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APS

Dynamical scaling in infinitely correlated many-body systems through a quantum phase transition

Oscar L. Acevedo, Luis Quiroga, Ferney J. Rodríguez, Neil F. Johnson

Published Mar 1, 2013• 0 citations
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We use exact diagonalization to explore the many-body localization transition in a random-field spin-1/2 chain. We examine the correlations within each many-body eigenstate, looking at all states and thus effectively working at infinite temperature. For weak random field the eigenstates are thermal, as expected in this nonlocalized, ergodic phase. For strong random field the eigenstates are localized, with only short-range entanglement. We roughly locate the localization transition and examine the probability distributions of the correlations, finding that this quantum phase transition at nonzero temperature may be showing infinite-randomness scaling.
The investigation of strongly-correlated quantum matter is difficult due to the curse of dimensionality and intricate entanglement structures. These challenges are particularly pronounced in the vicinity of continuous quantum phase transitions, where quantum fluctuations manifest across all length scales. While quantum simulators give controlled access to a number of strongly correlated systems, the study of critical phenomena has been hampered by finite-size effects arising from diverging correlation lengths. Moreover, the experimental investigation of entanglement in many-body systems has been hindered by limitations in measurement protocols. To address these challenges, we employ the multiscale entanglement renormalization ansatz (MERA) and implement a holographic scheme for subsystem tomography on a fully-connected trapped-ion quantum computer. Our method accurately represents infinite systems and long-range correlations with few qubits, facilitating the efficient extraction of observables and entanglement properties, even at criticality. We observe a quantum phase transition with spontaneous symmetry breaking and reveal the evolution of entanglement properties across the critical point. For the first time, we demonstrate log-law scaling of subsystem entanglement entropies at criticality on a digital quantum computer. This achievement highlights the potential of MERA for the investigation of strongly-correlated many-body systems on quantum computers.