Gapped Quantum Systems and Entanglement Area Law

Zeng, Bei; Xie, Changsheng; Zhou, D. L.; Wen, Xiao-Gang

doi:10.1007/978-1-4939-9084-9_5

Cited by 20 publications

(31 citation statements)

References 30 publications

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“…For the systems considered, quantum fluctuations can be understood in terms of fluctuations of the local occupation number. Quantum fluctuations specific to a certain many-body system collectively determine the macroscopic behavior of the system as described by its quantum order or, equivalently, its entanglement 21 – 24 . We believe the proposed interpretation may provide a new scenario for the characterization of certain aspects of ground-state entanglement of hardcore lattice bosons and may also inspire how to think of many-body entanglement for a broader class of models 25 .…”

Section: Conclusive Remarksmentioning

confidence: 99%

Braiding properties of worldline configurations in hardcore lattice bosons

Lingua

Wang

Shpani

et al. 2022

Sci Rep

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In this manuscript, we study braiding properties of worldline configurations for a variety of ground-states of hardcore Bose–Hubbard models in two dimensions. Configurations are collections of particle paths and result from the path-integral formulation of statistical mechanics. For hard-core bosons, configurations can be seen as geometric braids and therefore can be assigned a certain topological structure, i.e. a way to classify braiding events among worldlines. By means of Monte Carlo calculations, we study superfluid phase and a variety of insulating phases and observe that ground-states of different quantum phases correspond to different probability distributions of braiding properties.

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Section: Conclusive Remarksmentioning

confidence: 99%

Braiding properties of worldline configurations in hardcore lattice bosons

Lingua

Wang

Shpani

et al. 2022

Sci Rep

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“…In addition to the mechanisms of 'order from order' [115] and quantum amplification [118][119][120], currently, quantum informational approaches [125,126] are routinely invoked to understand, e.g., condensed matter [156] systems. However, we believe that the idea of considering a biological systems akin to a quantum computing machine is somewhat controversial.…”

Section: Ficationmentioning

confidence: 99%

A Quantum-Classical Model of Brain Dynamics

Sergi¹,

Messina²,

Vicario³

et al. 2023

Preprint

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The study of the human psyche has elucidated a bipartite structure of logic reflecting the quantum--classical nature of the world. Accordingly, we posited an approach toward studying the brain by means of the quantum--classical dynamics of a mixed Weyl symbol. The mixed Weyl symbol can be used to describe brain processes at the microscopic level and, when averaged over an appropriate ensemble, can provide a link to the results of measurements made at the meso and macro scale. Within this approach, quantum variables (such as, for example, nuclear and electron spins, dipole momenta of particles or molecules, tunneling degrees of freedom, and so on) can be represented by spinors, whereas the electromagnetic fields and phonon modes can be treated either classically or semi-classically in phase space by also considering quantum zero-point fluctuations. Quantum zero-point effects can be incorporated into numerical simulations by controlling the temperature of each field mode via coupling to a dedicated Nos\'e-Hoover chain thermostat. The temperature of each thermostat was chosen in order to reproduce quantum statistics in the canonical ensemble. In this first paper, we introduce a general quantum--classical Hamiltonian model that can be tailored to study physical processes at the interface between the quantum and the classical world in the brain. While the approach is discussed in detail, numerical calculations are not reported in the present paper, but they are planned for future work. Our theory of brain dynamics subsumes some compatible aspects of three well-known quantum approaches to brain dynamics, namely the electromagnetic field theory approach, the orchestrated objective reduction theory, and the dissipative quantum model of the brain. All three models are reviewed.

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“…In the context of quantum computers, with long-range entanglement the time taken for disentanglement depends on the size of the system, whereas for short-range entanglement it is size independent. More formal definition in terms of unitary evolution and Hilbert space constructions is given in [96,97].…”

Section: Emergent Gauge Symmetries In Quantum Condensed Matter Systemsmentioning

confidence: 99%

“…In condensed matter physics in 2+1 dimensions string-nets may be important for understanding quantum spin liquids. The mineral Herbertsmithite with Kagome lattice structure was discovered to exhibit properties of a quantum spin liquid [101] (whether gapped or gapless) with possible string-net like structure; for recent discussion see [97].…”

Section: Emergent Gauge Symmetries In Quantum Condensed Matter Systemsmentioning

confidence: 99%

Emergent gauge symmetries: making symmetry as well as breaking it

Bass

2021

Phil. Trans. R. Soc. A.

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Gauge symmetries play an essential role in determining the interactions of particle physics. Where do they come from? Might the gauge symmetries of the Standard Model unify in the ultraviolet or might they be emergent in the infrared, below some large scale close to the Planck scale? Emergent gauge symmetries are important in quantum many-body systems in quantum phases associated with long range entanglement and topological order, e.g. they arise in high temperature superconductors, with string-net condensation and in the A-phase of superfluid 3 He. String-nets and superfluid 3 He exhibit emergent properties similar to the building blocks of particle physics. Emergent gauge symmetries also play an important role in simulations of quantum field theories. This article discusses recent thinking on possible emergent gauge symmetries in particle physics, commenting also on Higgs phenomena and the vacuum energy or cosmological constant puzzle in emergent gauge systems. This article is part of the theme issue ‘Quantum technologies in particle physics’.

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Gapped Quantum Systems and Entanglement Area Law

Cited by 20 publications

References 30 publications

Braiding properties of worldline configurations in hardcore lattice bosons

Braiding properties of worldline configurations in hardcore lattice bosons

A Quantum-Classical Model of Brain Dynamics

Emergent gauge symmetries: making symmetry as well as breaking it

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