Entanglement entropy after selective measurements in quantum chains

Najafi, Khadijeh; Rajabpour, M. A.

doi:10.1007/jhep12(2016)124

Cited by 13 publications

(15 citation statements)

References 108 publications

(204 reference statements)

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“…We note that some of these results can also be extended to the post-measurement case, as has been show in Ref. [30].…”

Section: Entanglement Hamiltonian At Finite Temperaturesupporting

confidence: 63%

“…Inserting (26), the resulting double infinite sum (30) can be carried out exactly and delivers v F (x) = 2π x ( − x)/ , which is identical to the weight function in the CFT result (9). Hence, the function multiplying the energy density in the continuum treatment has now the interpretation of a local Fermi velocity (instead of a local inverse temperature) that follows from the lattice EH via (30). Remarkably, this relation can be generalized to arbitrary fillings and one obtains the exact same analytical result for v F (x) [88].…”

Section: Continuum Limitmentioning

confidence: 93%

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Entanglement Hamiltonians: from field theory, to lattice models and experiments

Dalmonte,

Eisler,

Falconi

et al. 2022

Preprint

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“…We note that some of these results can also be extended to the post-measurement case, as has been show in Ref. [30].…”

Section: Entanglement Hamiltonian At Finite Temperaturesupporting

confidence: 63%

Section: Continuum Limitmentioning

confidence: 93%

Entanglement Hamiltonians: from field theory, to lattice models and experiments

Dalmonte,

Eisler,

Falconi

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…where H(x) is the Hamiltonian density of the theory, and the speed of light has been set to unit. For a 2D CFT, the BW theorem can be extended to other geometries [25][26][27][28][29][30][31][32][33][34]. For a finite interval A = [0, ] on an infinite line in the ground state, the modular Hamiltonian is [26,29]…”

Section: The XX Spin-chainmentioning

confidence: 99%

“…In order to overcome this challenge, it was proposed in Refs. [23,24] to use the Bisognano-Wichmann (BW) theorem in quantum field theory [13,14] and its extension in conformal field theory (CFT) [25][26][27][28][29][30][31][32][33][34] to write approximate modular Hamiltonians for lattice models. From the BW modular Hamiltonian one can construct a RDM, which has been dubbed BW RDM.…”

Section: Introductionmentioning

confidence: 99%

Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

et al. 2020

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We carry out a comprehensive comparison between the exact modular Hamiltonian and the lattice version of the Bisognano-Wichmann (BW) one in one-dimensional critical quantum spin chains. As a warm-up, we first illustrate how the trace distance provides a more informative mean of comparison between reduced density matrices when compared to any other Schatten nn-distance, normalized or not. In particular, as noticed in earlier works, it provides a way to bound other correlation functions in a precise manner, i.e., providing both lower and upper bounds. Additionally, we show that two close reduced density matrices, i.e. with zero trace distance for large sizes, can have very different modular Hamiltonians. This means that, in terms of describing how two states are close to each other, it is more informative to compare their reduced density matrices rather than the corresponding modular Hamiltonians. After setting this framework, we consider the ground states for infinite and periodic XX spin chain and critical Ising chain. We provide robust numerical evidence that the trace distance between the lattice BW reduced density matrix and the exact one goes to zero as \ell^{-2}ℓ−2 for large length of the interval \ellℓ. This provides strong constraints on the difference between the corresponding entanglement entropies and correlation functions. Our results indicate that discretized BW reduced density matrices reproduce exact entanglement entropies and correlation functions of local operators in the limit of large subsystem sizes. Finally, we show that the BW reduced density matrices fall short of reproducing the exact behavior of the logarithmic emptiness formation probability in the ground state of the XX spin chain.

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“…14 is that for a system with its bulk at the critical point one can define a BE which decreases under boundary renormalization group and at the boundary fixed point is equal to a number which is related to the universality class of the corresponding boundary condition. This BE in the context of the entanglement entropy has been studied in CFT [15][16][17] , quantum spin chains [5][6][7][8]11,12,16,18,19 and integrable models 9 . In particular, using DMRG technique the authors of Ref.…”

Section: Introductionmentioning

confidence: 99%

Entanglement and boundary entropy in quantum spin chains with arbitrary direction of the boundary magnetic fields

Xavier,

Rajabpour

2020

Preprint

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We calculate the entanglement and the universal boundary entropy (BE) in the critical quantum spin chains, such as the transverse field Ising chain and the XXZ chain, with arbitrary direction of the boundary magnetic field (ADBMF). We determine the boundary universality class that an ADBMF induces. In particular, we show that the induced boundary conformal field theory (BCFT) depends on the point on the Bloch sphere where the boundary magnetic field directs. We show that the classification of the directions boils down to this simple fact that the boundary field breaks the bulk symmetry or not. We present a procedure to estimate the universal BE, based on the finitesize corrections of the entanglement entropy, that apply to ADBMF. To calculate the universal BE in the XXZ chain, we use density matrix renormalization group (DMRG). The transverse field XY chain with ADBMF after Jordan-Wigner (JW) transformation is not a quadratic free fermion Hamiltonian. We are able to map this model to a quadratic free fermion chain by introducing two extra ancillary spins coupled to the main chain at the boundaries, which makes the problem integrable. The eigenstates of the transverse field XY chain can be obtained by a proper projection in the enlarged chain. Using this mapping, we are able to calculate the entanglement entropy of the transverse field XY chain using the usual correlation matrix technique up to relatively large sizes.

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Entanglement entropy after selective measurements in quantum chains

Cited by 13 publications

References 108 publications

Entanglement Hamiltonians: from field theory, to lattice models and experiments

Entanglement Hamiltonians: from field theory, to lattice models and experiments

Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

Entanglement and boundary entropy in quantum spin chains with arbitrary direction of the boundary magnetic fields

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