Quantum renormalization group approach to geometric phases in spin chains

Jafari, R.

doi:10.1016/j.physleta.2013.10.034

Cited by 17 publications

(6 citation statements)

References 36 publications

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“…λ c = 1. These results were deduced before in several studyings 2,23,30,31 . The n -fold renormalization of the coupling constants can be obtained for a chain with spins, where n B is the number of spins in a block, in the Kadanoff’s block method.…”

Section: Renormalization Of the Itf Modelsupporting

confidence: 76%

Quantum Renormalization of Spin Squeezing in Spin Chains

Balazadeh

Najarbashi

Tavana

2018

Sci Rep

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By employing quantum renormalization group (QRG) method, we investigate quantum phase transitions (QPT) in the Ising transverse field (ITF) model and in the XXZ Heisenberg model, with and without Dzyaloshinskii Moriya (DM) interaction, on a periodic chain of N lattice sites. We adopt a new approach called spin squeezing as an indicator of QPT. Spin squeezing, through analytical expression of a spin squeezing parameter, is calculated after each step of QRG. As the scale of the system becomes larger, (after many QRG steps), the ground state (GS) spin squeezing parameters show an abrupt change at a quantum critical point (QCP). Moreover, in all of the studied models, the first derivative of the spin squeezing parameter with respect to the control parameter is discontinuous, which is a signature of QPT. The spin squeezing parameters develop their saturated values after enough QRG iterations. The divergence exponent of the first derivative of the spin squeezing parameter in the near vicinity of the QCP is associated with the critical exponent of the correlation length.

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Section: Renormalization Of the Itf Modelsupporting

confidence: 76%

Quantum Renormalization of Spin Squeezing in Spin Chains

Balazadeh

Najarbashi

Tavana

2018

Sci Rep

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“…If there exists more than one external parameter, this result can be generalized to the socalled quantum geometric tensor [12,40,42].…”

Section: Fidelity and Phase Diagrammentioning

confidence: 97%

Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field

Jafari

2016

J. Phys. A: Math. Theor.

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We study the ground state fidelity, fidelity susceptibility and quench dynamics of the extended quantum compass model in a transverse field. This model reveals a rich phase diagram which includes several critical surfaces depending on exchange couplings. We present a characterization of quantum phase transitions in terms of the ground state fidelity between two ground states obtained for two different values of external parameters. However, we derive scaling relations describing the singular behavior of fidelity susceptibility in the quantum critical surfaces. Moreover, we study the time evolution of the system after a critical quantum quench using the Loschmidt. We find that the revival times of Loschmidt echo are given by Trev = N/2vmax, where N is the size of the system and vmax is the maximum of lower bound group velocity of quasi-particles. Although the fidelity susceptibility shows the same exponent in all critical surfaces, the structure of the revivals after critical quantum quenches displays two different regimes reflecting different equilibration dynamics.

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“…We have also calculated the classical phase diagram by considering the spin structure as a spiral [28] At the end, attention should be paid to the importance of the exploration of quantum correlation, such as entanglement and quantum discord in the FAFST model. They can be easily done in the thermodynamics limit by applying the real Space Renormalization group method [46][47][48][49][50]. In particular, studying the four-leg spin tube frustrated by next-nearest-neighbor interaction on the leg, is an interesting topic that clearly deserves future investigations, which are not considered in the current work.…”

Section: Discussionmentioning

confidence: 99%

Geometrically frustrated anisotropic four-leg spin-1/2 nanotube

Jafari¹,

Mahdavifar²,

Akbari³

2019

J. Phys.: Condens. Matter

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We develop a real space quantum renormalization group (QRG) to explore a frustrated anisotropic four-leg spin-1/2 nanotube in the thermodynamic limit. We obtain the phase diagram, fixed points, critical points, the scaling of coupling constants and magnetization curves. Our investigation points out that in the case of strong leg coupling the diagonal frustrating interaction is marginal under QRG transformations and does not affect the universality class of the model. Remarkably, the renormalization equations express that the spin nanotube prepared in the strong leg coupling case goes to the strong plaquette coupling limit (weakly interacting plaquettes). Subsequently, in the limit of weakly interacting plaquettes, the model is mapped onto a 1D spin-1/2 XXZ chain in a longitudinal magnetic field under QRG transformation. Furthermore, the effective Hamiltonian of the spin nanotube inspires both first and second order phase transitions accompanied by the fractional magnetization plateaus. Our results show that the anisotropy changes the magnetization curve and the phase transition points, significantly. Finally, we report the numerical exact diagonalization results to compare the ground state phase diagram with our analytical visions.

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Quantum renormalization group approach to geometric phases in spin chains

Cited by 17 publications

References 36 publications

Quantum Renormalization of Spin Squeezing in Spin Chains

Quantum Renormalization of Spin Squeezing in Spin Chains

Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field

Geometrically frustrated anisotropic four-leg spin-1/2 nanotube

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