Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems

Leiman, Shaul; Eisenbach, Ariel; Berkovits, Richard

doi:10.1209/0295-5075/112/46003

Cited by 9 publications

(11 citation statements)

References 63 publications

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“…In the future, it would be interesting to see how our results extend to interacting systems [38,39,[62][63][64][65][66] (where the density matrix renormalization group [67,68] and related methods give direct access to the many-body density matrix and its spectrum), as well as to systems in higher dimensions [69,70].…”

Section: Discussionmentioning

confidence: 92%

Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain

Levy

Goldstein

2019

Universe

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In recent years, tools from quantum information theory have become indispensable in characterizing many-body systems. In this work, we employ measures of entanglement to study the interplay between disorder and the topological phase in 1D systems of the Kitaev type, which can host Majorana end modes at their edges. We find that the entanglement entropy may actually increase as a result of disorder, and identify the origin of this behavior in the appearance of an infinite-disorder critical point. We also employ the entanglement spectrum to accurately determine the phase diagram of the system, and find that disorder may enhance the topological phase, and lead to the appearance of Majorana zero modes in systems whose clean version is trivial.Entanglement is the quintessential characteristic of the quantum world. Recently, much attention has been devoted to manifestations of entanglement in quantum many-body systems [1,2]. Motivations include the prospect of using many-body ground and excited states as a resource for quantum communication and computation; the amount of entanglement controls the applicability of a powerful tensor-network-based numerical method; entanglement is an indicator of quantum correlations which is independent of the details of the system, allowing, in particular, one to identify quantum phase transitions even without knowing the relevant order parameter. In this work, we will concentrate on the latter property, in the context of disordered 1D quantum many-body systems.Majorana zero modes [3][4][5][6] and their more complicated relatives [7] have been studied extensively recently, both due to their predicted exotic non-abelian braiding statistics, which gives rise to the prospect of topologically-protected quantum computation [8], and to many concrete proposals for their realization in the laboratory. Leading candidates are semiconductor quantum wires with strong spin orbit interaction, which are rendered effectively spinless by the application of an appropriate magnetic field and gate voltage, and driven into a topological phase by proximity-coupling to a superconductor, leading to the formation of Majorana end modes [9,10]. Indications for these modes have recently been measured experimentally [11][12][13][14][15]. These Majorana zero modes show up not only in the presence of a real edge, but also in the entanglement spectrum, that is, in the spectrum of the reduced density matrix of a subsystem [16].Disorder naturally occurs in all these systems, and may hamper their topological characteristics, especially the Majorana edge modes of 1D systems . In this work, we will study the interplay of disorder and the topological phase from the entanglement point of view. After introducing the model and our method for calculating the entanglement spectrum and entropy in Section 2, we will

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Section: Discussionmentioning

confidence: 92%

Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain

Levy

Goldstein

2019

Universe

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“…For non‐interacting many‐particle systems the level spacing MBE distribution is expected to follow the Poisson distribution for excitation energies above the second spacing, without depending on the single‐level distribution . It turns out that this statement is oversimplified and as result of a shell structure a non‐universal spacing structure remains in the MBE even for higher excitations . Once repulsive interactions between the particles are considered, a transition to the Wigner distribution for higher excitations is observed , as well as the suppression of the shell structure .…”

Section: Introductionmentioning

confidence: 99%

“…Thus there is a connection between the ES and the many‐body excitation spectrum. Following their work, several authors studied the correspondence between low‐energy ES statistical properties and the true many‐body excitations (MBE) of the partitioned segment (region A) demonstrating a similarity in the statistical behavior of the MBE and ES for disordered systems.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, earlier studies have looked for a signature of the MBL transition in the MBE spectrum , but have been limited by the small system sizes for which the MBE spectrum can be calculated. Here we shall replace the MBE spectrum by the ES, and rely on Haldane's conjecture and on previous studies on the similarity between the statistical properties between low‐energy ES distribution and the true many‐body excitations (MBE) , to investigate the MBL transition. Using the ES has the advantage of enabling the calculation for much larger systems sizes.…”

Section: Introductionmentioning

confidence: 99%

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Signature of non‐ergodicity in low‐lying excitations of disordered many‐particle systems

Berkovits

2017

Annalen der Physik

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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 manybody 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.

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“…In this context, the central spirit lies in the so-called bulk-edge correspondence of the ES [12,13], a manifestation of the holographic principle [3,5,11]. Moreover, the importance of the ES has been discussed in the context of tensor networks [11,15], quantum criticality [16], symmetrybreaking phases [11,17,18], and, most recently, manybody localization [19][20][21] and eigenstate thermalization [22]. At the same time, it has been pointed out in the literature [23] that the ES can contain nonuniversal features requiring caution in using it as a tool to locate phase * hannes.pichler@cfa.harvard.edu † gzhu123@umd.edu transitions, in particular, for symmetry-breaking phases.…”

Section: Introductionmentioning

confidence: 99%

Measurement Protocol for the Entanglement Spectrum of Cold Atoms

et al. 2016

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Entanglement, and, in particular, the entanglement spectrum, plays a major role in characterizing manybody quantum systems. While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to date because of the lack of an implementable measurement scheme. Here, we propose a measurement protocol to access the entanglement spectrum of many-body states in experiments with cold atoms in optical lattices. Our scheme effectively performs a Ramsey spectroscopy of the entanglement Hamiltonian and is based on the ability to produce several copies of the state under investigation, together with the possibility to perform a global swap gate between two copies conditioned on the state of an auxiliary qubit. We show how the required conditional swap gate can be implemented with cold atoms, either by using Rydberg interactions or coupling the atoms to a cavity mode. We illustrate these ideas on a simple (extended) Bose-Hubbard model where such a measurement protocol reveals topological features of the Haldane phase.

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Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems

Cited by 9 publications

References 63 publications

Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain

Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain

Signature of non‐ergodicity in low‐lying excitations of disordered many‐particle systems

Measurement Protocol for the Entanglement Spectrum of Cold Atoms

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