臺灣博碩士論文加值系統

In this thesis, we use the new numerical method – density matrix renormalization group – to study the decoherence of spin qubit. Because of diverging Hilbert space in quantum system, the linear growth and effective truncation make us can simulate quantum system accurately. Also, time-dependent DMRG was developed to simulate the real-time dynamics of quantum system. We use this method to study the non-equilibrium properties.
Spin decoherence induced by a spin bath has recently been the subject of interest in the field of quantum computation and spintronics. Unlike the spin-boson model, the resulting decoherence depends crucially on the nature of the spin bath and its coupling to the central spin. In this work we investigate the decoherence of a central spin which is coupled non-uniformly to a spin chain by means of the time-dependent density matrix renormalization group technique. Using this technique the coupling between the central spin and the spin chain can take any form, in contrast to the typical uniform or on-site coupling taken in the literature. Two qubit decoherence is also an interesting subject in this thesis. The distance between
qubits affect the decoherence of qubits. We have studied the resulting spin
decoherence induced by spin chains in the Ising, XY, XXZ, and Heisenberg universality classes. Connection between the decoherence the quantum phase transition of the spin chain is discussed.
An exotic interaction, which can’t be realized in semiconductor wire, exist in a system : double wire loaded by fermionic polar molecules. Different interaction can be tuned by external electric field. We study the phase diagram of this system by means of static DMRG. An interesting phase – spontaneous interwire coherence -- is found.

In this thesis, we use the new numerical method – density matrix renormalization group – to study the decoherence of spin qubit. Because of diverging Hilbert space in quantum system, the linear growth and effective truncation make us can simulate quantum system accurately. Also, time-dependent DMRG was developed to simulate the real-time dynamics of quantum system. We use this method to study the non-equilibrium properties.
Spin decoherence induced by a spin bath has recently been the subject of interest in the field of quantum computation and spintronics. Unlike the spin-boson model, the resulting decoherence depends crucially on the nature of the spin bath and its coupling to the central spin. In this work we investigate the decoherence of a central spin which is coupled non-uniformly to a spin chain by means of the time-dependent density matrix renormalization group technique. Using this technique the coupling between the central spin and the spin chain can take any form, in contrast to the typical uniform or on-site coupling taken in the literature. Two qubit decoherence is also an interesting subject in this thesis. The distance between
qubits affect the decoherence of qubits. We have studied the resulting spin
decoherence induced by spin chains in the Ising, XY, XXZ, and Heisenberg universality classes. Connection between the decoherence the quantum phase transition of the spin chain is discussed.
An exotic interaction, which can’t be realized in semiconductor wire, exist in a system : double wire loaded by fermionic polar molecules. Different interaction can be tuned by external electric field. We study the phase diagram of this system by means of static DMRG. An interesting phase – spontaneous interwire coherence -- is found.

1 Introduction 3
2 Density Matrix Renormalization Group 5
2.1 Numerical Renormalizaion Group and Density Matrix Formulation . 5
2.1.1 Standard DMRG Procedure . . . . . . . . . . . . . . . . . . 7
2.1.2 Physical Quantity Calculation in DMRG . . . . . . . . . . . 11
2.1.3 Wave Function Transformation . . . . . . . . . . . . . . . . 14
2.2 Time-Dependent DMRG . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Suzuki-Trotter Formula . . . . . . . . . . . . . . . . . . . . . 17
3 Spin Qubit(s) Decoherence by Generalized Spin Bath 20
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 DMRG Procedure in Spin qubit(s) Dynamics . . . . . . . . . . . . . 22
3.4 Single Spin Decoherence . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4.1 Short Time Behavior of Loschmidt echo . . . . . . . . . . . 23
3.4.2 Spin Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5 Two Spins Decoherence . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5.1 Known Result in XY-bath . . . . . . . . . . . . . . . . . . . 34
3.5.2 Generalized Heisenberg Spin Bath . . . . . . . . . . . . . . . 36
4 Quantum Phase Diagram of Polar Molecules in 1D Double Wire System 38
4.1 The Model and Transformation . . . . . . . . . . . . . . . . . . . . 38
4.2 Phase Diagram and Order Parameter . . . . . . . . . . . . . . . . . 40
5 Conclusion 43
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
A Second Order Approximation of Loschmidt Echo 46

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