Microscopic Theories of Quantum Lattice Systems

Bishop, R. F.

doi:10.1007/978-1-4615-1937-9_20

Cited by 7 publications

(9 citation statements)

References 133 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The CCM [21][22][23], that we will employ here, has been very successfully applied to many models in quantum magnetism, including models on the honeycomb lattice [10,15,16] of interest here. It provides a well-structured means of studying various candidate GS phases and their regimes of stability, for each of which the description is systematically improvable in terms of well-defined truncation hierarchies for the quantum multispin correlations.…”

Section: Coupled Cluster Methodsmentioning

confidence: 99%

Valence-bond crystalline order in thes= 1/2J₁–J₂model on the honeycomb lattice

Bishop

Campbell

2013

J. Phys.: Condens. Matter

128

View full text Add to dashboard Cite

Using the coupled cluster method we study the phase diagram of the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice with nearest-neighbour exchange coupling J1 > 0 and frustrating next-nearest-neighbour coupling J2 ≡ xJ1 > 0. In the range 0 < x < 1 we find four phases exhibiting respectively Néel, 6-spin plaquette, staggered dimer and Néel-II orderings, with quantum critical points at xc1 ≈ 0.207(3), xc2 ≈ 0.385(10) and xc3 ≈ 0.65(5). The transitions at xc1 and xc3 appear to be continuous (and hence deconfined) ones, while that at xc2 appears to be a direct first-order one.

show abstract

Section: Coupled Cluster Methodsmentioning

confidence: 99%

Valence-bond crystalline order in thes= 1/2J₁–J₂model on the honeycomb lattice

Bishop

Campbell

2013

J. Phys.: Condens. Matter

128

View full text Add to dashboard Cite

show abstract

“…There have been a number of attempts to modify the coupledcluster (CC) theory [1], despite its spectacular success in elucidating the properties of a wide range of many-body systems [1][2][3]. One interesting case in point is the unitary coupled-cluster (UCC) theory which was first considered by Mukherjee et al [4] and later developed by Kutzelnigg [5].…”

Section: Introductionmentioning

confidence: 99%

Relativistic unitary coupled cluster theory and applications

Sur

Chaudhuri

Sahoo

et al. 2008

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

We present the first formulation and application of relativistic unitary coupled cluster theory to atomic properties. The remarkable features of this theory are highlighted, and it is used to calculate the lifetimes of 5 2 D 3/2 and 6 2 P 3/2 states of Ba + and P b + respectively. The results clearly suggest that it is very well suited for accurate ab initio calculations of properties of heavy atomic systems.PACS numbers: 31.15. Ar, 31.15.Dv, 31.25.Jf, 32.10.Fn There have been a number of attempts to modify coupled-cluster (CC) theory [1], despite its spectacular success in elucidating the properties of a wide range of many-body systems [1,2,3,4,5]. One interesting case in point is unitary coupled-cluster (UCC) theory which was first proposed by Kutzelnigg [6]. In this theory, the effective Hamiltonian is Hermitian by construction and the energy which is the expectation value of this operator in the reference state is unlike in CC theory, an upper bound to the ground state energy [5]. Another attractive feature of this theory which we shall discuss later is that at a given level of approximation it incorporates certain higher order excitations that are not present in CC theory. Furthermore, it is well suited for the calculation of properties where core relaxation effects are important [7,8]. In spite of the aforementioned advantages, there have been relatively few studies based on this method [9,10]. This work is the first relativistic formulation of unitary coupled cluster (UCC) theory and also the first application of this theory to atomic properties. In this letter, we first present the formal aspects of relativistic UCC theory and then apply it to calculate the lifetimes of the 5 2 D 3/2 and 6 2 P 3/2 states of Ba + and P b + respectively; which depend strongly on both relativistic and correlation effects. The comparison of the results of these calculations with accurate experimental data would constitute an important test of this theory.The exact wave function for a closed shell state in CC theory is obtained by the action of the operator exp(T ) on the reference state |Φ . However, in UCC theory [10], it is written aswhere σ = T − T † ; and T and T † are the excitation and deexcitation operators respectively. σ is clearly antiHermitian, since σ † = −σ. Using this unitary ansatz for the correlated wave function, the relativistic UCC equation in the Dirac-Coulomb approximation can be written aswhere H is the Dirac-Coulomb HamiltonianUsing the normal ordered Hamiltonian, Eq.(2) can be rewritten aswhere the normal ordered Hamiltonian is defined as H N = H − Φ| H |Φ and ∆E = E − Φ| H |Φ . . The choice of the operator σ makes the effective Hamiltonian H N = exp(−σ)H N exp(σ) Hermitian.The effective Hamiltonian is expressed by the Hausdorff expansion in CC theory as

show abstract

“…The CCM (see, e.g., refs. [29][30][31] and references cited therein) employed here is one of the most powerful and most versatile modern techniques in quantum many-body theory. It has been successfully applied to various quantum magnets (see refs.…”

mentioning

confidence: 99%

“…We now briefly describe the CCM means to solve the ground-state (gs) Schrödinger ket and bra equations, H|Ψ = E|Ψ and Ψ|H = E Ψ|, respectively, (and see refs. [29][30][31][32][33][34] The ket-and bra-state correlation coefficients (S I , SI ) are calculated by requiring the gs energy expectation value H ≡ Ψ|H|Ψ to be a minimum with respect to each of them. This immediately yields the coupled set of equations Φ|C − I e −S He S |Φ = 0 and Φ| S(e −S He S − E)C + I |Φ = 0 ; ∀I = 0, which we solve in practice for the correlation coefficients (S I , SI ) within specific truncation schemes described below, by making use of parallel computing routines [36].…”

mentioning

confidence: 99%

The quantum J ₁ –J ₁ ′–J ₂ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D

Bishop¹,

Li²,

Darradi³

et al. 2008

Europhys. Lett.

View full text Add to dashboard Cite

We study the phase diagram of the isotropic J1-J 1 -J2 Heisenberg model for spin-1 particles on an anisotropic square lattice, using the coupled-cluster method. We find no evidence for an intermediate phase between the Néel and stripe states, as compared with all previous results for the corresponding spin-1/2 case. However, we find a quantum tricritical point at J 1 /J1 ≈ 0.66 ± 0.03, J2/J1 ≈ 0.35 ± 0.02, where a line of second-order phase transitions between the quasi-classical Néel and stripe-ordered phases (for J 1 /J1 0.66) meets a line of first-order phase transitions between the same two states (for J 1 /J1 0.66).

show abstract

Microscopic Theories of Quantum Lattice Systems

Cited by 7 publications

References 133 publications

Valence-bond crystalline order in thes= 1/2J₁–J₂model on the honeycomb lattice

Valence-bond crystalline order in thes= 1/2J₁–J₂model on the honeycomb lattice

Relativistic unitary coupled cluster theory and applications

The quantum J ₁ –J ₁ ′–J ₂ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D

Contact Info

Product

Resources

About

Microscopic Theories of Quantum Lattice Systems

Cited by 7 publications

References 133 publications

Valence-bond crystalline order in thes= 1/2J1–J2model on the honeycomb lattice

Valence-bond crystalline order in thes= 1/2J1–J2model on the honeycomb lattice

Relativistic unitary coupled cluster theory and applications

The quantum J 1 –J 1 ′–J 2 spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D

Contact Info

Product

Resources

About

Valence-bond crystalline order in thes= 1/2J₁–J₂model on the honeycomb lattice

Valence-bond crystalline order in thes= 1/2J₁–J₂model on the honeycomb lattice

The quantum J ₁ –J ₁ ′–J ₂ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D