Low-energy Excitation Spectrum Research Articles

From the Jaynes–Cummings–Hubbard to the Dicke model

We discuss the Jaynes–Cummings–Hubbard model describing the superfluid–Mott insulator transition of polaritons (i.e., dressed photon–qubit states) in coupled qubit–cavity arrays in the crossover from strong to weak correlations. In the strongly correlated regime the phase diagram and the elementary excitations of lattice polaritons near the Mott lobes are calculated analytically using a slave-boson theory (SBT). The opposite regime of weakly interacting polariton superfluids is described by a weak-coupling mean-field theory for a generalized multi-mode Dicke model. We show that a remarkable relation between the two theories exists in the limit of large photon bandwidth and large negative detuning, i.e., when the nature of polariton quasiparticles becomes qubit-like. In this regime, the weak-coupling theory predicts the existence of a single Mott lobe with a change of the universality class of the phase transition at the tip of the lobe, in perfect agreement with the SBT. Moreover, the spectra of low energy excitations, i.e., the sound velocity of the Goldstone mode and the gap of the amplitude mode match exactly as calculated from both theories.

Conserving and gapless Hartree-Fock-Bogoliubov theory for the three-dimensional dilute Bose gas

The excitation spectrum for the three-dimensional Bose gas in the Bose-Einstein condensation phase is calculated nonperturbatively with the modified Hartree-Fock-Bogoliubov theory, which is both conserving and gapless. From improved $\ensuremath{\Phi}$-derivable theory, the diagrams needed to preserve the Ward-Takahashi identity are re-summed in a systematic and nonperturbative way. It is valid up to the critical temperature where the dispersion relation of the low-energy excitation spectrum changes from linear to quadratic. Because including the higher-order fluctuation, the results show significant improvement on the calculation of the shift of critical temperature with other conserving and gapless theories.

Microscopic analysis of the octupole phase transition in Th isotopes

A shape phase transition between stable octupole deformation and octupole vibrations in Th nuclei is analyzed in a microscopic framework based on nuclear density functional theory. The relativistic functional DD-PC1 is used to calculate axially-symmetric quadrupole-octupole constrained energy surfaces. Observables related to order parameters are computed using an interacting-boson Hamiltonian, with parameters determined by mapping the microscopic energy surfaces to the expectation value of the Hamiltonian in the boson condensate. The systematics of constrained energy surfaces and low-energy excitation spectra point to the occurrence of a phase transition between octupole-deformed shapes and shapes characterized by octupole-soft potentials.

Microscopic properties of the pinwheel kagome compound Rb(2)Cu(3)SnF(12).

Using (63,65)Cu nuclear magnetic resonance in magnetic fields up to 30 T, we study the microscopic properties of the 12-site valence-bond-solid ground state in the "pinwheel" kagome compound Rb(2)Cu(3)SnF(12). We find that the ground state is characterized by a strong transverse staggered spin polarization whose temperature and field dependence points to a mixing of the singlet and triplet states. This is further corroborated by the field dependence of the gap Δ(H), which has a level anticrossing with a large minimum gap value of ≈ Δ(0)/2, with no evidence of a phase transition down to 1.5 K. By the exact diagonalization of small clusters, we show that the observed anticrossing is mainly due to staggered tilts of the g tensors defined by the crystal structure and reveal symmetry properties of the low-energy excitation spectrum compatible with the absence of level crossing.

The Excitation Spectrum for Weakly Interacting Bosons in a Trap

We investigate the low-energy excitation spectrum of a Bose gas confined in a trap, with weak long-range repulsive interactions. In particular, we prove that the spectrum can be described in terms of the eigenvalues of an effective one-particle operator, as predicted by the Bogoliubov approximation.

Evolution from a nodeless gap to d(x(2)-y(2))-wave in underdoped La(2-x)Sr(x)CuO4.

Using angle-resolved photoemission spectroscopy (ARPES), it is revealed that the low-energy electronic excitation spectra of highly underdoped superconducting and nonsuperconducting La(2-x)Sr(x)CuO(4) cuprates are gapped along the entire underlying Fermi surface at low temperatures. We show how the gap function evolves to a d(x(2)-y(2)) form with increasing temperature or doping, consistent with the vast majority of ARPES studies of cuprates. Our results provide essential information for uncovering the symmetry of the order parameter(s) in strongly underdoped cuprates, which is a prerequisite for understanding the pairing mechanism and how superconductivity emerges from a Mott insulator.

