Two-particle Excitations Research Articles

Ising tricriticality in the extended Hubbard model with bond dimerization

We explore the quantum phase transition between Peierls and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge $c=7/10$. Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results.

Quasiparticle interactions in frustrated Heisenberg chains

Interactions between elementary excitations in quasi-one dimensional antiferromagnets are of experimental relevance and their quantitative theoretical treatment has been a theoretical challenge for many years. Using matrix product states, one can explicitly determine the wavefunctions of the one- and two-particle excitations, and, consequently, the contributions to dynamical correlations. We apply this framework to the (non integrable) frustrated dimerized spin-1/2 chain, a model for generic spin-Peierls systems, where low-energy quasi-particle excitations are bound states of topological solitons. The spin structure factor involving two quasi-particle scattering states is obtained in the thermodynamic limit with full momentum and frequency resolution. This allows very subtle features in the two-particle spectral function to be revealed which, we argue, could be seen, e.g., in inelastic neutron scattering of spin-Peierls compounds under a change of the external pressure.

Doping evolution of spin and charge excitations in the Hubbard model

To shed light on how electronic correlations vary across the phase diagram of the cuprate superconductors, we examine the doping evolution of spin and charge excitations in the single-band Hubbard model using determinant quantum Monte Carlo (DQMC). In the single-particle response, we observe that the effects of correlations weaken rapidly with doping, such that one may expect the random phase approximation (RPA) to provide an adequate description of the two-particle response. In contrast, when compared to RPA, we find that significant residual correlations in the two-particle excitations persist up to $40\%$ hole and $15\%$ electron doping (the range of dopings achieved in the cuprates). These fundamental differences between the doping evolution of single- and multi-particle renormalizations show that conclusions drawn from single-particle processes cannot necessarily be applied to multi-particle excitations. Eventually, the system smoothly transitions via a momentum-dependent crossover into a weakly correlated metallic state where the spin and charge excitation spectra exhibit similar behavior and where RPA provides an adequate description.

Scattering particles in quantum spin chains

A variational approach for constructing an effective particle description of the low-energy physics of one-dimensional quantum spin chains is presented. Based on the matrix product state formalism, we compute the one- and two-particle excitations as eigenstates of the full microscopic Hamiltonian. We interpret the excitations as particles on a strongly-correlated background with non-trivial dispersion relations, spectral weights and two-particle S matrices. Based on this information, we show how to describe a finite density of excitations as an interacting gas of bosons, using its approximate integrability at low densities. We apply our framework to the Heisenberg antiferromagnetic ladder: we compute the elementary excitation spectrum and the magnon-magnon S matrix, study the formation of bound states and determine both static and dynamic properties of the magnetized ladder.

Solid-state optical absorption from optimally tuned time-dependent range-separated hybrid density functional theory

We present a framework for obtaining reliable solid-state charge and optical excitations and spectra from optimally tuned range-separated hybrid density functional theory. The approach, which is fully couched within the formal framework of generalized Kohn-Sham theory, allows for the accurate prediction of exciton binding energies. We demonstrate our approach through first principles calculations of one- and two-particle excitations in pentacene, a molecular semiconducting crystal, where our work is in excellent agreement with experiments and prior computations. We further show that with one adjustable parameter, set to produce the known band gap, this method accurately predicts band structures and optical spectra of silicon and lithium fluoride, prototypical covalent and ionic solids. Our findings indicate that for a broad range of extended bulk systems, this method may provide a computationally inexpensive alternative to many-body perturbation theory, opening the door to studies of materials of increasing size and complexity.

Higgs mode in electric-field-induced superconductors

We develop a theory for the Higgs (gap-amplitude) mode excitation in electric-field-induced (EFI) superconductors. The Higgs mode can be excited directly by an oscillating electric field in EFI superconductors since the gap value depends sensitively on the external electric field that induces superconducting carriers. The mass of the Higgs mode in EFI superconductors does not coincide with the threshold energy of pair-breaking two-particle excitations.

Two-electron state from the Floquet scattering matrix perspective

Two single-particle sources coupled in series to a chiral electronic waveguide can serve as a probabilistic source of two-particle excitations with tunable properties. The second-order correlation function, characterizing the state of emitted electrons in space-time, is expressed in terms of the Floquet scattering matrix of a source. It is shown that the Fourier transform of the correlation function, characterizing the emitted state in energy space, can be accessed with the help of an energy resolved shot-noise measurement. The two-electron state emitted adiabatically is discussed in detail. In particular, the two-electron wave function is represented via two different sets of single-particle wave functions accessible experimentally.

Stability of supercurrents and condensates in type I superconductors

According to the BCS theory the superconducting condensate develops in a single quantum mode and no Cooper pairs out of the condensate are assumed. Here we discuss a mechanism by which the successful mode inhibits condensation in neighboring modes and suppresses a creation of noncondensed Cooper pairs. It is shown that condensed and noncondensed Cooper pairs are separated by an energy gap which is smaller than the superconducting gap but large enough to prevent nucleation in all other modes and to eliminate effects of noncondensed Cooper pairs on properties of superconductors. Our result thus justifies basic assumptions of the BCS theory and confirms that the BCS condensate is stable with respect to two-particle excitations.

