Observing Quasiparticles through the Entanglement Lens

You, Yizhi; Wybo, Elisabeth; Pollmann, Frank; Sondhi, S. L.

doi:10.48550/arxiv.2007.04318

Cited by 4 publications

(7 citation statements)

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“…Most of the early studies of the entanglement entropy and Rényi entropy were focused on the ground state, for the single-interval cases see and for multi-interval cases see . One can also find various studies of the excited state entanglement entropy and Rényi entropy in [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66].…”

Section: Introductionmentioning

confidence: 99%

Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains

Zhang,

Rajabpour

2020

Preprint

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We investigate the quasiparticle excited state Rényi entropy of single, double and more intervals in the fermionic chain, bosonic chain and XY chain. When the gap of the model is large or all the momenta of the quasiparticles are large, the Rényi Entropy is expected to take a super universal form, which is independent of, among others, the model, the quasiparticle momenta, and the subsystem connectedness. We calculate analytically the Rényi Entropy in the extremely gapped limit by writing the excited states in terms of the local excitations and find different additional contributions to the super universal Rényi entropy in various models. The additional contributions to the super universal Rényi entropy cannot be neglected when the momentum differences of the excited quasiparticles are small, however, they are negligible when all the momentum differences are large. The Rényi entropy with additional terms derived in the extremely gapped limit is universal in the sense that it is valid in the slightly gapped and critical models as long as all the momenta of the excited quasiparticles are large. In the case of double interval in XY chain we show analytically that the known super universal term fails completely to describe even the large momentum difference limit. We find new exact super universal term for the double interval XY chain as well as the universal results. In the case of the bosonic chain in the extremely massive limit we find analytically a novel formula, written as a permanent of a certain matrix, for the Rényi entropy. We support all of our analytical results with numerical calculations.

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Section: Introductionmentioning

confidence: 99%

Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains

Zhang,

Rajabpour

2020

Preprint

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“…As is pointed out in Ref. [35], this exact degeneracy of the Schmidt values arises from a combination of the reflection symmetry Assume that the entanglement spectrum contains a non-degenerate eigenvalue λ γ . Then the fact that the state |ψ 1M is symmetric under R whence |γ A = R|γ B up to a U (1) phase.…”

Section: A Z2 and Reflectionmentioning

confidence: 84%

“…In this section, we develop a universal criterion for the degeneracy of the QP ES based on a Kramers theorem. The basic idea can be traced back to our previous work [35] where we examined the symmetry representation of the QP reduced density matrix. For instance, if the reduced density matrix has a projective representation under a symmetry G, the entanglement spectrum must display a degeneracy for all energy levels.…”

Section: Kramers Theorem For Qp Entanglement Hamiltonianmentioning

confidence: 99%

“…To set the stage, we reiterate the QP ES degeneracy theorem in the 1D Ising paramagnetic phase of Ref. [35]. We define the model with an integrability-breaking term…”

Section: A Z2 and Reflectionmentioning

confidence: 99%

“…In our previous work [35], we scrutinized the QP entanglement in a 1D transverse-field Ising model with an integrability breaking perturbation. We demonstrated that the non-local QP states in the symmetry broken phase carry an additional 'universal entanglement entropy' solely determined by the underlying broken symmetry.…”

Section: Introductionmentioning

confidence: 99%

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Visualizing Quasiparticles from Quantum Entanglement for general 1D phases

Wybo,

Pollmann,

Sondhi

et al. 2020

Preprint

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In this work, we present a quantum information framework for the entanglement behavior of the low energy quasiparticle (QP) excitations in various quantum phases in one-dimensional (1D) systems. We first establish an exact correspondence between the correlation matrix and the QP entanglement Hamiltonian for free fermions and find an extended in-gap state in the QP entanglement Hamiltonian as a consequence of the position uncertainty of the QP. A more general understanding of such an in-gap state can be extended to a Kramers theorem for the QP entanglement Hamiltonian, which also applies to strongly interacting systems. Further, we present a set of ubiquitous entanglement spectrum features, dubbed entanglement fragmentation, conditional mutual information, and measurement induced non-local entanglement for QPs in 1D symmetry protected topological phases. Our result thus provides a new framework to identify different phases of matter in terms of their QP entanglement.

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Entanglement spreading after local and extended excitations in a free-fermion chain

Eisler

2021

J. Phys. A: Math. Theor.

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We study the time evolution of entanglement created by local or extended excitations upon the ground state of a free-fermion chain. A single particle or hole excitation produces a single bit of excess entropy for large times and subsystem lengths. In case of a double hole, some of the coherence between the excitations is preserved and the excess entropy becomes additive only for large hole separations. In contrast, the coherence is always lost for particle–hole excitations. Multiple hole excitations on a completely filled chain are also investigated. We find that for an extended contiguous hole the excess entropy scales logarithmically with the size, whereas the increase is linear for finite separations between the holes.

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Observing Quasiparticles through the Entanglement Lens

Cited by 4 publications

References 0 publications

Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains

Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains

Visualizing Quasiparticles from Quantum Entanglement for general 1D phases

Entanglement spreading after local and extended excitations in a free-fermion chain

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