Extended random phase approximation method for atomic excitation energies from correlated and variationally optimized second-order density matrices

Density matrix methods are typically ground state methods. They cannot describe excited states with the same symmetry as the ground state because they rely on energy minimization. The Random Phase Approximation (RPA) is a simple method to derive excitation energies from idempotent first-order density matrices, but the quality of the resulting excitation energies is poor. The quality of the excitation spectrum may be improved by extending the RPA to correlated states. Such an ‘extended RPA’ (ERPA) method depends only on the second-order density matrix (2DM). This work studies the main differences between the ERPA and the RPA – the influence of electron correlation, variational optimality, the ensemble nature of the density matrix and N-representability errors in the input 2DM – by applying the ERPA to exact 2DM’s and variationally optimized 2DM’s. Our findings are relevant for all methods similar to ERPA that determine excitation spectra from low-order density matrices. The inclusion of correlation makes it possible to describe the low-energy excitation spectra of the atoms He–Ne adequately, and the ERPA is thus a good starting point for further refinements, as higher-order excitations should be included to obtain chemical accuracy for many-electron systems. However, the ERPA fails for ensemble density matrices and requires a positive-definite double commutator matrix Ψ0ak†al,H,aj†aiΨ0 to guarantee that the excitation spectrum is real.

Rattler model of the boson peak at silica surfaces

Recent experiments unveiled two new aspects of the low-energy excitation spectrum of silica glass--commonly termed as the "boson peak" region. The first is that at low temperature the silica surface exhibits a different, softer boson peak than the bulk. The second is a giant thermal blueshift of the surface boson peak frequency causing it to cross and overcome the bulk peak with increasing temperature. Here we present a simple lattice model that reproduces this behavior in all its aspects. Each site consists of rigid tetrahedral units softly connected so as to be able to rotate anharmonically as "rattlers" in their cages. As shown by simulations, the model dynamics exhibits a boson-like peak, which has lower frequency at the surface where rattlers have a weaker restoring force. Upon heating however the larger angular freedom of surface units allows them to rattle more than in the bulk, leading to a steeper frequency increase similar to experiment.

Collective excitations and stability of the excitonic phase in the extended Falicov-Kimball model

We consider the excitonic insulator state (often associated with electronic ferroelectricity), which arises on the phase diagram of an extended spinless Falicov-Kimball model (FKM) at half-filling. Within the Hartree--Fock approach, we calculate the spectrum of low-energy collective excitations in this state up to second order in the narrow-band hopping and/or hybridization. This allows to probe the mean-field stability of the excitonic insulator. The latter is found to be unstable when the case of the pure FKM (no hybridization with a fully localized band) is approached. The instability is due to the presence of another, lower-lying ground state and not to the degeneracy of the excitonic phase in the pure FKM. The excitonic phase, however, may be stabilized further away from the pure FKM limit. In this case, the low-energy excitation spectrum contains important information about the properties of the excitonic condensate (including the strongly suppressed critical temperature).

Phase Transition of Light in Cavity QED Lattices

Systems of strongly interacting atoms and photons, which can be realized wiring up individual cavity QED systems into lattices, are perceived as a new platform for quantum simulation. While sharing important properties with other systems of interacting quantum particles, here we argue that the nature of light-matter interaction gives rise to unique features with no analogs in condensed matter or atomic physics setups. By discussing the physics of a lattice model of delocalized photons coupled locally with two-level systems through the elementary light-matter interaction described by the Rabi model, we argue that the inclusion of counterrotating terms, so far neglected, is crucial to stabilize finite-density quantum phases of correlated photons out of the vacuum, with no need for an artificially engineered chemical potential. We show that the competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z(2) parity symmetry-breaking quantum criticality between two gapped phases that share similarities with the Dicke transition of quantum optics and the Ising critical point of quantum magnetism. We discuss the phase diagram as well as the low-energy excitation spectrum and present analytic estimates for critical quantities.

Revealing the insulating gap in α′-NaV 2O5 with resonant inelastic x-ray scattering

We measured the low energy excitation spectrum of α′-NaV 2O5 across its charge ordering and crystallographic phase transition with resonant inelastic x-ray scattering (RIXS) at the V L3 edge. Exploiting the polarization dependence of the RIXS signal and the high resolution of the data, we reveal the excitation across the insulating gap at 1 eV and identify the excitations from occupied 3dxy bonding orbitals to unoccupied bonding 3dxy and 3dyz/3dxz orbitals. Furthermore we observe a progressive change of the electronic structure of α′-NaV 2O5 induced by soft x-ray irradiation, with the appearance of features characteristic of sodium deficient NaxV 2O5 (x < 1).

