One-particle density matrix characterization of many-body localization
One-particle density matrix characterization of many-body localization
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DOI：
10.1002/andp.201600356
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发表时间：
2017-07-01
影响因子：
2.4
通讯作者：
Bardarson, Jens H.
中科院分区：
文献类型：
--
作者：
Bera, Soumya;Martynec, Thomas;Bardarson, Jens H.
我们研究在一维的相互作用费米子随机，不相关的现场无序，多体局域化（MBL）的典范模型。该模型实现了相互作用驱动的遍历相和多体局域相之间的量子相变，相变发生在多体本征态中。我们提出了一个单粒子的框架来表征这些阶段的本征态（自然轨道）和本征值（占领频谱）的单粒子密度矩阵（OPDM）在个人的多体本征态。作为主要结果，我们发现自然轨道在MBL相中是定域的，但在遍历相中是离域的。这些单粒子态的这种质的变化是一种多体效应，因为没有相互作用，单粒子能量本征态都是局域的。在各态历经阶段的占领频谱是热的本征态热化假设的协议，而在MBL阶段的职业保持在紧急费米边缘的不连续性。这表明MBL本征态是弱修饰的斯莱特行列式，以潜在的安德森问题的本征态作为参考态。我们讨论了自然轨道的统计特性和占领频谱在这两个阶段，并作为过渡接近。我们的结果是一致的紧急可积性和本地化的运动积分，或准粒子，在MBL阶段的现有图片。我们强调密切类比的MBL相的零温度费米液体：在所研究的模型中，MBL相是dielectically连接到安德森绝缘体和占领频谱的不连续性直接表明存在准粒子定位在真实的空间。最后，我们表明，同样的图片出现在实验相关的双色晶格的存在下，相互作用的费米子，从而证明我们的研究结果并不限于一个特定的模型。
We study interacting fermions in one dimension subject to random, uncorrelated onsite disorder, a paradigmatic model of many-body localization (MBL). This model realizes an interaction-driven quantum phase transition between an ergodic and a many-body localized phase, with the transition occurring in the many-body eigenstates. We propose a single-particle framework to characterize these phases by the eigenstates (the natural orbitals) and the eigenvalues (the occupation spectrum) of the one-particle density matrix (OPDM) in individual many-body eigenstates. As a main result, we find that the natural orbitals are localized in the MBL phase, but delocalized in the ergodic phase. This qualitative change in these single-particle states is a many-body effect, since without interactions the single-particle energy eigenstates are all localized. The occupation spectrum in the ergodic phase is thermal in agreement with the eigenstate thermalization hypothesis, while in the MBL phase the occupations preserve a discontinuity at an emergent Fermi edge. This suggests that the MBL eigenstates are weakly dressed Slater determinants, with the eigenstates of the underlying Anderson problem as reference states. We discuss the statistical properties of the natural orbitals and of the occupation spectrum in the two phases and as the transition is approached. Our results are consistent with the existing picture of emergent integrability and localized integrals of motion, or quasiparticles, in the MBL phase. We emphasize the close analogy of the MBL phase to a zero-temperature Fermi liquid: in the studied model, the MBL phase is adiabatically connected to the Anderson insulator and the occupation-spectrum discontinuity directly indicates the presence of quasiparticles localized in real space. Finally, we show that the same picture emerges for interacting fermions in the presence of an experimentally-relevant bichromatic lattice and thereby demonstrate that our findings are not limited to a specific model.