Quasiparticle Operators Research Articles

Photoassisted current in the fractional quantum Hall effect as a probe of the quasiparticle operator scaling dimension

Photoassisted current in the fractional quantum Hall effect as a probe of the quasiparticle operator scaling dimension

Multibody expansion of the local integrals of motion: how many pairs of particle-hole do we really need to describe the quasiparticles in the many-body localized phase?

The emergent integrability in a many-body localized (MBL) system can be well characterized by the existence of the complete set of local integrals of motion (LIOMs). Such exactly conserved and exponentially localized operators are often understood as quasiparticle operators which can be expanded in terms of single-particle operators dressed with different numbers of particle-hole pairs. Here, we consider a one-dimensional XXZ spin- Heisenberg chain in the presence of a random field and try to quantify the corrections needed to be considered in the picture of quasiparticles associated with LIOMs due to the presence of particle-hole excitations. To this end, we explicitly present the multibody expansion of LIOM creation operators of the system in the MBL regime. We analytically obtain the coefficients of this expansion and discuss the effect of higher-order corrections associated with different numbers of particle-hole excitations. Our analysis shows that depending on the localization length of the system, there exist a regime in which the contributions that come from higher-order terms can break down the effective one-particle description of the LIOMs and such quasiparticles become essentially many-body-like.

Multinucleon excitations in neutrino–nucleus scattering: connecting different microscopic models for the correlations

The problem of nucleon-nucleon correlations and meson exchange currents has been vividly debated in connection with the neutrino-nucleus cross sections. In this work we focus on nucleon-nucleon correlations by discussing a formal correspondence between the approaches based on independent particles and the ab initio approaches involving correlated wave functions. We use a general technique based on unitary transformation mapping the Fermion operators relative to bare nucleons into quasi-particle operators relative to dressed nucleons. We derive formulas for spectral functions, response functions, momentum distribution, separation energy, general enough to be applied with any kind of effective nucleon-nucleon interaction. We establish the relation between the non-energy-weighted sum rule and the Fermi sea depopulation. With our tools we evaluate whether approaches based on effective interactions are compatible with the expected amount of correlations coming from ab initio calculations. For this purpose we use as a test the Fermi sea depopulation and the value of the kinetic energy per nucleon.

Bridging the quartet and pair pictures of isovector proton-neutron pairing

The formal implications of a quartet coherent-state ansatz for proton-neutron pairing are analyzed. Its nonlinear annihilation operators, which generalize the BCS linear quasiparticle operators, are computed in the quartetting case. Their structure is found to generate nontrivial relationships between the many-body correlation functions. The intrinsic structure of the quartet coherent state is detailed as it hints to the precise correspondence between the quartetting picture and the symmetry restored pair condensate picture for the proton-neutron pairing correlations.

Electron-Phonon Coupling from AbInitio Linear-Response Theory within the GW Method: Correlation-Enhanced Interactions and Superconductivity in Ba_{1-x}K_{x}BiO_{3}.

We present a new first-principles linear-response theory of changes due to perturbations in the quasiparticle self-energy operator within the GW method. This approach, named GW perturbation theory (GWPT), is applied to calculate the electron-phonon (e-ph) interactions with the full inclusion of the GW nonlocal, energy-dependent self-energy effects, going beyond density-functional perturbation theory. Avoiding limitations of the frozen-phonon technique, GWPT gives access to e-ph matrix elements at the GW level for all phonons and scattering processes, and the computational cost scales linearly with the number of phonon modes (wave vectors and branches) investigated. We demonstrate the capabilities of GWPT by studying the e-ph coupling and superconductivity in Ba_{0.6}K_{0.4}BiO_{3}. We show that many-electron correlations significantly enhance the e-ph interactions for states near the Fermi surface, and explain the observed high superconductivity transition temperature of Ba_{0.6}K_{0.4}BiO_{3} as well as its doping dependence.