Role of band structure and local-field effects in the low-energy collective electronic excitation spectra of 2H-NbSe2

We present a study of the electron dynamics in the layered compound 2$H$-NbSe${}_{2}$. First-principles calculations are used to obtain the band structure employed in the evaluation of the loss function with inclusion of local-field (LF) effects. Two different symmetry directions [(100) and (010)] were explored in the hexagonal basal plane. In both cases, a low-energy charge-carrier plasmon (CCP) at $\ensuremath{\sim}$1 eV presenting a negative dispersion over a wide momentum transfer range is found, in agreement with recent experimental results [Wezel et al., Phys. Rev. Lett. 107, 176404 (2011)]. On the contrary, in the (001) perpendicular direction, the CCP has negative dispersion at small momenta only, presenting strong positive dispersion at larger momenta. Our calculations reveal that this behavior can be explained without invoking many-body effects, as long as band structure effects are properly included in the evaluation of the excitation spectra. In addition to this CCP mode, we find another one with an arclike oscillating dispersion along the perpendicular direction, as well as the appearance of a CCP replica at high momenta due to LF effects.

Emergence of plasmaronic structure in the near-field optical response of graphene

The finite momentum optical response $\sigma({\boldsymbol{q}},\omega)$ of graphene can be probed with the innovative technique of infrared nanoscopy where mid-infrared radiation is confined by an atomic force microscope cantilever tip. In contrast to conventional $q\sim 0$ optical absorption which primarily involves Dirac fermions with momentum near the Fermi momentum, $k\sim k_F$, for finite $q$, $\sigma({\boldsymbol{q}},\omega)$ has the potential to provide information on many body renormalizations and collective phenomena which have been found at small $k< k_F$ near the Dirac point in electron-doped graphene. For electron-electron interactions, the low energy excitation spectrum characterizing the incoherent part of the quasiparticle spectral function of Dirac electrons with $k\sim k_F$ consists of a flat, small amplitude background which scales with chemical potential and Fermi momentum. However, probing of the states with $k$ near $k=0$ will reveal plasmarons, a collective state of a charge carrier and a plasmon. These collective modes in graphene have recently been seen in angle-resolved photoemission spectroscopy and here we describe how they manifest in near field optics.

Field theory analysis ofS=1antiferromagnetic bond-alternating chains in the dimer phase

Dynamics of S=1 antiferromagnetic bond-alternating chains in the dimer phase, in the vicinity of the critical point with the Haldane phase, is studied by a field theoretical method. This model is considered to represent the compound Ni(C$_9$H$_{24}$N$_4$)(NO$_2$)ClO$_4$ (abbreviated as NTENP). We construct the sine-Gordon (SG) field theory as a low-energy effective model of this system, starting from a Tomonaga-Luttinger liquid at the critical point. Using the exact solution of the SG theory, we give a field theoretical picture of the low-energy excitation spectrum of NTENP. Results derived from our picture are in a good agreement with results of inelastic neutron scattering experiments on NTENP and numerical calculation of the dynamical structure factor. Furthermore, on the basis of the obtained theoretical picture, we predict that the sharp peaks correspond to a single elementary excitation are absent in the Raman scattering spectrum of NTENP in contrast to the inelastic neutron scattering spectrum.

Effect of time-odd mean fields on inertial parameters of the quadrupole collective Hamiltonian

Most current implementations of the quadrupole collective Hamiltonian model do not include the contributions of time-odd mean fields to the moments of inertia and mass parameters (Thouless-Valatin dynamical rearrangement contributions). A hybrid model is introduced that allows a quantitative estimate of these contributions to the inertial functions of a five-dimensional collective Hamiltonian based on microscopic energy density functionals. Fully self-consistent constrained relativistic Hartree-Bogoliubov calculations of triaxial energy surfaces in the $\ensuremath{\beta}\ensuremath{-}\ensuremath{\gamma}$ plane are used to determine the parameters of an equivalent pairing-plus-quadrupole ($P+Q$) Hamiltonian. This Hamiltonian is employed in constrained Hartree-Fock-Bogoliubov (CHFB) plus local quasiparticle random-phase approximation (LQRPA) calculation of the deformation-dependent corrections to the Inglis-Belyaev moments of inertia and cranking mass parameters. This hybrid model is used to evaluate the influence of time-odd mean fields on vibrational and rotational collective masses and investigate their effect on the low-energy collective excitation spectra and transition rates of $\ensuremath{\gamma}$-soft Xe and Ba nuclei.

