Low-lying Excitation Spectrum Research Articles

First-principles treatment of Mott insulators: linearized QSGW+DMFT approach

AbstractThe theoretical understanding of emergent phenomena in quantum materials is one of the greatest challenges in condensed matter physics. In contrast to simple materials such as noble metals and semiconductors, macroscopic properties of quantum materials cannot be predicted by the properties of individual electrons. One of the examples of scientific importance is strongly correlated electron system. Neither localized nor itinerant behaviors of electrons in partially filled 3d, 4f, and 5f orbitals give rise to rich physics such as Mott insulators, high-temperature superconductors, and superior thermoelectricity, but hinder quantitative understanding of low-lying excitation spectrum. Here we present a new first-principles approach to strongly correlated solids. It is based on a combination of the quasiparticle self-consistent GW approximation and the dynamical mean-field theory. The sole input in this method is the projector to the set of correlated orbitals for which all local Feynman graphs are being evaluated. For that purpose, we choose very localized quasiatomic orbitals spanning large energy window, which contains most strongly hybridized bands, as well as upper and lower Hubbard bands. The self-consistency is carried out on the Matsubara axis. This method enables the first-principles study of Mott insulators in both their paramagnetic and antiferromagnetic phases. We illustrate the method on the archetypical charge transfer correlated insulators La2CuO4 and NiO, and obtain spectral properties and magnetic moments in good agreement with experiments.

Fractional Mott insulator-to-superfluid transition of Bose–Hubbard model in a trimerized Kagomé optical lattice

By generalizing the traditional single-site strong coupling expansion approach to a cluster one, we study the zero-temperature phase diagram of bosonic atoms in a trimerized Kagomé optical lattice. Some new features are present in this system. Due to the strong intra-trimer hopping interaction, there will be a new Mott insulator (MI), which is by definition incompressible but with a fractional filling per trimer. This is different from the traditional MI, which has an integral filling and originates only from the repulsive interaction between particles. We investigate the MI-to-superfluid transition and the nature of the fractional MI by calculating the critical exponents of phase transitions and the low-lying energy excitation spectra of quasiparticles (quasihole). We will show how the low-energy properties of this system can be understood qualitatively as a Bose–Hubbard model in triangular lattice from the point of view of the cluster strong coupling expansion. We also discuss how our results are related to experiment by studying the Bragg spectroscopy.

Dynamical gap generation in topological insulators

We developed a quantum field theoretical description for the surface states of three-dimensional topological insulators. Within the relativistic quantum field theory formulation, we investigated the dynamics of low-lying surface states in an applied transverse magnetic field. We argued that, by taking into account quantum fluctuations, in three-dimensional topological insulators there is dynamical generation of a gap by a rearrangement of the Dirac sea. By comparing with available experimental data we found that our theoretical results allowed a consistent and coherent description of the Landau level spectrum of the surface low-lying excitations. Finally, we showed that the recently detected zero-Hall plateau at the charge neutral point could be accounted for by chiral edge states residing at the magnetic domain boundaries between the top and bottom surfaces of the three-dimensional topological insulator.

Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems

Using exact diagonalization for non-interacting systems and density matrix renormalization group for interacting systems we show that Li and Haldane's conjecture on the correspondence between the low-lying many-particle excitation spectrum and the entanglement spectrum holds for disordered ballistic one-dimensional many-particle systems. In order to demonstrate the correspondence we develop a computationally efficient way to calculate the entanglement spectrum of low-lying excitation of non-interacting systems. We observe and explain the presence of an unexpected shell structure in the excitation spectrum. The low-lying shells are robust and survive even for strong electron-electron interactions.

Lieb-Liniger model: Emergence of dark solitons in the course of measurements of particle positions

Lieb-Liniger model describes bosons with contact interactions in one-dimensional space. In the limit of weak repulsive particle interactions, there are two types of low lying excitation spectrum. The first is reproduced by the Bogoliubov dispersion relation, the other is believed to correspond to dark soliton excitations. While there are various evidences that the type II spectrum is related to dark solitons, it has not been shown that measurements of positions of particles reveal dark soliton density profiles. Here, we employ the Bethe ansatz approach and show that dark solitons emerge in the measurement process if the system is prepared in an eigenstate corresponding to the type II spectrum. We analyze single and double dark solitons as well as weak and strong interaction regime.

