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arXiv:quant-ph/0301121

Decoherence in quantum spin systems

Hans A. De Raedt, V. V. Dobrovitski

Published Jan 23, 2003• 0 citations
arXivHTMLPDF

Abstract

Computer simulations of decoherence in quantum spin systems require the solution of the time-dependent Schrodinger equation for interacting quantum spin systems over extended periods of time. We use exact diagonalization, Chebyshev polynomial technique, four Suzuki-formula algorithms, and the short-iterative-Lanczos method to solve a simple model for decoherence of a quantum spin system by an environment consisting of quantum spins, and compare advantages and limitations of different algorithms.

DOI
10.48550/arxiv.quant-ph/0301121

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Computer simulations of decoherence in quantum spin systems require the solution of the time-dependent Schrodinger equation for interacting quantum spin systems over extended periods of time. We use exact diagonalization, Chebyshev polynomial technique, four Suzuki-formula algorithms, and the short-iterative-Lanczos method to solve a simple model for decoherence of a quantum spin system by an environment consisting of quantum spins, and compare advantages and limitations of different algorithms.
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We demonstrate that the Chebyshev expansion method is a very efficient numerical tool for studying spin-bath decoherence of quantum systems. We consider two typical problems arising in studying decoherence of quantum systems consisting of a few coupled spins: (i) determining the pointer states of the system and (ii) determining the temporal decay of quantum oscillations. As our results demonstrate, for determining the pointer states, the Chebyshev-based scheme is at least a factor of 8 faster than existing algorithms based on the Suzuki-Trotter decomposition. For problems of the second type, the Chebyshev-based approach is 3-4 times faster than the Suzuki-Trotter-based schemes. This conclusion holds qualitatively for a wide spectrum of systems, with different spin baths and different Hamiltonians.
In this review, we discuss the decoherence and thermalization of a quantum spin system interacting with a spin bath environment, by numerically solving the time-dependent Schrödinger equation of the whole system. The effects of the topologic structure and the initial state of the environment on the decoherence of the two-spin and many-spin system are discussed. The role of different spin-spin coupling is considered. We show under which conditions the environment drives the reduced density matrix of the system to a fully decoherent state, and how the diagonal elements of the reduced density matrix approach those expected for the system in the microcanonical or canonical ensemble, depending on the character of the additional integrals of motion. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the microcanonical distribution (in each eigenenergy subspace) and canonical ensemble are states that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics. Furthermore, our numerical results show that a fully decoherent quantum system prefers to stay in an equilibrium state with a maximum entropy, indicating the validity of the second law of thermodynamics in the decoherence process.
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Abstract We study quantum decoherence numerically in a system consisting of a relativistic quantum field theory coupled to a measuring device that is itself coupled to an environment. The measuring device and environment are treated as quantum, non-relativistic particles. We solve the Schrödinger equation for the wave function of this tripartite system using exact diagonalization. Although computational limitations on the size of the Hilbert space prevent us from exploring the regime where the device and environment consist of a truly macroscopic number of degrees of freedom, we nevertheless see clear evidence of decoherence: after tracing out the environment, the density matrix describing the system and measuring device evolves quickly towards a matrix that is close to diagonal in a subspace of pointer states. We measure the speed with which decoherence spreads in the relativistic quantum field theory for a range of parameters. We find that it is less than the speed of light but faster than the speed of the massive charges in the initial state.
The aim of this topical review is a systematic and concise presentation of the results of a series of theoretical works on the quantum dynamics of two-spin-qubit systems towards the elaboration of a physical mechanism of the quantum information transfer between two spin-qubits. For this purpose the main attention is paid to exactly solvable models of two-spin-qubit systems, since the analytical expressions of the elements of their reduced density matrices explicitly exhibit the mutual dependence of the quantum information encoded into the spin-qubits. The treatment of their decoherence due to the interaction with the environment is performed in the Markovian approximation. Rate equations for axially symmetric systems of two coupled spin-qubits non-interacting, as well as interacting, with the environment are exactly solved. It is shown how the solutions of rate equations demonstrate the physical mechanism of the quantum information exchange between the spin-qubits. This mechanism holds also in all two-spin-qubit systems whose rate equations can be solved only by means of numerical calculations. Exact solutions of rate equations for two uncoupled spin-qubits interacting with two separate environments reveal an interesting physical phenomenon in the time evolution of the qubit-qubit entanglement generated by their interaction with the environments: the entanglement sudden death and revival. A two-spin-qubit system with an asymptotically decoherence free subspace was also explicitly constructed. The presented calculations and reasonings can be extended for application to the study of spin-qubit chains or networks.