Dynamical quantum phase transitions in extended transverse Ising models

Bhattacharjee, Sourav; Dutta, Amit

doi:10.1103/physrevb.97.134306

Cited by 51 publications

(27 citation statements)

References 110 publications

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“…We also note in passing that for h 0 = 0, the Floquet Hamiltonian in Eq. ( 15) becomes similar to the extended Ising Hamiltonian which is reducible to spinless free fermionic system and thereby integrable [28][29][30].…”

Section: Periodic Driving With Transverse-field Ising Hamiltonian And...mentioning

confidence: 97%

Periodically driven many-body quantum battery

Mondal,

Bhattacharjee

2021

Preprint

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We explore the charging of a quantum battery based on spin systems through periodic modulation of a transverse-field like Ising Hamiltonian. In the integrable limit, we find that resonance tunnelling can lead to a higher transfer of energy to the battery at specific drive frequencies. When the integrability is broken in the presence of an additional longitudinal field, we find that the effective Floquet Hamiltonian contains terms which may lead to a global charging of the battery. However, we do not find any quantum advantage in the charging power, thus demonstrating that global charging is only a necessary and not sufficient condition for achieving quantum advantage.

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Section: Periodic Driving With Transverse-field Ising Hamiltonian And...mentioning

confidence: 97%

Periodically driven many-body quantum battery

Mondal,

Bhattacharjee

2021

Preprint

Self Cite

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“…Ising model is initially proposed to explain the phase transitions of magnetic materials, then it is largely expanded and becomes a useful method to explore criticality phenomena of multiple systems, such as the continuous quantum phase transitions [74], currency stability [75], and criticality of dynamics [76]. In this work, we expand Ising models in terms of two aspects: (a) we expand the application fields.…”

Section: Features Of Our Expanded Modelmentioning

confidence: 99%

Big data-drive agent-based modeling of online polarized opinions

Lü

Zhang

2021

Complex Intell. Syst.

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Under the mobile internet and big data era, more and more people are discussing and interacting online with each other. The forming process and evolutionary dynamics of public opinions online have been heavily investigated. Using agent-based modeling, we expand the Ising model to explore how individuals behave and the evolutionary mechanism of the life cycles. The big data platform of Douban.com is selected as the data source, and the online case “NeiYuanWaiFang” is applied as the real target, for our modeling and simulations to match. We run 10,000 simulations to find possible optimal solutions, and we run 10,000 times again to check the robustness and adaptability. The optimal solution simulations can reflect the whole life cycle process. In terms of different levels and indicators, the fitting or matching degrees achieve the highest levels. At the micro-level, the distributions of individual behaviors under real case and simulations are similar to each other, and they all follow normal distributions; at the middle-level, both discrete and continuous distributions of supportive and oppositive online comments are matched between real case and simulations; at the macro-level, the life cycle process (outbreak, rising, peak, and vanish) and durations can be well matched. Therefore, our model has properly seized the core mechanism of individual behaviors, and precisely simulated the evolutionary dynamics of online cases in reality.

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“…An analysis of these shapes and their topological properties can be found in [35]. These shapes are widely used in the study of extended TFIM, see, for example, [36].…”

Section: The Anisotropic Transverse-field Ising Modelmentioning

confidence: 99%

Hidden symmetries, the Bianchi classification and geodesics of the quantum geometric ground-state manifolds

Liska

Gritsev

2021

SciPost Phys.

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We study the Killing vectors of the quantum ground-state manifold of a parameter-dependent Hamiltonian. We find that the manifold may have symmetries that are not visible at the level of the Hamiltonian and that different quantum phases of matter exhibit different symmetries. We propose a Bianchi-based classification of the various ground-state manifolds using the Lie algebra of the Killing vector fields. Moreover, we explain how to exploit these symmetries to find geodesics and explore their behaviour when crossing critical lines. We briefly discuss the relation between geodesics, energy fluctuations and adiabatic preparation protocols. Our primary example is the anisotropic transverse-field Ising model. We also analyze the Ising limit and find analytic solutions to the geodesic equations for both cases.

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Dynamical quantum phase transitions in extended transverse Ising models

Cited by 51 publications

References 110 publications

Periodically driven many-body quantum battery

Periodically driven many-body quantum battery

Big data-drive agent-based modeling of online polarized opinions

Hidden symmetries, the Bianchi classification and geodesics of the quantum geometric ground-state manifolds

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