Microscopic study of low-lying spectra ofΛhypernuclei based on a beyond-mean-field approach with a covariant energy density functional

We present a detailed formalism of the microscopic particle-rotor model for hypernuclear low-lying states based on a covariant density functional theory. In this method, the hypernuclear states are constructed by coupling a hyperon to low-lying states of the core nucleus, which are described by the generator coordinate method (GCM) with the particle number and angular momentum projections. We apply this method to study in detail the low-lying spectrum of $_{\mathrm{\ensuremath{\Lambda}}}^{13}\mathrm{C}$ and $_{\mathrm{\ensuremath{\Lambda}}}^{21}\mathrm{Ne}$ hypernuclei. We also briefly discuss the structure of $_{\mathrm{\ensuremath{\Lambda}}}^{155}\mathrm{Sm}$ as an example of heavy deformed hypernuclei. It is shown that the low-lying excitation spectra with positive-parity states of the hypernuclei, which are dominated by $\mathrm{\ensuremath{\Lambda}}$ hyperon in the $s$ orbital coupled to the core states, are similar to that for the corresponding core states, while the electric quadrupole transition strength, $B(E2)$, from the ${2}_{1}^{+}$ state to the ground state is reduced according to the mass number of the hypernuclei. Our study indicates that the energy splitting between the first $1/{2}^{\ensuremath{-}}$ and $3/{2}^{\ensuremath{-}}$ hypernuclear states is generally small for all the hypernuclei which we study. However, their configurations depend much on the properties of a core nucleus, in particular on the sign of deformation parameter. That is, the first $1/{2}^{\ensuremath{-}}$ and $3/{2}^{\ensuremath{-}}$ states in ${}_{\mathrm{\ensuremath{\Lambda}}}^{13}\mathrm{C}$ are dominated by a single configuration with $\mathrm{\ensuremath{\Lambda}}$ particle in the $p$-wave orbits and thus provide good candidates for a study of the $\mathrm{\ensuremath{\Lambda}}$ spin-orbit splitting. On the other hand, those states in the other hypernuclei exhibit a large configuration mixing and thus their energy difference cannot be interpreted as the spin-orbit splitting for the $p$ orbits.

Diabatic-ramping spectroscopy of many-body excited states

Due to the experimental time constraints of state of the art quantum simulations, the direct preparation of the ground state by adiabatically ramping the field of a transverse-field Ising model becomes more and more difficult as the number of particles increase. We propose a spectroscopy protocol that intentionally creates excitations through diabatic ramping and measures a low-noise observable as a function of time for a constant Hamiltonian to reveal the structure of the coherent dynamics of the resulting many-body states. To simulate experimental data, noise from counting statistics and decoherence error are added. Compressive sensing is then applied to Fourier transform the simulated data into the frequency domain and extract the low-lying energy excitation spectrum. By using compressive sensing, the amount of data in time needed to extract this energy spectrum is sharply reduced, making such experiments feasible with current technology in, for example, ion trap quantum simulators.

C12properties with evolved chiral three-nucleon interactions

We investigate selected static and transition properties of $^{12}\mathrm{C}$ using ab initio no-core shell model (NCSM) methods with chiral two- and three-nucleon interactions. We adopt the similarity renormalization group (SRG) to assist convergence including up to three-nucleon ($3N$) contributions. We examine the dependencies of the ${}^{12}$C observables on the SRG evolution scale and on the model-space parameters. We obtain nearly converged low-lying excitation spectra. We compare results of the full NCSM with the importance truncated NCSM in large model spaces for benchmarking purposes. We highlight the effects of the chiral $3N$ interaction on several spectroscopic observables. The agreement of some observables with experiment is improved significantly by the inclusion of $3N$ interactions, e.g., the $B(M1)$ from the first ${J}^{\ensuremath{\pi}}T={1}^{+}1$ state to the ground state. However, in some cases the agreement deteriorates, e.g., for the excitation energy of the first ${1}^{+}0$ state, leaving room for improved next-generation chiral Hamiltonians.