Elementary excitations in dipolar spin-1 Bose-Einstein condensates

We have numerically solved the low-energy excitation spectra of ferromagnetic Bose-Einstein condensates subject to dipolar interparticle interactions. The system is assumed to be harmonically confined by purely optical means, thereby maintaining the spin degree of freedom of the condensate order parameter. Using a zero-temperature spin-1 model, we solve the Bogoliubov excitations for different spin textures, including a spin-vortex state in the absence of external magnetic fields and a rapidly rotating polarized spin texture in a finite homogeneous field. In particular, we consider the effect of dipolar interactions on excitations characteristic of ferromagnetic condensates. The energies of spin waves and magnetic quadrupole modes are found to increase rapidly with the dipolar coupling strength, whereas the energies of density oscillations change only slightly.

Critical excitation spectrum of a quantum chain with a local three-spin coupling

Using the phenomenological renormalization group (PRG), we evaluate the low-energy excitation spectrum along the critical line of a quantum spin chain having a local interaction between three Ising spins and longitudinal and transverse magnetic fields, i.e., a Turban model. The low-energy excitation spectrum found with the PRG agrees with the spectrum predicted for the (D(4),A(4)) conformal minimal model under a nontrivial correspondence between translations at the critical line and discrete lattice translations. Under this correspondence, the measurements confirm a prediction that the critical line of this quantum spin chain and the critical point of the two-dimensional three-state Potts model are in the same universality class.

Reexamining the Lyman-Birge-Hopfield band of N2

Motivated by fundamental molecular physics and by atmospheric and planetary sciences, the valence excitations of N${}_{2}$ gas have seen several decades of intensive study, especially by electron-energy-loss spectroscopy (EELS). It was consequently surprising when a comparison of nonresonant inelastic x-ray scattering (NIXS) and nonresonant EELS found strong evidence for violations of the first Born approximation for EELS when leaving the dipole scattering limit. Here we reassess the relative strengths of the constituent resonances of the lowest-energy excitations of N${}_{2}$, encompassed by the so-called Lyman-Birge-Hopfield (LBH) band, expanding on the prior, qualitative interpretation of the NIXS results for N${}_{2}$ by both quantifying the generalized oscillator strength of the lowest-energy excitations and also presenting a time-dependent density functional theory (TDDFT) calculation of the $q$ dependence of the entire low-energy electronic excitation spectrum. At high $q$, we find that the LBH band has an unexpectedly large contribution from the octupolar $w{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Delta}}_{u}$ resonance exactly in the regime where theory and EELS experiment for the presumed-dominant $a{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{g}$ resonance have previously had substantial disagreement, and also where the EELS results must now be expected to show violations of the Born approximation. After correcting for this contamination, the $a{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{g}$ generalized oscillator strength from the NIXS results is in good agreement with prior theory. The NIXS spectra, over their entire $q$ range, also find satisfactory agreement with the TDDFT calculations for both bound and continuum excitations.

Partial Disorder in the Periodic Anderson Model on a Triangular Lattice

We report our theoretical results on the emergence of a partially-disordered state at zero temperature and its detailed nature in the periodic Anderson model on a triangular lattice at half filling. The partially-disordered state is characterized by coexistence of a collinear antiferromagnetic order on an unfrustrated honeycomb subnetwork and nonmagnetic state at the remaining sites. This state appears with opening a charge gap between a noncollinear antiferromagnetic metal and Kondo insulator while changing the hybridization and Coulomb repulsion. We also find a characteristic crossover in the low-energy excitation spectrum as a result of coexistence of magnetic order and nonmagnetic sites. The result demonstrates that the partially-disordered state is observed distinctly even in the absence of spin anisotropy, in marked contrast to the partial Kondo screening state found in the previous study for the Kondo lattice model.

Birefringent breakup of Dirac fermions on a square optical lattice

We generalize a proposal by Sorensen et al. [Phys. Rev. Lett. 94, 086803 (2005)] for creating an artificial magnetic field in a cold atom system on a square optical lattice. This leads us to an effective lattice model with tunable spatially periodic modulation of the artificial magnetic field and the hopping amplitude. When there is an average flux of half a flux quantum per plaquette the spectrum of low-energy excitations can be described by massless Dirac fermions in which the usually doubly degenerate Dirac cones split into cones with different "speeds of light" which can be tuned to give a single Dirac cone and a flat band. These gapless birefringent Dirac fermions arise because of broken chiral symmetry in the kinetic energy term of the effective low energy Hamiltonian. We characterize the effects of various perturbations to the low-energy spectrum, including staggered potentials, interactions, and domain wall topological defects.