A study of shell structure in normal to exotic nuclides within relativistic Hartree–Bogoliubov approximation

The purpose of this work is to study theoretically the shell structure of even–even isotopes in Si, S, Ar and Ca and isotones at neutron number N = 0, 28, 50 and 82. We employed Covariant Relativistic self-consistent mean field models analogous to Kohn–Sham density functional theory to construct the Nuclear Density Functionals from Lagrangian densities based on meson exchange and point coupling models. The pairing correlations of nucleons are considered by the relativistic Hartree–Bogoliubov functional based on quasi-particle operators of Bogoliubov transformations. The theoretical calculations of shell closure parameter [Formula: see text](N) and the differential variation of the two-neutron separation energy [Formula: see text](Z, N) provide recognizable signature of shell closure at N = 14 and 20 in case of Si, N = 14, 20 and 28 in S, Ar and Ca isotopes and are consistent with recent experimental investigations of new sub-shell gaps.

Generalization of Laughlin’s theory for the fractional quantum Hall effect

Motivated by the structure of the quasiparticle wavefunction in the composite fermion (CF) theory for fractional quantum Hall filling factor (m odd), I consider a suitable quasiparticle operator in differential form, as a modified form of Laughlin’s quasiparticle operator, that reproduces quasiparticle wave function as predicted in the CF theory, without a priori assumption of the presence of CFs. I further consider the conjugate of this operator as quasihole operator for obtaining a novel quasihole wave function for 1/m state. Each of these wave functions is interpreted as expelling an electron into a different Hilbert subspace from the original Hilbert space of the Laughlin condensate while still maintaining its correlation (although changed) with the electrons in the condensate such that the expelled electron behaves as a CF with respect to the electrons in the condensate. With this interpretation, I show that the ground state wavefunctions for general states at filling fractions , respectively, can be constructed as coherent superposition of n coupled Laughlin condensates and their ‘conjugates’, formed at different Hilbert subspaces. The corresponding wave functions, specially surprising for sequence of states, are identical with those proposed in the theory of noninteracting CFs. The states which were considered as fractional quantum Hall effect of interacting CFs, can also be treated in the same footing as for the prominent sequences of states describing as the coupled condensates among which one is a non-Laughlin condensate in a different Hilbert subspace. Further, I predict that the half filling of the lowest Landau level is a quantum critical point for phase transition between two topologically distinct phases each corresponding to a family of states: one consists of large number of coupled Laughlin condensates of filling factor 1/3 and the other corresponds to large number of coupled conjugate Laughlin condensates of filling factor 1, which may be distinguished, respectively, by the absence and presence of upstream edge modes.

Universal spectral signatures in pnictides and cuprates: the role of quasiparticle-pair coupling

Understanding the physical properties of a large variety of high-Tc superconductors (SC), the cuprate family as well as the more recent iron-based superconductors, is still a major challenge. In particular, these materials exhibit the ‘peak-dip-hump’ structure in the quasiparticle density of states (DOS). The origin of this structure is explained within our pair–pair interaction (PPI) model: The non-superconducting state consists of incoherent pairs, a ‘Cooper-pair glass’ which, due to the PPI, undergoes a Bose-like condensation below Tc to the coherent SC state. We derive the equations of motion for the quasiparticle operators showing that the DOS ‘peak-dip-hump’ is caused by the coupling between quasiparticles and excited pair states, or ‘super-quasiparticles’. The renormalized SC gap function becomes energy-dependent and non retarded, reproducing accurately the experimental spectra of both pnictides and cuprates, despite the large difference in gap value.

Quasiparticle operators for high-temperature cuprate superconductors

A complete set of quasiparticle operators diagonalizing operators of the Coulomb and exchange interactions of copper and oxygen holes in cuprate high-temperature superconductors (HTSCs) is obtained. A scheme of energy bands in the regime of strong electron correlations is constructed. The effective operator for the singleband approximation is obtained with this scheme. It is found that the role of three-site correlations in hole HTSCs is negligibly small. This circumstance explains both the sharp increase in critical temperatures of hole HTSCs in comparison with electron-doped ones and the asymmetry between the spectra of collective spin excitations in these compounds.

