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Non-Markovian Reduced Dynamics and Entanglement Evolution of Central Spin Models in Quantum Spin Environments

Hsi‐Sheng Goan

We discuss two central spin models coupled, respectively, to a quantum Heisenberg XY spin star environment [1] and to an antiferromagnetic environment [2]. In the first model [1], the exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg XY spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using a novel operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment and the interaction between the constituents of the spin environment. We also investigate the effect of detuning which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two spin qubits.We discuss two central spin models coupled, respectively, to a quantum Heisenberg XY spin star environment [1] and to an antiferromagnetic environment [2]. In the first model [1], the exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg XY spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using a novel operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment and the interaction between the constituents of the spin environment. We also investigate the effect of detuning which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two spin qubits.

OSA Workshop on Entanglement and Quantum DecoherenceJan 1, 20080 citations

Dynamics of the one-dimensional Heisenberg spin system

Alf Sjölander

Lecture notes in physicsJan 1, 19790 citations

Dynamic scaling for longitudinal critical dynamics of dilute Heisenberg and quantum XY chains

Anthony C. Maggs, L.L. Gonçalves, Robin B. Stinchcombe

By averaging over chain segments, the response function and density of states is obtained for the longitudinal dynamics of two dilute one-dimensional models: the Heisenberg ferromagnet in the spin wave approximation and the quantum XY model in a transverse field. Dynamic scaling descriptions are derived, and the associated exponents and universal scaling functions obtained, for scaling limits where the percolation correlation length diverges and the wavevector tends to 0 or pi .

Journal of Physics A Mathematical and GeneralJul 11, 19862 citations

Spin Dynamics of Heisenberg Chains

T. Schneider, E. Stoll

Modern problems in condensed matter sciencesJan 1, 19861 citation

Spin Dynamics Calculations in the Two-Dimensional Classical XY-Model

Hans Gerd Evertz, David Paul Landau

Springer proceedings in physicsJan 1, 19950 citations

Observation of the Ground-State Geometric Phase in a Heisenberg XY Model

Xinhua Peng, Sanfeng Wu, Jun Li +2 more

Geometric phases play a central role in a variety of quantum phenomena, especially in condensed matter physics. Recently, it was shown that this fundamental concept exhibits a connection to quantum phase transitions where the system undergoes a qualitative change in the ground state when a control parameter in its Hamiltonian is varied. Here we report the first experimental study using the geometric phase as a topological test of quantum transitions of the ground state in a Heisenberg XY spin model. Using NMR interferometry, we measure the geometric phase for different adiabatic circuits that do not pass through points of degeneracy.Geometric phases play a central role in a variety of quantum phenomena, especially in condensed matter physics. Recently, it was shown that this fundamental concept exhibits a connection to quantum phase transitions where the system undergoes a qualitative change in the ground state when a control parameter in its Hamiltonian is varied. Here we report the first experimental study using the geometric phase as a topological test of quantum transitions of the ground state in a Heisenberg XY spin model. Using NMR interferometry, we measure the geometric phase for different adiabatic circuits that do not pass through points of degeneracy.

arXiv:1011.2814Physical Review LettersDec 10, 201050 citations

The dynamics of a central spin in quantum Heisenberg XY model

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