Brillouin-Wigner Methods for Many-Body Systems

We study the quasiparticle spectrum of 2D topological s-wave superconductors with the Zeeman magnetic field and the Rashba spin-orbit coupling in the presence of spatial inhomogeneity. Solving the real-space Bogoliubov-de Gennes equations, we focus on the excitations within the superconducting gap amplitude, i.e., the appearance of mid-gap states. Two kinds of potential functions, line-type (a chain of impurities) and point-type (a single impurity) ones are examined to take spatial inhomogeneity into account. The line setting shows a link of the mid-gap states with the gapless surface modes indicated by the bulk-boundary correspondence in topological superfluid. The point one shows that the quasiparticles with mid-gap energy are much easily excited by an impurity when the Zeeman magnetic field increases within the topological number to be unchanged. Thus, we obtain insights into the robustness of a topological superconductor against non-magnetic impurities. Moreover, we derive an effective theory applicable to high magnetic fields. The effective gap is the mixture of the chiral p-wave and s-wave characters. The former is predominant when the magnetic field increases. Therefore, we claim that a chiral p-wave character of the effective gap function creates the mid-gap states.

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“…(A·1) in Appendix . Then, the 2nd-order Brillouin-Wigner approach 31 leads to an effective Hamiltonian,…”

Section: Mixture Of Chiral P-wave and S-wave Componentsmentioning

confidence: 99%

Topological s-Wave Pairing Superconductivity with Spatial Inhomogeneity: Midgap-State Appearance and Robustness of Superconductivity

2015

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“…In Sec. II, we introduce our model and numerically calculate the bound states of the SC, which is further confirmed by the Brillouin-Wigner perturbation theory [18]. Based on the single-photon scattering mechanism given in Sec.…”

Section: Introductionmentioning

confidence: 61%

“…We hope that our work will stimulate the further studies on multi-photon scattering effects induced by the CRW interaction in many diverse systems. To study the bound state, we have resort to BrillouinWigner perturbation theory [18] instead of the RayleighSchrödinger perturbation theory [23] in that the former will essentially avoid the possible divergences.…”

Section: Discussionmentioning

confidence: 99%

Single-photon scattering with counter rotating wave interaction

Zhu

Wang

et al. 2017

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

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Recent experiments have pushed the studies on atom-photon interactions to the ultrastrong regime, which motivates the exploration of physics beyond the rotation wave approximation. Here we study the single-photon scattering on a system composed by a coupling cavity array with a two-level atom in the center cavity, which, by varying two outside coupling parameters, corresponds to a model from a supercavity QED to a waveguide QED with counter-rotating wave (CRW) interaction. By applying a time-independent scattering theory based on the bound states in the scattering region, we find that the CRW interaction obviously changes the transmission valley even in the weak atom-cavity coupling regime; In particular, the CRW interaction leads to an inelastic scattering process and a Fano-type resonance, which is directly observed in the crossover from the supercavity QED case to the waveguide QED case. Predictably, our findings provide the potential of manipulating the CRW effects in realistic systems.

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“…In contrast to the SU CC methods, the wave operator U i (as well as the cluster operator) now carries the index of the target state i. This equation played the role of Bloch equation for the BWCC theory [141] and it is, of course, equivalent to the Schrödinger equation for the state |Ψ i . It turns out that the derivation of the amplitude equations is actually simpler if one inserts the JM Ansatz (17-19) with a SS wave operator U j directly into the Schrödinger equation (H − E j )|Ψ j = 0, which yields…”

Section: Brillouin -Wigner Mr CC Methodsmentioning

confidence: 98%

“…For a recent detailed account of BW MBPTbased approaches we refer the reader to a forthcoming monograph by Hubač and Wilson [141].…”

Section: Brillouin -Wigner Mr CC Methodsmentioning

confidence: 99%

Multireference Coupled-Cluster Methods: Recent Developments

Paldus

Pittner

Čárský

2010

Challenges and Advances in Computational Chemistry and Physics

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Abstract:The objective of this paper is to provide an overview of various multi-reference (MR) coupled-cluster (CC) approaches, particularly those relating to our own research. Although MR CC methods have been around for almost three decades and much work has been expended on their development and implementation, no general purpose codes are presently available. In view of the complexity, inherent difficulties, and computational demands of both genuine valence and state universal (VU and SU) MR CC methods, attention has been directed towards the state selective or state specific (SS) approaches that focus on one state at a time. These methods are based on either the genuine MR CC formalism or on a singlereference (SR) CC Ansatz, in which higher-than-pair clusters are accounted for by relying on basic ideas of general MR approaches. This is achieved either internally by relying on CC or MBPT formalism or by exploiting some external source providing approximate values of these clusters and accomplished by either correcting equations yielding the cluster amplitudes or directly by evaluating the corrections to the CCSD energy. Nowadays there exists a whole plethora of such various approaches for handling of quasi-degenerate states with a various degree of MR character and our goal is to outline their basic features and comment on their pro's and con's, their usefulness and weaknesses, as well as point out their mutual relationship.

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Brillouin-Wigner Methods for Many-Body Systems

Cited by 56 publications

References 0 publications

Topological s-Wave Pairing Superconductivity with Spatial Inhomogeneity: Midgap-State Appearance and Robustness of Superconductivity

Topological s-Wave Pairing Superconductivity with Spatial Inhomogeneity: Midgap-State Appearance and Robustness of Superconductivity

Single-photon scattering with counter rotating wave interaction

Multireference Coupled-Cluster Methods: Recent Developments

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