A novel quantum field approach to photoexcited insulators

In order to predict optical properties of insulating materials under intensive laser excitation, we generalized methods of quantum electrodynamics, allowing us to simulate excitation of electrons and holes, interacting with each other and acoustic phonons. The prototypical model considers a two-band dielectric material characterized by the dispersion relations for electron and hole states. We developed a universal description of excited electrons, holes and acoustic phonons within joint quantum kinetics formalism. Illustrative solutions for the quasiparticle birth-annihilation operators, applicable at short laser pulses at 0 K, are obtained by the transition from the macroscopic description to the quantum field formalism.

Multiband superconductivity with competing intra- and interband pair channels

In multiband superconductivity interband interaction channels creating the pairs of intraband [Formula: see text] and interband [Formula: see text] compositions can appear. Simultaneous functioning of these channels is investigated here. A three-band model where two similar bands [Formula: see text] interact with the itinerant-band has been proposed. The mean field Hamiltonian incorporates three order parameters [Formula: see text]; [Formula: see text]; [Formula: see text] genetically associated with dispersive bands. Calculated quasiparticle energies and operator averages lead to a coupled nonlinear equation system for the order parameters. Illustrative calculations versus temperature have been made for overlapping bands. At fixed parameters, the basic system has two independent solutions. The free energy has a complicated structure of extremal points. The interaction of channels with intra- and interband points is seen. These channels compete in general. From the point where the gap, type parameters associated with one channel become zero, the other continues as the first channel was logged out. The general behaviour of order parameters distribution is very sensible to [Formula: see text]. Events of critical nature appear. Weakening of [Formula: see text] stimulates the formation of closed bubbles built up by the same type parameters from different parallel solutions.

Non-equilibrium thermo-field dynamics for anti-ferromagnetic spin system

The non-equilibrium thermo-field dynamics for an anti-ferromagnetic spin system interacting with a phonon reservoir is proposed for the case of a non-bilinear unperturbed Hamiltonian, which includes not only a bilinear part but also a non-bilinear part, in the spin–wave approximation. The two kinds of quasi-particle operators are introduced, and their forms are derived for the semi-free boson fields. It is shown that the two quasi-particles decay exponentially with the frequencies and life-times which are different from each other. It is also shown that each quasi-particle changes to the other tilde quasi-particle through the spin–phonon interaction. The spin–spin correlation functions and longitudinal magnetization for the anti-ferromagnetic spin system under an external static magnetic field are derived in the forms convenient for the perturbation expansions. The expectation values of the spin–wave energy and longitudinal magnetization and the spin–spin correlation functions are investigated numerically for an anti-ferromagnetic system of one-dimensional infinite spins interacting with a damped phonon-reservoir, in the region valid for the lowest spin–wave approximation and the narrowing-limit approximation in which the relaxation times of the spin system are much larger than the correlation time of the phonon reservoir. The two-point Green’s function of the semi-free spin–wave for the anti-ferromagnetic spin system is derived by introducing the thermal quartet notation, and it is given in a form of 4×4 matrix.

A second-order multi-reference quasiparticle-based perturbation theory

The purpose of this paper is to introduce a second-order perturbation theory derived from the mathematical framework of the quasiparticle-based multi-reference coupled-cluster approach (Rolik and Kallay in J Chem Phys 141:134112, 2014). The quasiparticles are introduced via a unitary transformation which allows us to represent a complete active space reference function and other elements of an orthonormal multi-reference basis in a determinant-like form. The quasiparticle creation and annihilation operators satisfy the fermion anti-commutation relations. As the consequence of the many-particle nature of the applied unitary transformation these quasiparticles are also many-particle objects, and the Hamilton operator in the quasiparticle basis contains higher than two-body terms. The definition of the new theory strictly follows the form of the single-reference many-body perturbation theory and retains several of its beneficial properties like the extensivity. The efficient implementation of the method is briefly discussed, and test results are also presented.