The tensor hypercontracted parametric reduced density matrix algorithm: Coupled-cluster accuracy with O(r4) scaling

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r4), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the standard p2RDM algorithm, somewhere between that of CCSD and CCSD(T).

Low-lying quasiparticle excitations in strongly correlated superconductors: An ansatz from BCS quasiparticle excitations?

The question about the existence of Bogoliubov's quasiparticles in the BCS wave functions underneath Gutzwiller's projection is of importance to strongly correlated systems. We develop a method to examine the two-particle excitations of Gutzwiller-projected BCS wave functions by using the variational Monte Carlo approach. We find that the exact Gutzwiller-projected quasiparticle (GQP) dispersions are quantitatively reproduced by the Gutzwiller-projected Bogoliubov quasiparticles (GBQP) except the regions where d-wave Cooper pairing is strong. We believe GBQP provides a reasonable description to the low-energy excitations in strongly correlated superconducting systems because GBQP becomes more stable than GQP near the antinodes. Our framework offers a route to understand the intimate connection between Gutzwiller's projection and d-wave Cooper pairing.

Excitation spectra and spin gap of the half-filled Holstein-Hubbard model

Single-- and two-particle excitation spectra of the one-dimensional, half-filled Holstein-Hubbard model are calculated using the continuous-time quantum Monte Carlo method. In the metallic phase, the results are consistent with a Luther-Emery liquid that has gapped spin and single-particle excitations but a gapless charge mode. However, given the initially exponential dependence of the spin gap on the backscattering matrix element, the numerical excitation spectra appear gapless in the weak-coupling regime, and therefore resemble those of a Luttinger liquid. The Mott phase has the expected charge gap and gapless spin excitations. The Peierls state shows a charge, spin and single-particle gap, a soft phonon mode, backfolded shadow bands and soliton excitations. Arguments and numerical evidence for the existence of a nonzero spin gap throughout the metallic phase are provided in terms of equal-time spin and charge correlation functions.

Low-rank spectral expansions of two electron excitations for the acceleration of quantum chemistry calculations

Treatment of two-electron excitations is a fundamental but computationally expensive part of ab initio calculations of many-electron correlation. In this paper we develop a low-rank spectral expansion of two-electron excitations for accelerated electronic-structure calculations. The spectral expansion differs from previous approaches by relying upon both (i) a sum of three expansions to increase the rank reduction of the tensor and (ii) a factorization of the tensor into geminal (rank-two) tensors rather than orbital (rank-one) tensors. We combine three spectral expansions from the three distinct forms of the two-electron reduced density matrix (2-RDM), (i) the two-particle (2)D, (ii) the two-hole (2)Q, and the (iii) particle-hole (2)G matrices, to produce a single spectral expansion with significantly accelerated convergence. While the resulting expansion is applicable to any quantum-chemistry calculation with two-particle excitation amplitudes, it is employed here in the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. The low-rank parametric 2-RDM method scales quartically with the basis-set size, but like its full-rank version it can capture multi-reference correlation effects that are difficult to treat efficiently by traditional single-reference wavefunction methods. Applications are made to computing potential energy curves of HF and triplet OH(+), equilibrium bond distances and frequencies, the HCN-HNC isomerization, and the energies of hydrocarbon chains. Computed 2-RDMs nearly satisfy necessary N-representability conditions. The low-rank spectral expansion has the potential to expand the applicability of the parametric 2-RDM method as well as other ab initio methods to large-scale molecular systems that are often only treatable by mean-field or density functional theories.

Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides

Quasiparticle band structures and optical properties of MoS${}_{2}$, MoSe${}_{2}$, MoTe${}_{2}$, WS${}_{2}$, and WSe${}_{2}$ monolayers are studied using the GW approximation in conjunction with the Bethe-Salpeter equation (BSE). The inclusion of two-particle excitations in the BSE approach reveals the presence of two strongly bound excitons ($A$ and $B$) below the quasiparticle absorption onset arising from vertical transitions between a spin-orbit-split valence band and the conduction band at the $K$ point of the Brillouin zone. The transition energies for monolayer MoS${}_{2}$, in particular, are shown to be in excellent agreement with available absorption and photoluminescence measurements. Excitation energies for the remaining monolayers are predicted to lie in the range of 1--2 eV. Systematic trends are identified for quasiparticle band gaps, transition energies, and exciton binding energies within as well as across the Mo and W families of dichalcogenides. Overall, the results suggest that quantum confinement of carriers within monolayers can be exploited in conjunction with chemical composition to tune the optoelectronic properties of layered transition-metal dichalcogenides at the nanoscale.

