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Entanglement in quantum spin glass and its applications
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Type
Thesis
Author
Koh, Chee Yeong
Supervisor
Kwek, Leong Chuan
Abstract
Well-known theories like Edwards-Anderson and Sherrington-Kirkpatrick models together with some important experimental results for spin glass are introduced in chapter 1. However, there is no single model, capable of explaining all the experimental results obtained from the spin glass materials. We use the theory of quantum entanglement (concurrence) to explore the quantum correlations of a spin glass. Quantum entanglement is a useful physical resource for quantum information and communication. In chapter 2, we discuss how information is encoded and measured. The applications of quantum information in algorithms are also mentioned. As quantum information science is built upon the foundation of quantum mechanics, two important aspects of this area: Einstein, Podolsky and Rosen (EPR) gedanken experiment and the Bell's inequality are introduced in chapter 3.
In chapter 4, we discuss the idea of density operator, together with the use of trace and partial trace, to describe the state of the composite system. In chapter 5, a short introduction is made on the various entanglement measures. In chapter 6, the analytical calculations of the concurrence for a 3- and 4-qubit XX model are presented. The plots of concurrence with different means and standard deviations for the 3- and 4-qubit are also presented and analyzed. The concurrence of a 2-qubit system coupled to a spin glass bath of n = 2 to 4 qubits is studied in chapter 7. With an initial separable state, the 2-qubit system reached a steady state in concurrence through time evolution when it is coupled to a quantum spin glass environment. The result is general and the behavior of the concurrence is believed to be similar for n > 4. The quantum discord is used for analyzing the XX model and presented in chapter 8. In addition, the concurrence and discord for the next nearest neighbour interaction have been plotted for 3- and 4-qubit.
In chapter 9, the concurrence of the probes that are attached to a spin glass is investigated by varying the external applied magnetic field and the J coupling. By using the quantum dots (qubits) as the probe, it is possible to distinguish a spin glass from a non-spin glass with the di erent signatures (drop and spike) in the concurrence between the probes. The derived entanglement witness for susceptibility and speci c heat capacity are used to distinguish an entangled region from an unentangled region for two different spin glass alloys: LiHoxY1-xF4 and CuxMn in chapter 10. In chapter 11, the entanglement properties of the XXZ Heisenberg (with Dzyaloshinskii-Moriya interaction) and Ising transverse field spin glass models are examined with the use of concurrence for N qubits at one-dimensional level. The concurrence for both models are obtained by using the Kadanoff''s renormalization group (RG) approach. By following the RG fl ow, a first-order and second-order phase transitions are observed by varying the standard deviation of the renormalized couplings. This thesis ends with a conclusion in chapter 12 with suggestions for future research.
In chapter 4, we discuss the idea of density operator, together with the use of trace and partial trace, to describe the state of the composite system. In chapter 5, a short introduction is made on the various entanglement measures. In chapter 6, the analytical calculations of the concurrence for a 3- and 4-qubit XX model are presented. The plots of concurrence with different means and standard deviations for the 3- and 4-qubit are also presented and analyzed. The concurrence of a 2-qubit system coupled to a spin glass bath of n = 2 to 4 qubits is studied in chapter 7. With an initial separable state, the 2-qubit system reached a steady state in concurrence through time evolution when it is coupled to a quantum spin glass environment. The result is general and the behavior of the concurrence is believed to be similar for n > 4. The quantum discord is used for analyzing the XX model and presented in chapter 8. In addition, the concurrence and discord for the next nearest neighbour interaction have been plotted for 3- and 4-qubit.
In chapter 9, the concurrence of the probes that are attached to a spin glass is investigated by varying the external applied magnetic field and the J coupling. By using the quantum dots (qubits) as the probe, it is possible to distinguish a spin glass from a non-spin glass with the di erent signatures (drop and spike) in the concurrence between the probes. The derived entanglement witness for susceptibility and speci c heat capacity are used to distinguish an entangled region from an unentangled region for two different spin glass alloys: LiHoxY1-xF4 and CuxMn in chapter 10. In chapter 11, the entanglement properties of the XXZ Heisenberg (with Dzyaloshinskii-Moriya interaction) and Ising transverse field spin glass models are examined with the use of concurrence for N qubits at one-dimensional level. The concurrence for both models are obtained by using the Kadanoff''s renormalization group (RG) approach. By following the RG fl ow, a first-order and second-order phase transitions are observed by varying the standard deviation of the renormalized couplings. This thesis ends with a conclusion in chapter 12 with suggestions for future research.
Date Issued
2014
Call Number
QC176.8.S68 Koh
Date Submitted
2014