A Two Subsystem Ground-State Approximation

An approximation hierarchy, called the lattice-path-based subsystem (LPSUB $m$ ) approximation scheme, is described for the coupled-cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin- $\frac{1}{2}$ Heisenberg antiferromagnetic) spin-lattice models, namely, the $\mathit{XXZ}$ and the $\mathit{XY}$ models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization, and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods, and the CCM using the alternative lattice-animal-based subsystem (LSUB $m$ ) and the distance-based subsystem (DSUB $m$ ) schemes. Each of the three CCM schemes (LSUB $m$ , DSUB $m$ , and LPSUB $m$ ) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications.An approximation hierarchy, called the lattice-path-based subsystem (LPSUB$m$) approximation scheme, is described for the coupled-cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-$\frac{1}{2}$ Heisenberg antiferromagnetic) spin-lattice models, namely, the $\mathit{XXZ}$ and the $\mathit{XY}$ models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization, and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods, and the CCM using the alternative lattice-animal-based subsystem (LSUB$m$) and the distance-based subsystem (DSUB$m$) schemes. Each of the three CCM schemes (LSUB$m$, DSUB$m$, and LPSUB$m$) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications.

arXiv:1010.2159Physical Review AApr 29, 201116 citations

Evaluation of ground-state entanglement in spin systems with the random phase approximation

J. M. Matera, R. Rossignoli, N. Canosa

We discuss a general treatment based on the mean field plus random-phase approximation (RPA) for the evaluation of subsystem entropies and negativities in ground states of spin systems. The approach leads to a tractable general method that becomes straightforward in translationally invariant arrays. The method is examined in arrays of arbitrary spin with $\mathit{XYZ}$ couplings of general range in a uniform transverse field, where the RPA around both the normal and parity-breaking mean-field state, together with parity-restoration effects, is discussed in detail. In the case of a uniformly connected $\mathit{XYZ}$ array of arbitrary size, the method is shown to provide simple analytic expressions for the entanglement entropy of any global bipartition, as well as for the negativity between any two subsystems, which become exact for large spin. The limit case of a spin $s$ pair is also discussed.We discuss a general treatment based on the mean field plus random-phase approximation (RPA) for the evaluation of subsystem entropies and negativities in ground states of spin systems. The approach leads to a tractable general method that becomes straightforward in translationally invariant arrays. The method is examined in arrays of arbitrary spin with $\mathit{XYZ}$ couplings of general range in a uniform transverse field, where the RPA around both the normal and parity-breaking mean-field state, together with parity-restoration effects, is discussed in detail. In the case of a uniformly connected $\mathit{XYZ}$ array of arbitrary size, the method is shown to provide simple analytic expressions for the entanglement entropy of any global bipartition, as well as for the negativity between any two subsystems, which become exact for large spin. The limit case of a spin $s$ pair is also discussed.

arXiv:1009.1750Physical Review ANov 29, 201012 citations

The strongly coupled two level system

N. K. Rahman

Physics Letters AAug 1, 19759 citations

Near-Optimal Ground State Preparation

Yu Tong, Lin Lin

Bulletin of the American Physical SocietyMar 19, 20210 citations

Quantum Fisher information and its super additivity in an anisotropic quantum Rabi model

Bo Jiang, Jin‐Hui Wu, Zhihai Wang

Abstract In this paper, we study the additivity of quantum Fisher information (QFI) in a coupled system composed by a two-level system and a bosonic mode, which is described by an anisotropic Rabi model. Utilizing a unitary transformation approach, we obtain the approximate ground state for the global state and the reduced density matrix for each subsystem. We find the additivity of QFI, that is, the summation of QFI for two subsystems is always larger than that of the global system. We hope our work will stimulate the studies of quantum metrology in hybrid system.Abstract In this paper, we study the additivity of quantum Fisher information (QFI) in a coupled system composed by a two-level system and a bosonic mode, which is described by an anisotropic Rabi model. Utilizing a unitary transformation approach, we obtain the approximate ground state for the global state and the reduced density matrix for each subsystem. We find the additivity of QFI, that is, the summation of QFI for two subsystems is always larger than that of the global system. We hope our work will stimulate the studies of quantum metrology in hybrid system.

Laser PhysicsJul 20, 20210 citations

An approximation hierarchy, called the lattice-path-based subsystem (LPSUB

m

) approximation scheme, is described for the coupled-cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-

\frac{1}{2}

Heisenberg antiferromagnetic) spin-lattice models, namely, the

\mathit{XXZ}

and the

\mathit{XY}

models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization, and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods, and the CCM using the alternative lattice-animal-based subsystem (LSUB

m

) and the distance-based subsystem (DSUB

m

) schemes. Each of the three CCM schemes (LSUB

m

, DSUB

m

, and LPSUB

m

) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications.

\mathit{XYZ}

couplings of general range in a uniform transverse field, where the RPA around both the normal and parity-breaking mean-field state, together with parity-restoration effects, is discussed in detail. In the case of a uniformly connected

\mathit{XYZ}

array of arbitrary size, the method is shown to provide simple analytic expressions for the entanglement entropy of any global bipartition, as well as for the negativity between any two subsystems, which become exact for large spin. The limit case of a spin

s

pair is also discussed.