Application of the Dyson-type boson mapping for low-lying electron excited states in molecules

In this paper, we propose a bosonization method of the system in which a quasi-particle consists of electron-hole pairs. Electron excitation energies of low-lying electron excited states are obtained by finding out the quantized normal mode oscillations around a ground state in the molecular electronic structure. These excited states are approximately considered as the collective motion states of the quasi-particles that correspond to the quantized normal mode oscillations, and each of these quasi- particles consists of the electron-hole pairs. We introduce the quasi-particle operators which create the low-lying electron excited states. These introduced quasi-particle operators, however, do not satisfy the commutation relations as bosons. Therefore, by using the Dyson-type boson mapping method, we transform these operators into those which satisfy exactly the boson commutation relations. We discuss how to map the operators of the fermion space onto the Dyson-type boson space, and obtain the Dyson-type boson representation Hamiltonian. By using this Hamiltonian, we discuss the low-lying excited states as a many-body problem of the boson system. We apply this method to the π-electrons system of the ethylene molecule, and obtain the low-lying electronexcitedstateenergiesintherandom-phaseapproximation(RPA).Inthenextstep,toimprove the accuracy of the these obtained excitation energy values, we carry out additional calculations by

A quasiparticle-based multi-reference coupled-cluster method.

The purpose of this paper is to introduce a quasiparticle-based multi-reference coupled-cluster (MRCC) approach. The quasiparticles are introduced via a unitary transformation which allows us to represent a complete active space reference function and other elements of an orthonormal multi-reference (MR) basis in a determinant-like form. The quasiparticle creation and annihilation operators satisfy the fermion anti-commutation relations. On the basis of these quasiparticles, a generalization of the normal-ordered operator products for the MR case can be introduced as an alternative to the approach of Mukherjee and Kutzelnigg [Recent Prog. Many-Body Theor. 4, 127 (1995); Mukherjee and Kutzelnigg, J. Chem. Phys. 107, 432 (1997)]. Based on the new normal ordering any quasiparticle-based theory can be formulated using the well-known diagram techniques. Beyond the general quasiparticle framework we also present a possible realization of the unitary transformation. The suggested transformation has an exponential form where the parameters, holding exclusively active indices, are defined in a form similar to the wave operator of the unitary coupled-cluster approach. The definition of our quasiparticle-based MRCC approach strictly follows the form of the single-reference coupled-cluster method and retains several of its beneficial properties. Test results for small systems are presented using a pilot implementation of the new approach and compared to those obtained by other MR methods.

Linearizing neutrino evolution equations includingνν¯pairing correlations

We linearize the neutrino mean-field evolution equations describing the neutrino propagation in a background of matter and of neutrinos, using techniques from many-body microscopic approaches. The procedure leads to an eigenvalue equation that allows to identify instabilities in the evolution, associated with a change of the curvature of the neutrino energy-density surface. Our result includes all contributions from the neutrino Hamiltonian and is generalizable to linearize the equations of motion at an arbitrary point of the evolution. We then consider the extended equations that comprise the normal mean field as well as the abnormal mean field that is associated with neutrino-antineutrino pairing correlations. We first re-derive the extended neutrino Hamiltonian and show that such a Hamiltonian can be diagonalized by introducing a generalized Bogoliubov-Valatin transformation with quasi-particle operators that mix neutrinos and antineutrinos. We give the eigenvalue equations that determine the energies of the quasi-particles eigenstates. Finally we derive the eigenvalue equation of the extended equations of motion, valid in the small amplitude approximation. Our results apply to an arbitrary number of neutrino families.

