We explore the dynamics of spin-boson model for the Ohmic bath by employing the master equation approach and obtain an explicit expression of reduced density matrix. We also calculate the geometric phases of the spin-boson model by making use of the analytical results and discuss how the dissipative bosonic environment affects geometric phases. Furthermore, we investigate the dynamics of quantum discord and entanglement of two qubits each locally interacting with its own independent bosonic environments. It is found that the decay properties of quantum discord and entanglement are sensitive to the choice of initial state's parameter and coupling strength between system and bath.
We explore the dynamics of spin-boson model for the Ohmic bath by employing the master equation approach and obtain an explicit expression of reduced density matrix. We also calculate the geometric phases of the spin-boson model by making use of the analytical results and discuss how the dissipative bosonic environment affects geometric phases. Furthermore, we investigate the dynamics of quantum discord and entanglement of two qubits each locally interacting with its own independent bosonic environments. It is found that the decay properties of quantum discord and entanglement are sensitive to the choice of initial state's parameter and coupling strength between system and bath.
The quantum entanglement, discord, and coherence dynamics of two spins in the model of a spin coupled to a spin bath through an intermediate spin are studied. The effects of the important physical parameters including the coupling strength of two spins, the interaction strength between the intermediate spin and the spin bath, the number of bath spins and the temperature of the system on quantum coherence and correlation dynamics are discussed in different cases. The frozen quantum discord can be observed whereas coherence does not when the initial state is the Bell-diagonal state. At finite temperature, we find that coherence is more robust than quantum discord, which is better than entanglement, in terms of resisting the influence of environment. Therefore, quantum coherence is more tenacious than quantum correlation as an important resource.
By employing the spin-boson model in a dense limit of environmental modes, quantum entanglement and correlation of sub-Ohmic and Ohmic baths for dissipative quantum phase transitions are numerically investigated based on the variational principle. With several measures borrowed from quantum information theory, three different types of singularities are found for the first-order, second-order, and Kosterlitz-Thouless phase transitions, respectively, and the values of transition points and critical exponents are accurately determined. Besides, the scaling form of the quantum discord in the Ohmic case is identified, quite different from that in the sub-Ohmic regime. In a two-spin model, two distinct behaviors of the quantum discord are uncovered: one is related to the quantum entanglement between two spins and the other is decided by the correlation function in the position space rather than the entanglement.
In this paper, we study the dynamical processes of quantum coherence and correlations for two central qubits system coupled with a transverse Ising spin chain. Suppose the initial state of quantum system is the Werner state and the initial state of environment is the ground state of spin chain, and the corresponding time evolution operator, decoherence factor and reduced density matrix are given. We deduce the analytical expressions of evolution of quantum coherence, entanglement and quantum discord. We find that when the spin chain undergoes quantum phase transition (QPT), the entanglement vanished at time [Formula: see text], and the coherence and discord vanished when the decoherence factor decayed to zero. Besides, we also find that the environmental scale N, coupling strength g and parameter P of Werner state do not change the evolution rules of quantum correlation, but accelerate their decay rate with these parameters’ increase.
We have studied the entanglement dynamics for a two-qubit system coupled to a spin environment of different configurations by a z–x-type interaction. Quantum dynamics of the models considered in this paper is solved analytically. Moreover, we show that simple and concise results may be obtained when certain approximations are properly made. Our purpose is to find out how the entanglement of a central spin system is affected by the pre-designed factors of the system and its environment, such as their initial states and the coupling constants between the system and its environment. Clearly, how the system is coupled to its environment will inevitably change the feature of entanglement evolution of the central spin system. Our major findings include the following: (i) the entanglement of the system of interest is sensitive to the number of spins in the environment, (ii) the initial states of the environment can profoundly affect the dynamics of the entanglement of the central spin system and (iii) the entangled environment can speed up the decay and revival of the entanglement of the central spin system. Our results exhibit some interesting features that have not been found for a bosonic environment.
We explore how the dissipative geometric phase evolves within the spin-boson model, focusing specifically on coupling to an Ohmic bath in the weakly coherent regime. To determine the non-unitary time evolution of the system's reduced density matrix, we employ the non-interacting blip approximation (NIBA). For the localized pure initial state used throughout, we derive a compact Bloch-sphere expression showing that the mixed-state geometric phase is a weighted azimuthal winding of the dissipative trajectory. We then map geometric-phase accumulation across various system-bath coupling strengths, temperatures, static biases, and bath cutoff frequencies. Benchmarking representative results against the numerically exact time-evolving matrix product operator (TEMPO) technique shows that NIBA reproduces the population dynamics almost indistinguishably. It also captures the geometric phase quantitatively and qualitatively, although TEMPO reveals a clearer trend in the stationary coherence. Our results show that quantum dissipation suppresses the geometric phase through two complementary mechanisms: thermal noise reduces the state's purity, while static bias localizes the dynamics and reduces the accessible geometric area.
We study the dynamics of geometric measure of quantum discord. The model under consideration is a physical system of two qubits coupled with two independent bosonic reservoirs described by Ohmic-like spectral densities. We aim to find how the system's geometric measure of quantum discord evolves, and whether and in what conditions it may remain constant for a time interval or be frozen forever. Our result shows that by properly choosing the system's initial states, geometric measure of quantum discord may hold a frozen phenomenon in a time interval for all the three types of reservoirs, sub-Ohmic, Ohmic, and super-Ohmic reservoirs, and it may also hold a time-invariant phenomenon for super-Ohmic reservoirs. The conditions satisfied by the coefficients of standard Bell-diagonal states, in which the frozen phenomenon in a time interval or the time-invariant phenomenon of geometric measure of quantum discord appears, are given.