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arXiv:1310.1556 · Physical Review B

Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization

Richard Berkovits

Published May 30, 2014• 11 citations
arXivHTMLPDF

Abstract

The properties of the entanglement entropy (EE) of low-lying excitations in one-dimensional disordered interacting systems are studied. The ground state EE shows a clear signature of localization, while low-lying excitations show a significantly longer localization length. The dependence of the localization as a function of interaction strength and sample length is studied using the density matrix renormalization group (DMRG). This behavior corresponds to the presence of the predicted many-particle critical energy in the vicinity of the ground state energy. The implications of these results on experiments are discussed.

DOI
10.1103/physrevb.89.205137

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Journal of Statistical Mechanics Theory and Experiment•Apr 1, 2019•1 citation
The properties of the entanglement entropy (EE) of low-lying excitations in one-dimensional disordered interacting systems are studied. The ground state EE shows a clear signature of localization, while low-lying excitations show a significantly longer localization length. The dependence of the localization as a function of interaction strength and sample length is studied using the density matrix renormalization group (DMRG). This behavior corresponds to the presence of the predicted many-particle critical energy in the vicinity of the ground state energy. The implications of these results on experiments are discussed.
The properties of the entanglement entropy (EE) in one-dimensional disordered interacting systems are studied. Anderson localization leaves a clear signature on the average EE, as it saturates on the length scale exceeding the localization length. This is verified by numerically calculating the EE for an ensemble of disordered realizations using the density matrix renormalization group method. A heuristic expression describing the dependence of the EE on the localization length, which takes into account finite-size effects, is proposed. This is used to extract the localization length as a function of the interaction strength. The localization length dependence on the interaction fits nicely with the expectations.
The properties of the low-lying eigenvalues of the entanglement Hamiltonian and their relation to the localization length of a disordered interacting one-dimensional many-particle system are studied. The average of the first entanglement Hamiltonian level spacing is proportional to the ground-state localization length and shows the same dependence on the disorder and interaction strength as the localization length. This is the result of the fact that entanglement is limited to distances of order of the localization length. The distribution of the first entanglement level spacing shows a Gaussian-type behavior as expected for level spacings much larger than the disorder broadening. For weakly disordered systems (localization length larger than sample length), the distribution shows an additional peak at low-level spacings. This stems from rare regions in some samples which exhibit metalliclike behavior of large entanglement and large particle-number fluctuations. These intermediate microemulsion metallic regions embedded in the insulating phase are discussed.
We study the entanglement entropy(EE) of disordered one-dimensional spinless fermions with attractive interactions. With intensive numerical calculation of the EE using the density matrix renormalization group method, we find clear signatures of the transition between the localized and delocalized phase. In the delocalized phase, the fluctuations of the EE becomes minimum and independent of the system size. Meanwhile the EE's logarithmic scaling behavior is found to recover to that of a clean system. We present a general scheme of finite size scaling of the EE at the critical regime of the Anderson transition, from which we extract the critical parameters of the transition with good accuracy, including the critical exponent, critical point and a power-law divergent localization length.
Statistical properties of the low‐lying states of the entanglement spectrum of a one‐dimensional interacting disordered system are studied in order to understand the localized to extended transition as function of interaction strength and excitation number expected from the many‐body localization transition. It is shown that such a transition is observed in the statistics of the level‐spacing of the entanglement spectrum. For an intermediate range of excitation numbers and strong interaction strength where the entanglement spectrum shows a clear extended behavior, a signature of non‐ergodic behavior also emerges. We interpret this as evidence for a non‐ergodic‐extended phase suggested by previous studies.
The entanglement entropy of the ν=1/3 and ν=5/2 quantum Hall states in the presence of short-range random disorder has been calculated using direct diagonalization. A microscopic model of electron–electron interaction is used and spin-polarized electrons are confined to a single Landau level and interact with long-range Coulomb interaction. In the case of very weak disorder, the values of topological entanglement entropy are roughly consistent with the expected theoretical results. By considering a broad range of disorder strengths, entanglement entropy was studied in an effort to detect quantum phase transitions. In particular, there is a signature of the transition as the function of the disorder strength for the ν=5/2 state. Prospects of using the density matrix renormalization group to compute the entanglement entropy for larger system sizes are discussed.
Abstract The entanglement entropy (EE) distribution of strongly disordered one dimensional spin chains, which are equivalent to spinless fermions at half-filling on a bond (hopping) disordered one-dimensional Anderson model, has been shown to exhibit very distinct features such as peaks at integer multiplications of , essentially counting the number of singlets traversing the boundary. Here we show that for a canonical Anderson model with box distribution on-site disorder and repulsive nearest-neighbor interactions the EE distribution also exhibits interesting features, albeit different than the distribution seen for the bond disordered Anderson model. The canonical Anderson model shows a broad peak at low entanglement values and one narrower peak at . Density matrix renormalization group calculations reveal this structure and the influence of the disorder strength and the interaction strength on its shape. A modified real space renormalization group method was used to get a better understanding of this behavior. As might be expected the peak centered at low values of EE has a tendency to shift to lower values as disorder is enhanced. A second peak appears around the EE value of , this peak is broadened and no additional peaks at higher integer multiplications of are seen. We attribute the differences in the distribution between the canonical model and the broad hopping disorder to the influence of the on-site disorder which breaks the symmetry across the boundary.