neighbor interactions, which break the integrability of the model. Although the massive phase of the nonintegrable model also has T∼exp($aN$), in the gapless phase T appears to saturate to a constant value.

Domaines: Physique [physics]; Electrons fortement corrélés [cond-mat.str-el]; Mécanique statistique [cond-mat.stat-mech]; Physique Quantique [quant-ph]

Grégoire Misguich, Vincent Pasquier, Jean-Marc Luck. Inverse participation ratios in the XXZ spin chain. Physical Review B, 2016, 94, pp.155110. ⟨10.1103/PhysRevB.94.155110⟩. ⟨cea-01377658⟩