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Bulletin of the American Physical Society

Many-body localization of fermions with attractive interactions

Fabian Heidrich‐Meisner, Sheng-Hsuan Lin, Florian Dorfner

Published Mar 13, 2017• 0 citations
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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.

arXiv:1707.06759•SciPost Physics•Jan 18, 2018•23 citations
We study the entanglement in momentum space of a disordered one-dimentional fermion lattice model with attractive interaction and distinguish two components in it. One of the components is related to paired-fermion entanglement and thus the long-range correlation in position space, and the vanishing of it indicates many-body localization phenomenon. Based on this picture, we investigate the critical point between delocalized and localized phases for different interaction. Also, we find a new signal to distinguish two phases originating from the system only with the interaction, and show this phase transition is not influenced by the disorder. This letter shows key characteristics of this kind of systems, and provides a novel perspective to understand many-body localization phenomenon.
We study the entanglement in momentum space of a disordered one-dimensional fermion lattice model with attractive interaction. We observe that the many-body localization transition can be characterized by behaviors of two components in entanglement spectrum. One of the components is related to paired-fermion entanglement which contributes to the long-range correlation in position space, and the vanishing of it indicates the emerged many-body localized phase. Based on this understanding, we identify the critical point between delocalized and localized phases for interaction of different strength. Additionally by method of entanglement spectrum, we provide a new evidence to show the transition of two phases induced by interaction, and find this phase transition is not influenced by the disorder. Our result shows key characteristics in entanglement for different phases in the system, and provides a novel perspective to understand many-body localization phenomenon.
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.