2000
DOI: 10.1103/physrevb.61.15546
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Low-energy transition in spectral statistics of two-dimensional interacting fermions

Abstract: We study the level spacing statistics P (s) and eigenstate properties of spinless fermions with Coulomb interaction on a two dimensional lattice at constant filling factor and various disorder strength. In the limit of large lattice size, P (s) undergoes a transition from the Poisson to the Wigner-Dyson distribution at a critical total energy independent of the number of fermions. This implies the emergence of quantum ergodicity induced by interaction and delocalization in the Hilbert space at zero temperature… Show more

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Cited by 24 publications
(26 citation statements)
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“…This distinction is blurred as the interactions become stronger and P (S i ) for any i approaches the GOE distribution. This is in agreement with the observations for the distribution of interacting MBE [36][37][38][39][40][41] which show a transition to GOE statistics as interactions become stronger. Thus, it seems that the Li and Haldane conjecture holds even for the ES of interacting systems.…”
supporting
confidence: 92%
“…This distinction is blurred as the interactions become stronger and P (S i ) for any i approaches the GOE distribution. This is in agreement with the observations for the distribution of interacting MBE [36][37][38][39][40][41] which show a transition to GOE statistics as interactions become stronger. Thus, it seems that the Li and Haldane conjecture holds even for the ES of interacting systems.…”
supporting
confidence: 92%
“…5 shows behavior similar to that found in Ref. 8, although the physics of the evolution of levels is quite different in our case.…”
supporting
confidence: 88%
“…where < L/2. The two constraints (5) and (9) imply that the cut averaged entanglement entropyS( ) is a concave function of subsystem size with positive slope for 0 ≤ ≤ L/2 and negative slope for L/2 ≤ ≤ L. Its negative second derivative makes the slope of larger subsystems at most equal to or smaller than the slope of smaller subsystems. It should be emphasized that these considerations are only valid for the cut averaged entanglement entropy in periodic systems.…”
Section: Strong Subadditivity and Entanglement Entropy Under Perimentioning
confidence: 99%
“…On the other hand, in the MBL phase at stronger disorder the ETH is no longer valid. While ETH is a consequence of quantum chaos (a generic feature of interacting nonintegrable systems 6 ), the MBL phase shows features of integrability, most prominently signaled in a change of the spectral statistics that was explored in several pioneering works [7][8][9] and are now a standard measure for the detection of MBL [10][11][12][13][14] . The integrability in the MBL phase is due to an emergent extensive number of local conserved quantum operators 15,16 , which prohibit thermalization and lead to a subextensive (area law) entanglement entropy; this has been numerically verified in many studies 12,[17][18][19][20][21] .…”
Section: Introductionmentioning
confidence: 99%