Finite-size scaling of entanglement entropy at the Anderson transition with interactions

Zhao, An; Chu, Rui-Lin; Shen, Shun-Qing

doi:10.1103/physrevb.87.205140

Cited by 22 publications

(24 citation statements)

References 37 publications

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“…[29]. Entanglement measures were used to locate this transition in [73,74] and it was pointed out [74] that large system sizes are needed to be in the correct scaling regime, due to the large localization length. Here, we show the phase diagram from Ref.…”

Section: Occupation-spectrum Discontinuitymentioning

confidence: 99%

Many-body localization of spinless fermions with attractive interactions in one dimension

et al. 2018

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We study the finite-energy density phase diagram of spinless fermions with attractive interactions in one dimension in the presence of uncorrelated diagonal disorder. Unlike the case of repulsive interactions, a delocalized Luttinger-liquid phase persists at weak disorder in the ground state, which is a well-known result. We revisit the ground-state phase diagram and show that the recently introduced occupation-spectrum discontinuity computed from the eigenspectrum of the one-particle density matrix is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization group scheme to study the finite-size dependence of the conductance, which also resolves the existence of the Luttinger liquid and is computationally cheap. Our main results concern the finite-energy density case. Using exact diagonalization and by computing various established measures of the many-body localization-delocalization transition, we argue that the zero-temperature Luttinger liquid smoothly evolves into a finite-energy density ergodic phase without any intermediate phase transition.

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Section: Occupation-spectrum Discontinuitymentioning

confidence: 99%

Many-body localization of spinless fermions with attractive interactions in one dimension

et al. 2018

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“…This entanglement entropy is used e.g. to identify phases of many-body systems such as insulator or metallic phases [8][9][10][11], or topological phases [12][13][14].…”

mentioning

confidence: 99%

Extracting many-particle entanglement entropy from observables using supervised machine learning

Berkovits

2018

Phys. Rev. B

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Entanglement, which quantifies non-local correlations in quantum mechanics, is the fascinating concept behind much of aspiration towards quantum technologies. Nevertheless, directly measuring the entanglement of a many-particle system is very challenging. Here we show that via supervised machine learning using a convolutional neural network, we can infer the entanglement from a measurable observable for a disordered interacting quantum many-particle system. Several structures of neural networks were tested and a convolutional neural network akin to structures used for image and speech recognition performed the best. After training on a set of 500 realizations of disorder, the network was applied to 200 new realizations and its results for the entanglement entropy were compared to a direct computation of the entanglement entropy. Excellent agreement was found, except for several rare region which in a previous study were identified as belonging to an inclusion of a Griffiths-like quantum phase. Training the network on a test set with different parameters (in the same phase) also works quite well.

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“…Therefore, considering that the chaotic component becomes more important as W increases, only when all ∂ W S α have the same sign at a certain W , paired-particle component is completely destroyed. This value of W , which will be identified later, indicates the critical point of a phase transition 31 , the other aspects of which have been manifested in some previous works on the ground state of this model 32,34,35 .…”

Section: Entanglement Of Positive-negative Momentummentioning

confidence: 63%

Investigating disordered many-body system with entanglement in momentum space

Ye¹,

Han²,

Mu³

et al. 2017

Sci Rep

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We study the entanglement in momentum space of the ground state of a disordered one-dimensional fermion lattice model with attractive interaction. We observe two components in the entanglement spectrum, one of which is related to paired-fermion entanglement and contributes to the long-range correlation in position space. The vanishing point of it indicates the localization phenomenon in the ground state of this model. Additionally, by method of entanglement spectrum, we provide a new evidence to show the transition of two phases induced by interaction, and find that this phase transition is not influenced by the disorder. Our result show key characteristics in entanglement for different phases in the system, and provide a novel perspective to understand localization phenomena.

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Finite-size scaling of entanglement entropy at the Anderson transition with interactions

Cited by 22 publications

References 37 publications

Many-body localization of spinless fermions with attractive interactions in one dimension

Many-body localization of spinless fermions with attractive interactions in one dimension

Extracting many-particle entanglement entropy from observables using supervised machine learning

Investigating disordered many-body system with entanglement in momentum space

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