Loschmidt echo and Berry phase of a quantum system coupled to an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math>spin chain: Proximity to a quantum phase transition

Yuan, Zi-Gang; Zhang, Ping; Li, Shu-Shen

doi:10.1103/physreva.75.012102

Cited by 87 publications

(44 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(6), (8) and (10), one can re-express the HamiltonianĤ EI as (11) where the operatorκ = (1 −Λ)/|1 −Λ|.…”

Section: Solution Of the Modelmentioning

confidence: 99%

“…Quan et al considered influence of the Ising-type correlated environment on the Loschmidt echo (LE), and found that the quantum critical behavior of the environmental system strongly affects its capability of enhancing the decay of the LE [7]. Since then the LE of a coupled system consisting of a central spin (or two central spins) and its surrounding environment [8][9][10] has been discussed extensively. The results show that the decaying behavior of the LE is sensitively affected by the anisotropy of the environment.…”

Section: Introductionmentioning

confidence: 99%

“…As for decoherence caused by different spin-chain environments, much progress has been achieved so far [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], and these investigations can be separated into at least two kinds. The first kind is mainly about investigating effects of the uncorrelated environment (i.e., constituents of the environ-E-mail address: mingliang0301@xupt.edu.cn.…”

Section: Introductionmentioning

confidence: 99%

“…The first kind is mainly about investigating effects of the uncorrelated environment (i.e., constituents of the environ-E-mail address: mingliang0301@xupt.edu.cn. ment have no intra-interactions) on system dynamics [4][5][6], while the second kind is about investigating effects of the correlated environment on quantum dynamics of the system [7][8][9][10][11][12][13][14][15][16][17][18][19], for in the real situation, particles constitute the environment may have interactions with each other.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Disentanglement dynamics of interacting two qubits and two qutrits in an XY spin-chain environment with the Dzyaloshinsky–Moriya interaction

2010

Physics Letters A

View full text Add to dashboard Cite

We investigate disentanglement dynamics of two coupled qubits and qutrits which interact uniformly to a general X Y spin-chain environment with the Dzyaloshinsky-Moriya (DM) interaction. We obtained exact expression of the time evolution operator and analyzed the dynamical process of the decoherence factors. Through explicitly calculating the concurrence and the negativity, we examined disentanglement behaviors of two coupled central spins evolve from different initial pure states, which are found to be nontrivially different from those of the uncorrelated ones, in particular, the enhanced decay of the entanglement induced by quantum criticality of the surrounding environment may be broken by introducing self-Hamiltonian of the central spin system. Moreover, the DM interaction may have different influences on decay of the entanglement depending on the strength of the system-environment coupling, the anisotropy of the environmental spin chain and the intensity of the transverse magnetic field, as well as the explicit form of the initial states of the central spin system.

show abstract

“…(6), (8) and (10), one can re-express the HamiltonianĤ EI as (11) where the operatorκ = (1 −Λ)/|1 −Λ|.…”

Section: Solution Of the Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Disentanglement dynamics of interacting two qubits and two qutrits in an XY spin-chain environment with the Dzyaloshinsky–Moriya interaction

2010

Physics Letters A

View full text Add to dashboard Cite

show abstract

“…There are some studies [2][3][4][5][6][7][8] on the effects of decoherence induced by a correlated environment on quantum states, and the frequently used physical quantity is the quantum Loschmidt echo (LE). LE comes from NMR experiments and has been studied extensively in the context of Fermi edge singularities in x-ray spectra of metals [9], quantum chaos [10,11], and out-of-equilibrium fluctuations [12].…”

Section: Introductionmentioning

confidence: 99%

Loschmidt echo of a two-level qubit coupled to nonuniform anisotropicXYchains in a transverse field

Zhong

Tong

2011

Phys. Rev. A

View full text Add to dashboard Cite

The Loschmidt echo (LE) of a central two-level qubit coupled to nonuniform anisotropic XY chains in a transverse field is studied. A general formula for LE is derived, which we use to discuss the influence of the criticality of the environment on LE. It is found that for the periodic XY chain the behaviors of LE in the vicinity of the critical points are similar to those of the uniform case. It is different for the disordered transverse Ising chains. For the aperiodic chains, if the surrounding systems are bounded chains, the behaviors of LE are similar to those of the uniform case, while if the surrounding systems are unbounded chains, they are similar to those of the disordered case.

show abstract

Fidelity as a marker of topological phase transitions in 2D Dirac materials

Bolívar

Cordero

Nagy

et al. 2018

Int J of Quantum Chemistry

View full text Add to dashboard Cite

Silicene, as other 2D buckled structures, is a gapped Dirac material with intrinsic spin-orbit coupling whose band structure can be controlled by applying a perpendicular electric field. It presents a topological phase transition from a topological insulator to a band insulator at the charge neutrality point. We present in this article a characterization of this phase transition by using fidelity of Loschmidt echoes when a magnetic and two slightly different electric fields are applied by considering the time evolution of two kinds of wave packets, one with a single Gaussian profile and the other with a double Gaussian profile creating a cat state. We also show that Zitterbewegung, classical, and revival Loschmidt periods diverge close to but not exactly at the charge neutrality point and explain this behavior.Silicene is a two dimensional crystal of silicon, belonging to a group of 2D gapped Dirac materials analogous to graphene but with a relevant intrinsic spin-orbit coupling (as compared to graphene) and a buckled structure. It has been studied theoretically [1,2] and experimentally. [3][4][5][6][7] Other gapped Dirac materials are germanene, stannene, and Pb. [8] In the case of silicene, the low energy electronic properties can be described by a Dirac Hamiltonian with a Fermi velocity v F = 4:2 × 10 5 ms − 1 and a value of the spin-orbit coupling Δ so = 4:2 meV. It has a buckling length l = 0:22Å which allows to control the band structure by applying an electric field, ℰ z = Δ z =l, perpendicular to the silicene monolayer generating a tunable band gap jΔ s, ξ j = jðΔ z − sξΔ so Þ=2j (s and ξ denote spin and valley, respectively). Silicene has a topological phase transition (TPT) [9] from a topological insulator (TI, jΔ z j < Δ so ) to a band insulator (BI, jΔ z j > Δ so ), at a charge neutrality point (CNP) Δ ð0Þ z = sξΔ so , with a gap cancellation between the perpendicular electric field and the spin-orbit coupling, thus exhibiting a semimetal behavior.Topological phases are characterized by topological charges like Chern numbers. Theoretical information measures and uncertainty relations have been used to characterize TPTs. [10][11][12][13] Recently, we have studied the time evolution of electron wave packets in silicene under perpendicular magnetic and electric fields to characterize topological-band insulator transitions. [14]

show abstract

Loschmidt echo and Berry phase of a quantum system coupled to anXYspin chain: Proximity to a quantum phase transition

Cited by 87 publications

References 21 publications

Disentanglement dynamics of interacting two qubits and two qutrits in an XY spin-chain environment with the Dzyaloshinsky–Moriya interaction

Disentanglement dynamics of interacting two qubits and two qutrits in an XY spin-chain environment with the Dzyaloshinsky–Moriya interaction

Loschmidt echo of a two-level qubit coupled to nonuniform anisotropicXYchains in a transverse field

Fidelity as a marker of topological phase transitions in 2D Dirac materials

Contact Info

Product

Resources

About