Stable computation of entanglement entropy for two-dimensional interacting fermion systems

Pan, Gaopei; Da Liao, Yuan; Jiang, Weilun; D'Emidio, Jonathan; Qi, Yang; Meng, Zi Yang

doi:10.1103/physrevb.108.l081123

Cited by 13 publications

(2 citation statements)

References 71 publications

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“…Early attempts [11,12] are often plagued by large fluctuations. Implementing replicas [13,[20][21][22]89] allows one to circumvent these issues but is then numerically demanding. The same holds for the entanglement spectra and Hamiltonian [14].…”

Section: Discussionmentioning

confidence: 99%

“…But the necessity of using replica renders the already difficult determinant QMC simulations (DQMC, usually the computational complexity scales as O(β N 3 ) with β = 1/T and N = L d for the d spatial dimension) even heavier, and such computational burden has hinged the usage and discussion of the scaling behavior of EE in the exploration of the highly entangled fermionic quantum matter. We note the recent progresses in this regard, with better data quality and the approximate O(β N 3 ) complexity [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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Many versus one: The disorder operator and entanglement entropy in fermionic quantum matter

Jiang,

Chen,

Liu

et al. 2023

SciPost Phys.

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Motivated by recent development of the concept of the disorder operator and its relation with entanglement entropy in bosonic systems, here we show the disorder operator successfully probes many aspects of quantum entanglement in fermionic many-body systems. From both analytical and numerical computations in free and interacting fermion systems in 1D and 2D, we find the disorder operator and the entanglement entropy exhibit similar universal scaling behavior, as a function of the boundary length of the subsystem, but with subtle yet important differences. In 1D they both follow the \log{L}logL scaling behavior with the coefficient determined by the Luttinger parameter for disorder operator, and the conformal central charge for entanglement entropy. In 2D they both show the universal L\log LLlogL scaling behavior in free and interacting Fermi liquid states, with the coefficients depending on the geometry of the Fermi surfaces. However at a 2D quantum critical point with non-Fermi-liquid state, extra symmetry information is needed in the design of the disorder operator, so as to reveal the critical fluctuations as does the entanglement entropy. Our results demonstrate the fermion disorder operator can be used to probe quantum many-body entanglement related to global symmetry, and provide new tools to explore the still largely unknown territory of highly entangled fermion quantum matter in 2 or higher dimensions.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Many versus one: The disorder operator and entanglement entropy in fermionic quantum matter

Jiang,

Chen,

Liu

et al. 2023

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

Duality transformations and the entanglement entropy of gauge theories

Bulgarelli,

Panero

2024

J. High Energ. Phys.

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The study of entanglement in gauge theories is expected to provide insights into many fundamental phenomena, including confinement. However, calculations of quantities related to entanglement in gauge theories are limited by ambiguities that stem from the non-factorizability of the Hilbert space. In this work we study lattice gauge theories that admit a dual description in terms of spin models, for which the replica trick and Rényi entropies are well defined. In the first part of this work, we explicitly perform the duality transformation in a replica geometry, deriving the structure of a replica space for a gauge theory. Then, in the second part, we calculate, by means of Monte Carlo simulations, the entropic c-function of the ℤ2 gauge theory in three spacetime dimensions, exploiting its dual description in terms of the three-dimensional Ising model.

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Incremental SWAP operator for entanglement entropy: Application for exponential observables in quantum Monte Carlo simulation

Zhou,

Meng,

et al. 2024

Phys. Rev. B

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Stable computation of entanglement entropy for two-dimensional interacting fermion systems

Cited by 13 publications

References 71 publications

Many versus one: The disorder operator and entanglement entropy in fermionic quantum matter

Many versus one: The disorder operator and entanglement entropy in fermionic quantum matter

Duality transformations and the entanglement entropy of gauge theories

Incremental SWAP operator for entanglement entropy: Application for exponential observables in quantum Monte Carlo simulation

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