Abstract
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.
Highlights
It is known that a vanishing density of states at fermi level leads to an insulator in band theory of condensed matter physics
Related with entanglement spectrum (ES), the entanglement can be quantified by the Rényi entropy of the reduced density matrix, which can characterize the local convertibility of the bipartite quantum states and can be used to study quantum phase transition[31]
By partitioning the reciprocal lattice into two subsystems in different ways, we investigate the entanglement in momentum space of a fermion lattice model with interaction and disorder
Summary
It is known that a vanishing density of states at fermi level leads to an insulator in band theory of condensed matter physics. ES in momentum space[23,24,25,26,27,28,29] and angular momentum space[30] can help to explore new phases of quantum matters of many-body systems such as Chern insulators In these cases, only the ES of ground states is studied, which still indicates the property of excitations in the system. Features and intuitive picture of two components of it: one component related to the entanglement between particles with opposite momentum would be destroyed by the other component as the strength of disorder grows This indicates localizations in the low-lying states, which could herald the higher-energy MBL phenomenon[38]. We show that the behavior of this transition is robust in the presence of on-site disorder
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