Villain transformation theory of the anisotropy ferrimagnetic spin chain

By using the Villain transformation, the Heisenberg ferrimagnetic spin chain with anisotropy D˜ as well as an external field is explored. We obtain two branches of the low-lying excitation spectrum with the presence of magnetic field. The thermodynamic quantities, like free energy, specific heat and magnetization at finite temperature, are calculated. And the effects of the anisotropy parameter D˜ on these thermodynamic quantities are explicitly discussed. The results show that a phase transition may occur at the critical value of anisotropy D˜=0.3.

Excited electronic states from a variational approach based on symmetry-projected Hartree–Fock configurations

Recent work from our research group has demonstrated that symmetry-projected Hartree-Fock (HF) methods provide a compact representation of molecular ground state wavefunctions based on a superposition of non-orthogonal Slater determinants. The symmetry-projected ansatz can account for static correlations in a computationally efficient way. Here we present a variational extension of this methodology applicable to excited states of the same symmetry as the ground state. Benchmark calculations on the C2 dimer with a modest basis set, which allows comparison with full configuration interaction results, indicate that this extension provides a high quality description of the low-lying spectrum for the entire dissociation profile. We apply the same methodology to obtain the full low-lying vertical excitation spectrum of formaldehyde, in good agreement with available theoretical and experimental data, as well as to a challenging model C2v insertion pathway for BeH2. The variational excited state methodology developed in this work has two remarkable traits: it is fully black-box and will be applicable to fairly large systems thanks to its mean-field computational cost.

Zero-energy states in rotating trapped Bose–Einstein condensates

We have calculated low-lying quasiparticle excitation spectra of rotating three-dimensional Bose–Einstein condensates. We find, as opposed to the prediction of hydrodynamic continuum theories, a minimum in the Tkachenko mode spectrum at intermediate rotation frequencies of the harmonic trap. Such a minimum can harbour a Tkachenko quasiparticle with zero excitation energy. We discuss the experimental signatures of such a zero mode.

Multicomponent Skyrmion Lattices and Their Excitations

We study quantum Hall ferromagnets with a finite density of topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrized by a d-component spinor field. In the absence of anisotropies we find a hexagonal Skyrmion lattice that completely breaks the underlying SU(d) symmetry with the low-lying excitation spectrum separating into d(2) - 1 gapless acoustic magnetic modes and a magnetophonon. The ground state charge density modulations, which inevitably exist in these lattices, vanish exponentially in d. We discuss the role of effective mass anisotropy for SU(3)-valley Skyrmions relevant to experiments with AlAs quantum wells. Here we find a transition which breaks a sixfold rotational symmetry of the triangular lattice, followed by the formation of a square lattice at large values of anisotropy strength.

Resonant Inelastic Light Scattering Investigation of Low-Lying Gapped Excitations in the Quantum Fluid atν=5/2

The low-lying neutral excitation spectrum of the incompressible quantum Hall fluid at ν=5/2 is investigated by inelastic light scattering. Gapped modes are observable only in a very narrow filling factor range centered at 5/2 at energies that overlap estimates from transport activation gaps. The modes are interpreted as critical points in the wave-vector dispersion of excitations that preserve spin orientation. For very small changes |δν|≲0.01 the gapped modes disappear and a continuum of low-lying excitations takes over indicating the transition from an incompressible fluid at 5/2 to a compressible state. Observations of spin wave modes indicate spin polarization of the 5/2 and 2+1/3 quantum Hall fluids.

Tuning Charge and Spin Excitations in Zigzag Edge Nanographene Ribbons

Graphene and its quasi-one-dimensional counterpart, graphene nanoribbons, present an ideal platform for tweaking their unique electronic, magnetic and mechanical properties by various means for potential next-generation device applications. However, such tweaking requires knowledge of the electron-electron interactions that play a crucial role in these confined geometries. Here, we have investigated the magnetic and conducting properties of zigzag edge graphene nanoribbons (ZGNRs) using the many-body configuration interaction (CI) method on the basis of the Hubbard Hamiltonian. For the half-filled case, the many-body ground state shows a ferromagnetic spin-spin correlation along the zigzag edge, which supports the picture obtained from one-electron theory. However, hole doping reduces the spin and charge excitation gap, making the ground state conducting and magnetic. We also provide a two-state model that explains the low-lying charge and spin excitation spectrum of ZGNRs. An experimental setup to confirm the hole-mediated conducting and magnetic states is discussed.

