Signature of non‐ergodicity in low‐lying excitations of disordered many‐particle systems

Abstract

Statistical properties of the low-lying states of the entanglement spectrum of a one-dimensional interacting disordered system are studied in order to understand the localized to extended transition as function of interaction strength and excitation number expected from the manybody localization transition. It is shown that such a transition is observed in the statistics of the level-spacing of the entanglement spectrum. For an intermediate range of excitation numbers and strong interaction strength where the entanglement spectrum shows a clear extended behavior, a signature of non-ergodic behavior also emerges. We interpret this as evidence for a non-ergodic-extended phase suggested by previous studies.

From ergodic to non-ergodic chaos in Rosenzweig–Porter model

“…Such a region appears at the metallic side of the many-body localization transition in an array of Josephson junctions [23,24,25,26,27]. This nonergodic behaviour has also been analyzed in other quantum systems [28,29,30,31,32] and it has been suggested that it can play an important role for quantum information [33]. On top of that, there are several teams that have obtained a sub-diffusive but ergodic behaviour in one-dimensional spin chains at the metallic side of the many-body localization transition [34,35,36,37,35,38,39].…”

Scaling up the Anderson transition in random-regular graphs

“…An ergodic wavefunction roughly means that it has a uniform amplitude in the region of Hilbert space allowed by symmetry constraints [12]. Some groups have observed that metallic wavefunctions near this transition are not ergodic [13][14][15][16][17][18], while others support its ergodicity [19][20][21][22]. Given this controversy, it seems sensible to step down and consider simpler models that may exhibit similar behavior than the one expected in the metallic side of the manybody localization transition.…”

“…We choose D 1 because this quantity has much smaller corrections to scaling that D 2 or D ∞ . We use a small disorder interval W = [16,20] so that we can use a first order expansion in the fields ρ and η of Eq. 2.…”

“…FIG.4. Best data collapse for the derivative of first fractal dimension D 1 (N ) = S / log(N ) for disorder W =[16,20] and sizes N = 62, 124, 250, . .…”

On super-Poissonian behavior of the Rosenzweig-Porter model in the non-ergodic extended regime

“…There has been a recent surge in interest in the critical behavior of the transition. Part of this interest stems from the realization that for the many body localization phenomenon the localized and extended regions may be separated by a critical regime [16][17][18][19][20][21][22][23][24][25]. An additional motivation pertains to the Sachdev-Ye-Kitaev (SYK) model, originally introduced in the study of spin liquids [26] and recently gaining relevance to holographic dualities in string theory [27] and quantum gravity [28].…”