Duality and topology

Sacramento, P. D.; Vieira, V. R.

doi:10.1016/j.aop.2018.02.017

Cited by 4 publications

(4 citation statements)

References 73 publications

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“…where q(k) = −2J cos k − µ + 2i∆ sin k. The winding number can be calculated using the definition [47] w…”

Section: Mathematically For Our Model Hamiltonian Berry Connection Is...mentioning

confidence: 99%

“…Topological properties can also be determined by the complex analysis of the parameter space [25,26]. Topological phase transition points are considered as the singularity points in the parameter space.…”

mentioning

confidence: 99%

“…Complex analysis is a effective way to describe the state of a system. Depending on the on the position of poles and zeroes, topological state of the system is determined [26,42].…”

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confidence: 99%

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A Study of Berry Connection and Complex Analysis for Topological Characterization

Kartik,

et al. 2019

Preprint

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We study and present the results of Berry connection for the topological states in quantum matter. The Berry connection plays a central role in the geometric phase and topological phenomenon in quantum many-body system. We present the necessary and sufficient conditions to characterize the topological nature of the system through the complex analysis. We also present the different topological aspects of the system in the momentum space.

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“…where q(k) = −2J cos k − µ + 2i∆ sin k. The winding number can be calculated using the definition [47] w…”

Section: Mathematically For Our Model Hamiltonian Berry Connection Is...mentioning

confidence: 99%

mentioning

confidence: 99%

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A Study of Berry Connection and Complex Analysis for Topological Characterization

Kartik,

et al. 2019

Preprint

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“…Multiple quenches have been studied in only several works [100,101,112]. In [100] it has been shown that for quenches of a type A→B→A, where A and B label different equilibrium phases, that DQPTs is by no means inevitable and can be tuned away by choosing the second quench time T appropriately.…”

Section: Introductionmentioning

confidence: 99%

Dynamical quantum phase transitions following double quenches: persistence of the initial state vs dynamical phases

Cheraghi,

Sedlmayr

2023

New J. Phys.

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Dynamical quantum phase transitions can occur following quenches in quantum systems when the rate function, a dynamical analogue of the free energy, becomes non-analytic at critical times. Here we exhaustively investigate in an exemplary model how the dynamically evolving state responds to a second quench. We demonstrate that for quenches where the initial and final Hamiltonian belong to different phases always result in dynamical quantum phase transitions, irrespective of the intermediate quench and dynamics or the time of the second quench. However, if the initial and final Hamiltonian belong to the same equilibrium phase then the intermediate Hamiltonian must belong to a different phase. In this case, the second quench time in relation to the critical times of the first quench becomes crucial to the existence of dynamical quantum phase transitions.

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Vanishing k-space fidelity and phase diagram’s bulk–edge–bulk correspondence

2019

Self Cite

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The fidelity between two infinitesimally close states or the fidelity susceptibility of a system are known to detect quantum phase transitions. Here we show that the k-space fidelity between two states far from each other and taken deep inside (bulk) of two phases, generically vanishes at the k-points where there are gapless points in the energy spectrum that give origin to the lines (edges) separating the phases in the phase diagram. We consider a general case of two-band models and present a sufficient condition for the existence of gapless points, given there are pairs of parameter points for which the fidelity between the corresponding states is zero. By presenting an explicit counter-example, we showed that the sufficient condition is not necessary. Further, we showed that, unless the set of parameter points is suitably constrained, the existence of gapless points generically imply the accompanied pairs of parameter points with vanishing fidelity. Also, we showed the connection between the vanishing fidelity and gapless points on a number of concrete examples (topological triplet superconductor, topological insulator, 1d Kitaev model of spinless fermions, BCS superconductor, Ising model in a transverse field, graphene and Haldane Chern insulator), as well as for the more general case of Dirac-like Hamiltonians. We also briefly discuss the relation between the vanishing fidelity and gapless points at finite temperatures.

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Duality and topology

Cited by 4 publications

References 73 publications

A Study of Berry Connection and Complex Analysis for Topological Characterization

A Study of Berry Connection and Complex Analysis for Topological Characterization

Dynamical quantum phase transitions following double quenches: persistence of the initial state vs dynamical phases

Vanishing k-space fidelity and phase diagram’s bulk–edge–bulk correspondence

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