Solitons in Bose–Einstein condensates

The Gross–Pitaevskii equation (GPE) describing the evolution of the Bose–Einstein condensate (BEC) order parameter for weakly interacting bosons supports dark solitons for repulsive interactions and bright solitons for attractive interactions. After a brief introduction to BEC and a general review of GPE solitons, we present our results on solitons that arise in the BEC of hard-core bosons, which is a system with strongly repulsive interactions. For a given background density, this system is found to support both a dark soliton and an antidark soliton (i.e., a bright soliton on a pedestal) for the density profile. When the background has more (less) holes than particles, the dark (antidark) soliton solution dies down as its velocity approaches the sound velocity of the system, while the antidark (dark) soliton persists all the way up to the sound velocity. This persistence is in contrast to the behaviour of the GPE dark soliton, which dies down at the Bogoliubov sound velocity. The energy–momentum dispersion relation for the solitons is shown to be similar to the exact quantum low-lying excitation spectrum found by Lieb for bosons with a delta-function interaction.

Importance of counter-rotating coupling in the superfluid-to-Mott-insulator quantum phase transition of light in the Jaynes-Cummings lattice

The quantum phase transition between Mott insulator and superfluid is studied in the two-dimensional Jaynes-Cummings square lattice in which the counter-rotating coupling (CRC) is included. Both the ground state and the spectra of low-lying excitations are obtained with use of a sophisticated unitary transformation. This CRC is shown not only to induce a long-range interaction between cavities, favoring the long-range superfluid order, but also to break the conservation of local polariton number at each site, leading to the absence of the Mott lobes in the phase diagram, in sharp contrast with the case without the CRC as well as that of the Bose-Hubbard model.

Pair Excitations and Parameters of State of Imbalanced Fermi Gases at Finite Temperatures

The spectra of low-lying pair excitations for an imbalanced two-component superfluid Fermi gas are analytically derived within the path-integral formalism taking into account Gaussian fluctuations about the saddle point. The spectra are obtained for nonzero temperatures, both with and without imbalance, and for arbitrary interaction strength. On the basis of the pair excitation spectrum, we have calculated the thermodynamic parameters of state of cold fermions and the first and second sound velocities. The parameters of pair excitations show a remarkable agreement with the Monte Carlo data and with experiment.

Simulating strongly correlated multiparticle systems in a truncated Hilbert space

Representing a strongly interacting multi-particle wave function in a finite product basis leads to errors. Simple rescaling of the contact interaction can preserve the low-lying energy spectrum and long-wavelength structure of wave functions in one-dimensional systems and thus correct for the basis set truncation error. The analytic form of the rescaling is found for a two-particle system where the rescaling is exact. Detailed comparison between finite Hilbert space calculations and exact results for up to 5 particles show that rescaling can significantly improve the accuracy of numerical calculations in various external potentials. In addition to ground state energies, the low-lying excitation spectrum, density profile and correlation functions are studied. The results give a promising outlook for numerical simulations of trapped ultracold atoms.

Exact yrast spectra of cold atoms on a ring

We propose a methodology to construct excited states with a fixed angular momentum, namely, ``yrast excited states'' of finite-size one-dimensional bosonic systems with periodic boundary conditions. The excitation energies such as the first yrast excited energy are calculated through the system-size asymptotic expansion and expressed analytically by dressed energy. Interestingly, they are grouped into sets of almost degenerate energy levels. The low-lying excitation spectrum near the yrast state is consistent with the $\text{U}(1)$ conformal field theories if the total angular momentum is given by an integral multiple of particle number; i.e., if the system is supercurrent.

Magneto-roton excitation in a holographic quantum Hall fluid

We compute the neutral bosonic excitation spectra of the holographic quantum Hall fluid described by the D3-D7' system. We find that the system is stable, gapped, and, in a range of parameters, exhibits a spectrum of low-lying excitations very similar to that of a quantum Hall fluid, including a magneto-roton excitation.