Theory of fractional quantum Hall interferometers

Interference of fractionally charged quasi-particles is expected to lead to Aharonov-Bohm oscillations with periods larger than the flux quantum. However, according to the Byers-Yang theorem, observables of an electronic system are invariant under an adiabatic insertion of a quantum of singular flux. We resolve this seeming paradox by considering a microscopic model of electronic interferometers made from a quantum Hall liquid at filling factor 1/m. An approximate ground state of such interferometers is described by a Laughlin type wave function, and low-energy excitations are incompressible deformations of this state. We construct a low-energy effective theory by restricting the microscopic Hamiltonian of electrons to the space of incompressible deformations and show that the theory of the quantum Hall edge so obtained is a generalization of a chiral conformal field theory. In our theory, a quasi-particle tunneling operator is found to be a single-valued function of tunneling point coordinates, and its phase depends on the topology determined by the positions of Ohmic contacts. We describe strong coupling of the edge states to Ohmic contacts and the resulting quasi-particle current through the interferometer with the help of a master equation. We find that the coherent contribution to the average quasi-particle current through Mach-Zehnder interferometers does not vanish after summation over quasi-particle degrees of freedom. However, it acquires oscillations with the electronic period, in agreement with the Byers-Yang theorem. Importantly, our theory does not rely on any ad-hoc constructions, such as Klein factors, etc. When the magnetic flux through an FP interferometer is varied with a modulation gate, current oscillations have the quasi-particle periodicity, thus allowing for spectroscopy of quantum Hall edge states.

Non-Equilibrium Thermo-Field Dynamics for a Fourth-Order Hamiltonian

The non-equilibrium thermo-field dynamics proposed by Arimitsu and Umezawa are generalized to the case of a fourth-order unperturbed Hamiltonian which includes not only a second-order (quadratic) part but also a fourth-order part. Fujita’s analysis for effects of the initial particle correlation of a quantum gas is proved generally in terms of TFD. The forms of the quasi-particle operators for a semi-free boson field are derived. It is shown that the energies and life-times of the quasi-particles depend on the adiabatic boson-reservoir interaction which leads to the fourth-order part of the unperturbed Hamiltonian. The form of the two-point Green’s function for the semi-free boson field is evaluated. A form of the admittance for a boson system interacting with its heat reservoir, which includes effects of the initial correlation and memory, is derived using the TCLE method formulated in terms of the generalized non-equilibrium thermo-field dynamics. A calculation method of the higher-order parts of the admittance in powers of the boson-boson interaction is given. Furthermore, a calculation method of the perturbation expansions of the two-point Green’s function for the boson system is given. Subject Index: 130

Non-equilibrium thermo-field dynamics for a non-bilinear Hamiltonian

The non-equilibrium thermo-field dynamics proposed by Arimitsu and Umezawa are generalized to the case of a non-bilinear unperturbed Hamiltonian which includes not only a bilinear part but also a non-bilinear part with momentum mixing. The forms of the quasi-particle operators for a semi-free boson field are derived. The form of the two-point Green’s function for the semi-free boson field is evaluated. A form of the admittance for a boson system interacting with its heat reservoir, which includes effects of the initial correlation and memory, is derived using the TCLE method formulated in terms of generalized non-equilibrium thermo-field dynamics. The expressions of the zeroth-order, first-order and second-order parts of the admittance in powers of the boson–boson interaction, are derived.

Effects of ground state correlations on the structure of odd-mass spherical nuclei

It is well known that the Pauli principle plays a substantial role at low energies because the quasiparticle and phonon operators, used to describe them, are built of fermions and as a consequence they are not ideal bosons. The correct treatment of this problem requires calculation of the exact commutators between the quasiparticle and phonon operators and in this way to take into account the Pauli principle corrections. In addition to the correlations due to the quasiparticle interaction in the ground-state influence the single-particle fragmentation as well. In this article, we generalize the basic equations of the quasiparticle-phonon nuclear model to account for both effects mentioned above. As an illustration of our approach, calculations of the structure of the low-lying states in the odd-mass nuclei $^{131\ensuremath{-}137}\mathrm{Ba}$ have been performed.