arXiv subjects

Da-Chuan Zheng

Publications and source records attributed to Da-Chuan Zheng.

3 recordsLinked to original sources

arXiv2018

Impurity-Induced Environmental Quantum Phase Transitions in the Quadratic-Coupling Spin-Boson Model

We study the zero temperature properties of the sub-Ohmic spin-boson model with quadratic spin-boson coupling. This model describes experimental set ups at the optimal working point where the linear-coupling between the qubit (spin) and the environmental noise (bosons) is zero and the leading coupling is quadratic. In the strong coupling regime, we find that the existence of spin induces quantum phase transitions (QPTs) between two states of environment: the normal state and a state with local distortions. The phase diagram contains both continuous and the first-order QPTs, with non-trivial critical properties obtained exactly. At the QPTs, the equilibrium state spin dynamics bears power-law $ω$ dependence in the small frequency limit and a robust coherent Rabi oscillation at high frequency. We discuss the feasibility of observing such environmental QPTs in the qubit-related experiments.

cond-mat.mes-hall↗

arXiv2017

Dynamical Correlation Functions of the Quadratic Coupling Spin-Boson Model

The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method. We focus on the dynamical auto-correlation functions $C_{O}(ω)$, with the operator $\hat{O}$ taken as $\hatσ_x$, $\hatσ_z$, and $\hat{X}$, respectively. In the weak-coupling regime $α< α_c$, these functions show power law $ω$-dependence in the small frequency limit, with the powers $1+2s$, $1+2s$, and $s$, respectively. At the critical point $α= α_c$ of the boson-unstable quantum phase transition, the critical exponents $y_{O}$ of these correlation functions are obtained as $y_{σ_x} = y_{σ_z} = 1-2s$ and $y_{X}=-s$, respectively. Here $s$ is the bath index and $X$ is the boson displacement operator. Close to the spin flip point, the high frequency peak of $C_{σ_{x}}(ω)$ is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.

cond-mat.mes-hall↗

arXiv2017

Equilibrium Dynamics of the Sub-Ohmic Spin-boson Model Under Bias

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function $C(ω)$ of the spin operator $σ_z$ for the biased sub-Ohmic spin-boson model. The small-$ω$ behavior $C(ω) \propto ω^s$ is found to be universal and independent of the bias $ε$ and the coupling strength $α$ (except at the quantum critical point $α=α_c$ and $ε=0$). Our NRG data also show $C(ω) \propto χ^{2}ω^{s}$ for a wide range of parameters, including the biased strong coupling regime ($ε\neq 0$ and $α> α_c$), supporting the general validity of the Shiba relation. Close to the quantum critical point $α_c$, the dependence of $C(ω)$ on $α$ and $ε$ is understood in terms of the competition between $ε$ and the crossover energy scale $ω_{0}^{\ast}$ of the unbiased case. $C(ω)$ is stable with respect to $ε$ for $ε\ll ε^{\ast}$. For $ε\gg ε^{\ast}$, it is suppressed by $ε$ in the low frequency regime. We establish that $ε^{\ast} \propto (ω_0^{\ast})^{1/θ}$ holds for all sub-Ohmic regime $0 \leqslant s < 1$, with $θ=2/(3s)$ for $0 < s \leqslant 1/2$ and $θ= 2/(1+s)$ for $1/2 < s < 1$. The variation of $C(ω)$ with $α$ and $ε$ is summarized into a crossover phase diagram on the $α-ε$ plane.

cond-mat.mes-hall↗