Quench dynamics and scaling laws in topological nodal loop semimetals

Sim, Karin; Читра, Р.; Molignini, Paolo

doi:10.1103/physrevb.106.224302

Cited by 14 publications

(4 citation statements)

References 53 publications

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“…DQPT displays a phase transition between dynamically emerging quantum phases, that takes place during the nonequilibrium coherent quantum time evolution under sudden/ramped quench or timeperiodic modulation of Hamiltonian [16,[85][86][87][88][89][90][91]. In addition, a dynamical topological order parameter (DTOP) has been proposed to capture DQPTs [92,93], analogous to order parameters at equilibrium quantum phase transition. DTOP reveals integer values as a function of time and its unit magnitude jumps, at the dynamical phase transition times, manifest the topological distinctive feature of DQPTs [94][95][96].…”

Section: Introductionmentioning

confidence: 99%

Scaling and universality at ramped quench dynamical quantum phase transitions

Zamani,

Naji,

Jafari

et al. 2024

J. Phys.: Condens. Matter

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The nonequilibrium dynamics of a periodically driven extended XY model, in the presence oflinear time dependent magnetic filed, is investigated using the notion of dynamical quantum phasetransitions (DQPTs). Along the similar lines to the equilibrium phase transition, the main purposeof this work is to search the fundamental concepts such as scaling and universality at the rampedquench DQPTs. We have shown that the critical points of the model, where the gap closing occurs,can be moved by tuning the driven frequency and consequently the presence/absence of DQPTscan be flexibly controlled by adjusting the driven frequency. We have uncovered that, for a rampacross the single quantum critical point, the critical mode at which DQPTs occur is classified intothree regions: the Kibble-Zurek (KZ) region, where the critical mode scales linearly with the squareroot of the sweep velocity, pre-saturated (PS) region, and the saturated (S) region where the criticalmode makes a plateau versus the sweep velocity. While for a ramp that crosses two critical points,the critical modes disclose just KZ and PS regions. On the basis of numerical simulations, we findthat the dynamical free energy scales linerly with time, as approaches to DQPT time, with theexponent ν = 1 ± 0.01 for all sweep velocities and driven frequencies.

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Section: Introductionmentioning

confidence: 99%

Scaling and universality at ramped quench dynamical quantum phase transitions

Zamani,

Naji,

Jafari

et al. 2024

J. Phys.: Condens. Matter

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show abstract

“…More contrasts between time-dependent and time-independent KZMs can be found in [10,12]. While there have been many theoretical [35][36][37][38][39][40][41][42][43][44] and experimental [45][46][47][48][49][50][51][52][53][54][55][56] studies on the time-dependent KZM, the time-independent KZM has been less explored and awaits more investigations.…”

Section: Introductionmentioning

confidence: 99%

Structure and scaling of Kitaev chain across a quantum critical point in real space

He,

Chien

2024

J. Phys.: Condens. Matter

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The spatial Kibble-Zurek mechanism (KZM) is applied to the Kitaev chain with inhomogeneous pairing interactions that vanish in half of the lattice and result in a quantum critical point separating the superfluid and normal-gas phases in real space. The weakly-interacting BCS theory predicts scaling behavior of the penetration of the pair wavefunction into the normal-gas region different from conventional power-law results due to the non-analytic dependence of the BCS order parameter on the interaction. The Bogoliubov-de Gennes (BdG) equation produces numerical results confirming the scaling behavior and hints complications in the strong-interaction regime. The limiting case of the step-function quench reveals the dominance of the BCS coherence length in absence of additional length scale. Furthermore, the energy spectrum and wavefunctions from the BdG equation show abundant in-gap states from the normal-gas region in addition to the topological edge states.

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“…The multicritical points which favor the transition are found to have quadratic dispersion. In general, they are the intersection points of the distinct criticalities and are studied in different contexts [41][42][43]. The scaling theory developed to identify the topological transition between gapped phases, are reframed to identify the topological transition between HS critical phases [26,40].…”

Section: Introductionmentioning

confidence: 99%

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

2023

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The interplay between topology and criticality has been a recent interest of study in condensed matter physics. A unique topological transition between certain critical phases has been observed as a consequence of the edge modes living at criticalities. In this work, we generalize this phenomenon by investigating possible transitions between critical phases which are non-high symmetry in nature. We find the triviality and non-triviality of these critical phases in terms of the decay length of the edge modes and also characterize them using the winding numbers. The distinct non-high symmetry critical phases are separated by multicritical points with linear dispersion at which the winding number exhibits the quantized jump, indicating a change in the topology (number of edge modes) at the critical phases. Moreover, we reframe the scaling theory based on the curvature function, i.e. curvature function renormalization group method to efficiently address the non-high symmetry criticalities and multicriticalities. Using this we identify the conventional topological transition between gapped phases through non-high symmetry critical points, and also the unique topological transition between critical phases through multicritical points. The renormalization group flow, critical exponents and correlation function of Wannier states enable the characterization of non-high symmetry criticalities along with multicriticalities.

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Quench dynamics and scaling laws in topological nodal loop semimetals

Cited by 14 publications

References 53 publications

Scaling and universality at ramped quench dynamical quantum phase transitions

Scaling and universality at ramped quench dynamical quantum phase transitions

Structure and scaling of Kitaev chain across a quantum critical point in real space

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

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