Evidence for Unbounded Growth of the Number Entropy in Many-Body Localized Phases

Kiefer-Emmanouilidis, Maximilian; Unanyan, R. G.; Fleischhauer, Michael; Sirker, Jesko

doi:10.1103/physrevlett.124.243601

Cited by 175 publications

(144 citation statements)

References 41 publications

Supporting

Mentioning

135

Contrasting

Order By: Relevance

“…Even for the very large number of disorder realizations used in this work, we did not observe realizations with number entropies which exceed this limit, which leads us to conclude that there is no particle transport for sufficiently strong disorder, and the observed growth of the number entropy in time in Ref. [30] is pertinent to the critical regime and likely disappears for stronger disorder or larger system sizes. This article is an open data publication and the raw data is available as a standard HDF5 file [44].…”

Section: Fig 3 Distribution Of the Time-averaged Entanglement Entromentioning

confidence: 60%

“…Within the l-bit model the production of entanglement deep in the MBL phase does not rely on particle transport, since due to the emergent conservation laws the particle number in any part of the system is essentially constant for all times [29]. This view was challenged very recently in a study of the entropy of the subsystem particle number distribution [30], where a long growth regime of the number entropy was observed, which was argued to continue indefinitely in the thermodynamic limit in the MBL phase, suggesting that there is very slow transport in the MBL phase.…”

mentioning

confidence: 99%

“…In the context of MBL it is useful to split the contributions to entanglement from particle number fluctuations and the configurations of the particles, by introducing the configurational entropy S C , which is the difference S E − S N [30,38]. The wave function |ψ (t ) of the system evolves according to…”

mentioning

confidence: 99%

See 2 more Smart Citations

Absence of slow particle transport in the many-body localized phase

Luitz

Lev

2020

Phys. Rev. B

View full text Add to dashboard Cite

We analyze the saturation value of the bipartite entanglement and number entropy starting from a random product state deep in the many-body localized (MBL) phase. By studying the probability distributions of these entropies we find that the growth of the saturation value of the entanglement entropy stems from a significant reshuffling of the weight in the probability distributions from the bulk to the exponential tails. In contrast, the probability distributions of the saturation value of the number entropy are converged with system size, and exhibit a sharp cutoff for values of the number entropy which correspond to one particle fluctuating across the boundary between the two halves of the system. Our results therefore rule out slow particle transport deep in the MBL phase and confirm that the slow entanglement entropy production stems uniquely from configurational entanglement.

show abstract

Section: Fig 3 Distribution Of the Time-averaged Entanglement Entromentioning

confidence: 60%

mentioning

confidence: 99%

See 1 more Smart Citation

Absence of slow particle transport in the many-body localized phase

Luitz

Lev

2020

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…It is then easy to show that 12) from which it follows that (2.13) and hence the only independent quantity is F T |1,1 min (ϑ, n). We can use eq.…”

Section: Jhep11(2020)131mentioning

confidence: 97%

Symmetry resolved entanglement in integrable field theories via form factor bootstrap

Horváth

Calabrese

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

We consider the form factor bootstrap approach of integrable field theories to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The bootstrap equations are determined in an intuitive way and their solution is presented for the massive Ising field theory and for the genuinely interacting sinh-Gordon model, both possessing a ℤ2 symmetry. The solutions are carefully cross-checked by performing various limits and by the application of the ∆-theorem. The issue of symmetry resolution for discrete symmetries is also discussed. We show that entanglement equipartition is generically expected and we identify the first subleading term (in the UV cutoff) breaking it. We also present the complete computation of the symmetry resolved von Neumann entropy for an interval in the ground state of the paramagnetic phase of the Ising model. In particular, we compute the universal functions entering in the charged and symmetry resolved entanglement.

show abstract

“…The configurational entropy is also related to the operationally accessible entanglement entropy of refs. [27][28][29], while the number entropy is the subject of a substantial recent activity [12,17,[30][31][32]. The calculation of the symmetry resolved entropies by the definition (2.2) requires the knowledge of the entanglement JHEP08(2020)073 spectrum of ρ A and its resolution in the charge sectors.…”

Section: Symmetry Resolved Entanglementmentioning

confidence: 99%

Entanglement and symmetry resolution in two dimensional free quantum field theories

Murciano

Giulio

Calabrese

2020

J. High Energ. Phys.

115

127

View full text Add to dashboard Cite

We present a thorough analysis of the entanglement entropies related to different symmetry sectors of free quantum field theories (QFT) with an internal U(1) symmetry. We provide explicit analytic computations for the charged moments of Dirac and complex scalar fields in two spacetime dimensions, both in the massive and massless cases, using two different approaches. The first one is based on the replica trick, the computation of the partition function on Riemann surfaces with the insertion of a flux α, and the introduction of properly modified twist fields, whose two-point function directly gives the scaling limit of the charged moments. With the second method, the diagonalisation in replica space maps the problem to the computation of a partition function on a cut plane, that can be written exactly in terms of the solutions of non-linear differential equations of the Painlevé V type. Within this approach, we also derive an asymptotic expansion for the short and long distance behaviour of the charged moments. Finally, the Fourier transform provides the desired symmetry resolved entropies: at the leading order, they satisfy entanglement equipartition and we identify the subleading terms that break it. Our analytical findings are tested against exact numerical calculations in lattice models.

show abstract

Evidence for Unbounded Growth of the Number Entropy in Many-Body Localized Phases

Cited by 175 publications

References 41 publications

Absence of slow particle transport in the many-body localized phase

Absence of slow particle transport in the many-body localized phase

Symmetry resolved entanglement in integrable field theories via form factor bootstrap

Entanglement and symmetry resolution in two dimensional free quantum field theories

Contact Info

Product

Resources

About