arXiv subjects

Zhiguo Lü

Publications and source records attributed to Zhiguo Lü.

22 records · Page 2Linked to original sources

arXiv2013

Quantum critical point of spin-boson model and infrared catastrophe in bosonic bath

An analytic ground state is proposed for the unbiased spin-boson Hamiltonian, which is non-Gaussian and beyond the Silbey-Harris ground state with lower ground state energy. The infrared catastrophe in Ohmic and sub-Ohmic bosonic bath plays an important role in determining the degeneracy of the ground state. We show that the infrared divergence associated with the displacement of the nonadiabatic modes in bath may be removed from the proposed ground state for the coupling $α<α_c$. Then $α_c$ is the quantum critical point of a transition from non-degenerate to degenerate ground state and our calculated $α_c$ agrees with previous numerical results.

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arXiv2011

Does temperature favor quantum coherence of a dissipative two-level system?

The quantum dynamics of a two-level system coupled to an Ohmic spin- bath is studied by means of the perturbation approach based on a unitary transformation. A scattering function $ξ_k$ is introduced in the transformation to take into account quantum fluctuations. By the master equation within the Born approximation, nonequilibrium dynamics quantities are calculated. The method works well for the coupling constant $0 < α< α_c$ and a finite bare tunneling $Δ$. It is found that (i) only at zero temperature with small coupling or moderate one does the spin-spin-bath model display identical behavior as the well known spin-boson-bath model; (ii) in comparison with the known results of spin-boson-bath model, the coherence-incoherence transition point, which occurs at $α_c={1/2}[1+ηΔ/ω_c]$, is temperature independent; (iii) the nonequilibrium correlation function $P(t)=<τ_z(t)>$, evolves without temperature dependence while $<τ_x(t)>$ depends on temperature. Both $P(t)$ and $<τ_x(t)>$ not only satisfy their initial conditions, respectively, and also have correct long time limits. Besides, the Shiba's relation and sum rule are exactly satisfied in the coherent regime for this method. Our results show that increasing temperature does not help the system suppress decoherence in the coherent regime, i.e., finite temperature does not favor the coherent dynamics in this regime. Thus, the finite-temperature dynamics induced by two kinds of baths spin-bath and boson-bath exhibit distinctly different physics.

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arXiv2011

Non-Markovian dynamical effects and time evolution of entanglement entropy of a dissipative two-state system

We investigate the dynamical information exchange between a two-state system and its environment which is measured by von Neumann entropy. It is found that in the underdamping regime, the entropy dynamics exhibits an extremely non-Markovian oscillation-hump feature, in which oscillations manifest quantum coherence and a hump of envelop demonstrates temporal memory of bath. It indicates that the process of entropy exchange is bidirectional. When the coupling strength increases a certain threshold, the hump along with ripple disappears, which is indicative of the coherent-incoherent dynamical crossover. The long-time limit of entropy evolution reaches the ground state value which agrees with that of numerical renormalization group.

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arXiv2006

Quantum dynamics of the dissipative two-state system coupled with a sub-Ohmic bath

The decoherence of a two-state system coupled with a sub-Ohmic bath is investigated theoretically by means of the perturbation approach based on a unitary transformation. It is shown that the decoherence depends strongly and sensitively on the structure of environment. Nonadiabatic effect is treated through the introduction of a function $ξ_k$ which depends on the boson frequency and renormalized tunneling. The results are as follows:(1) the non-equilibrium correlation function $P(t)$, the dynamical susceptibility $χ''(ω)$ and the equilibrium correlation function $C(t)$ are analytically obtained for $s\leq 1$; (2) the phase diagram of thermodynamic transition shows the delocalized-localized transition point $α_l$ which agrees with exact results and numerical data from the Numerical Renormalization Group; (3) the dynamical transition point $α_c$ between coherent and incoherent phase is explicitly given for the first time. A crossover from the coherent oscillation to incoherent relaxation appears with increasing coupling (for $α> α_c $, the coherent dynamics disappear); (4) the Shiba's relation and sum rule are exactly satisfied when $α\leq α_c $; (5) an underdamping-overdamping transition point $α_c^{*}$ exists in the function $S(ω)$. Consequently, the dynamical phase diagrams in both ohmic and sub-Ohmic case are mapped out. For $Δ\ll ω_c$, the critical couplings ($α_l, α_c$ and $α_c^{*}$) are proportional to $Δ^{1-s}$.

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