The electronic spin in quantum dots can be described by central spin models (CSMs) with a very large number ${N}_{\text{eff}}\ensuremath{\approx}{10}^{4}$ to ${10}^{6}$ of bath spins posing a tremendous challenge to theoretical simulations. Here, a fully quantum mechanical theory is developed for the limit ${N}_{\text{eff}}\ensuremath{\rightarrow}\ensuremath{\infty}$ by means of iterated equations of motion (iEoM). We find that the CSM can be mapped to a four-dimensional impurity coupled to a noninteracting bosonic bath in this limit. Remarkably, even for infinite bath the CSM does not become completely classical. The data obtained by the proposed iEoM approach are tested successfully against data from other, established approaches. Thus the iEoM mapping extends the set of theoretical tools that can be used to understand the spin dynamics in large CSMs.The electronic spin in quantum dots can be described by central spin models (CSMs) with a very large number ${N}_{\text{eff}}\ensuremath{\approx}{10}^{4}$ to ${10}^{6}$ of bath spins posing a tremendous challenge to theoretical simulations. Here, a fully quantum mechanical theory is developed for the limit ${N}_{\text{eff}}\ensuremath{\rightarrow}\ensuremath{\infty}$ by means of iterated equations of motion (iEoM). We find that the CSM can be mapped to a four-dimensional impurity coupled to a noninteracting bosonic bath in this limit. Remarkably, even for infinite bath the CSM does not become completely classical. The data obtained by the proposed iEoM approach are tested successfully against data from other, established approaches. Thus the iEoM mapping extends the set of theoretical tools that can be used to understand the spin dynamics in large CSMs.

arXiv:1711.08919Physical review. B./Physical review. BApr 23, 20189 citations

Separation-dependent localization in a two-impurity spin-boson model

Dara P. S. McCutcheon, Ahsan Nazir, Sougato Bose +1 more

Using a variational approach we investigate the delocalized to localized crossover in the ground state of an Ohmic two-impurity spin-boson model, describing two otherwise noninteracting spins coupled to a common bosonic environment. We show that a competition between an environment-induced Ising spin interaction and externally applied fields leads to variations in the system-bath coupling strength, ${\ensuremath{\alpha}}_{c}$, at which the delocalized-localized crossover occurs. Specifically, the crossover regime lies between ${\ensuremath{\alpha}}_{c}=0.5$ and ${\ensuremath{\alpha}}_{c}=1$ depending upon the spin separation and the strength of the transverse tunneling field. This is in contrast to the analogous single-spin case, for which the crossover occurs (in the scaling limit) at fixed ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}1$. We also discuss links between the two-impurity spin-boson model and a dissipative two-spin transverse Ising model, showing that the latter possesses the same qualitative features as the Ising strength is varied. Finally, we show that signatures of the crossover may be observed in single impurity observables, as well as in the behavior of the system-environment entanglement.Using a variational approach we investigate the delocalized to localized crossover in the ground state of an Ohmic two-impurity spin-boson model, describing two otherwise noninteracting spins coupled to a common bosonic environment. We show that a competition between an environment-induced Ising spin interaction and externally applied fields leads to variations in the system-bath coupling strength, ${\ensuremath{\alpha}}_{c}$, at which the delocalized-localized crossover occurs. Specifically, the crossover regime lies between ${\ensuremath{\alpha}}_{c}=0.5$ and ${\ensuremath{\alpha}}_{c}=1$ depending upon the spin separation and the strength of the transverse tunneling field. This is in contrast to the analogous single-spin case, for which the crossover occurs (in the scaling limit) at fixed ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}1$. We also discuss links between the two-impurity spin-boson model and a dissipative two-spin transverse Ising model, showing that the latter possesses the same qualitative features as the Ising strength is varied. Finally, we show that signatures of the crossover may be observed in single impurity observables, as well as in the behavior of the system-environment entanglement.

arXiv:1004.0198Physical Review BJun 18, 201037 citations

The Interacting Spin Models and the Equivalent Boson Systems

Chih-Chun Chang

Jan 1, 19950 citations

Topologically protected Bell-cat states in a simple spin model

B. Lajci, Duncan H J O’Dell, J. Mumford

We consider the topological properties of the so-called central spin model that consists of $N$ identical spins coupled to a single distinguishable central spin which arises in physical systems such as circuit-QED and bosonic Josephson junctions coupled to an impurity atom. The model closely corresponds to the Su-Schrieffer-Heeger (SSH) model except that the chain of sites in the SSH model is replaced by a chain of states in Fock space specifying the magnetization. We find that the model accommodates topologically protected eigenstates that are `Bell-cat' states consisting of a Schrödinger cat state of the $N$ spins that is maximally entangled with the central spin, and show how this state can be adiabatically created and moved along the chain by driving the central spin. The Bell-cat states are visualized by plotting their Wigner function and we explore their robustness against random noise by solving the master equation for the density matrix. We also explain the essential topological difference between identical spins and the excitations of a bosonic mode.We consider the topological properties of the so-called central spin model that consists of $N$ identical spins coupled to a single distinguishable central spin which arises in physical systems such as circuit-QED and bosonic Josephson junctions coupled to an impurity atom. The model closely corresponds to the Su-Schrieffer-Heeger (SSH) model except that the chain of sites in the SSH model is replaced by a chain of states in Fock space specifying the magnetization. We find that the model accommodates topologically protected eigenstates that are `Bell-cat' states consisting of a Schrödinger cat state of the $N$ spins that is maximally entangled with the central spin, and show how this state can be adiabatically created and moved along the chain by driving the central spin. The Bell-cat states are visualized by plotting their Wigner function and we explore their robustness against random noise by solving the master equation for the density matrix. We also explain the essential topological difference between identical spins and the excitations of a bosonic mode.

arXiv:2410.23532Physical Review ADec 23, 20252 citations

The electronic spin in quantum dots can be described by central spin models (CSMs) with a very large number ${N}_{\text{eff}}\ensuremath{\approx}{10}^{4}$ to

{10}^{6}

of bath spins posing a tremendous challenge to theoretical simulations. Here, a fully quantum mechanical theory is developed for the limit ${N}_{\text{eff}}\ensuremath{\rightarrow}\ensuremath{\infty}$ by means of iterated equations of motion (iEoM). We find that the CSM can be mapped to a four-dimensional impurity coupled to a noninteracting bosonic bath in this limit. Remarkably, even for infinite bath the CSM does not become completely classical. The data obtained by the proposed iEoM approach are tested successfully against data from other, established approaches. Thus the iEoM mapping extends the set of theoretical tools that can be used to understand the spin dynamics in large CSMs.

We consider the topological properties of the so-called central spin model that consists of

N

identical spins coupled to a single distinguishable central spin which arises in physical systems such as circuit-QED and bosonic Josephson junctions coupled to an impurity atom. The model closely corresponds to the Su-Schrieffer-Heeger (SSH) model except that the chain of sites in the SSH model is replaced by a chain of states in Fock space specifying the magnetization. We find that the model accommodates topologically protected eigenstates that are `Bell-cat' states consisting of a Schrödinger cat state of the

N

spins that is maximally entangled with the central spin, and show how this state can be adiabatically created and moved along the chain by driving the central spin. The Bell-cat states are visualized by plotting their Wigner function and we explore their robustness against random noise by solving the master equation for the density matrix. We also explain the essential topological difference between identical spins and the excitations of a bosonic mode.