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

Abstract

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.

Ansatz for the quantum phase transition in a dissipative two-qubit system

“…However, for the single-qubit system in Ohmic bath both the criteria η → 0 and σ z = 0 give the same critical value α c = 1, at least in the scaling limit ∆/ω c → 0(Refs. [2][3][4][5][6][7][8][9][10][11][12]). This difference comes from the two-qubit correlation and the renormalized Ising coupling V (Eq.…”

“…Various numerical methods were used for this purpose, such as the numerical renormalization group (NRG) [4,5,6], the quantum Monte Carlo (QMC) [7], the method of sparse polynomial space representation [8], the extended coherent state approach [9], and the variational matrix product state approach [10]. In addition, an extension of the Silbey-Harris [11] ground state has been recently employed by us [12] to study the QPT of the single-qubit SBM in the Ohmic (s = 1) and sub-Ohmic (s < 1) bath.…”

Zero-temperature localization in a sub-Ohmic spin-boson model investigated by an extended hierarchy equation of motion

“…The numerical renormalization group [4], quantum Monte Carlo (QMC) [5], and sparse polynomial space representation [6] have been used to generate numerically accurate predictions of the DL transition from the standpoint of quantum equilibrium and investigate the critical behavior. The variational polaron antasz and its extensions provide a meanfield picture of understanding the DL transition [7][8][9][10][11]. In particular, an analytical expression of the critical Kondo parameter is obtained in the strong sub-Ohmic regime [8].…”

Variational Study of the Two‐Impurity Spin–Boson Model with a Common Ohmic Bath: Ground‐State Phase Transitions

“…The latter can be realized in the context of waveguide quantum electrodynamics by coupling a superconducting qubit to a uniform Josephson junction array [17][18][19]. In recent years, the transition boundary and the critical exponents have been estimated by a variety of approaches, such as the numerical renormalization group (NRG), exact diagonalization (ED), variational matrix product states (VMPS), quantum Monte Carlo (QMC), and variational methods (VM) [20][21][22][23][24][25][26]. Numerical results of the critical couplings agree well in the deep sub-Ohmic regime s < 0.5, but differ considerably in the shallow one s > 0.5, let alone those in the Ohmic case s = 1 due to the sensitivity of Kosterlitz-Thouless transition.…”