The electronic structure and optical response of rutile, anatase and brookite TiO2

In this study, we present a combined density functional theory and many-body perturbation theory study on the electronic and optical properties of TiO2 brookite as well as the tetragonal phases rutile and anatase. The electronic structure and linear optical response have been calculated from the Kohn–Sham band structure applying (semi)local as well as nonlocal screened hybrid exchange–correlation density functionals. Single-particle excitations are treated within the GW approximation for independent quasiparticles. For optical response calculations, two-particle excitations have been included by solving the Bethe–Salpeter equation for Coulomb correlated electron–hole pairs. On this methodological basis, gap data and optical spectra for the three major phases of TiO2 are provided. The common characteristics of brookite with the rutile and anatase phases, which have been discussed more comprehensively in the literature, are highlighted. Furthermore, the comparison of the present calculations with measured optical response data of rutile indicate that discrepancies discussed in numerous earlier studies are due to the measurements rather than related to an insufficient theoretical description.

Series expansion analysis of a frustrated four-spin tube

We study the magnetism of a frustrated four-leg spin-$1/2$ ladder with transverse periodic boundary conditions: the frustrated four-spin tube (FFST). Using a combination of series expansion (SE), based on the continuous unitary transformation method and density-matrix renormalization group (DMRG) we analyze the ground-state, the one-, and the two-particle excitations in the regime of strong rung coupling. We find several marked differences of the FFST with respect to standard two-leg ladders. First, we show that frustration destabilizes the spin-gap phase of the FFST, which is adiabatically connected to the limit of decoupled rung singlets, leading to a first-order quantum phase transition at finite interrung coupling. Second, we show that apart from the well-known triplon branch of spin ladders, the FFST sustains additional elementary excitations, including a singlon and additional triplons. Finally, we find that in the two-particle sector, the FFST exhibits collective (anti)bound states similar to two-leg ladders, however, with a different ordering of the spin-quantum numbers. We show that frustration has significant impact on the FFST leading to a flattening of the ground-state energy landscape, a mass-enhancement of the excitations, and to a relative enhancement of the (anti)binding strength. Where possible, we use DMRG to benchmark the findings from our SE calculations, showing excellent agreement.

The 3-band Hubbard-model versus the 1-band model for the high-T c cuprates: Pairing dynamics, superconductivity and the ground-state phase diagram

One central challenge in high-$T_c$ superconductivity (SC) is to derive a detailed understanding for the specific role of the $Cu$-$d_{x^2-y^2}$ and $O$-$p_{x,y}$ orbital degrees of freedom. In most theoretical studies an effective one-band Hubbard (1BH) or t-J model has been used. Here, the physics is that of doping into a Mott-insulator, whereas the actual high-$T_c$ cuprates are doped charge-transfer insulators. To shed light on the related question, where the material-dependent physics enters, we compare the competing magnetic and superconducting phases in the ground state, the single- and two-particle excitations and, in particular, the pairing interaction and its dynamics in the three-band Hubbard (3BH) and 1BH-models. Using a cluster embedding scheme, i.e. the variational cluster approach (VCA), we find which frequencies are relevant for pairing in the two models as a function of interaction strength and doping: in the 3BH-models the interaction in the low- to optimal-doping regime is dominated by retarded pairing due to low-energy spin fluctuations with surprisingly little influence of inter-band (p-d charge) fluctuations. On the other hand, in the 1BH-model, in addition a part comes from "high-energy" excited states (Hubbard band), which may be identified with a non-retarded contribution. We find these differences between a charge-transfer and a Mott insulator to be renormalized away for the ground-state phase diagram of the 3BH- and 1BH-models, which are in close overall agreement, i.e. are "universal". On the other hand, we expect the differences - and thus, the material dependence to show up in the "non-universal" finite-T phase diagram ($T_c$-values).

Two-particle photoemission from strongly correlated systems: A dynamical mean-field approach

We study theoretically the simultaneous, photo-induced two-particle excitations of strongly correlated systems on the basis of the Hubbard model. Under certain conditions specified in this work, the corre- sponding transition probability is related to the two-particle spectral function which we calculate using three different methods: the dynamical-mean field theory combined with quantum Monte Carlo (DMFT- QMC) technique, the first order perturbation theory and the ladder approximations. The results are analyzed and compared for systems at the verge of the metal-insulator transitions. The dependencies on the electronic correlation strength and on doping are explored. In addition, the account for the orbital degeneracy allows an insight into the influence of interband correlations on the two particle excitations. A suitable experimental realization is discussed.

Effects of disorder and interactions in the quantum Hall ferromagnet

This work treats the effects of disorder and interactions in a quantum Hall ferromagnet, which is realized in a two-dimensional electron gas (2DEG) in a perpendicular magnetic field at Landau level filling factor equal one. We study the problem by projecting the original fermionic Hamiltonian into magnon states, which behave as bosons in the vicinity of the ferromagnetic ground state. The approach permits the reformulation of a strongly interacting model into a non-interacting one. The latter is a non-perturbative scheme that consists in treating the two-particle neutral excitations of the electron system as a bosonic single-particle. Indeed, the employment of bosonization facilitates the inclusion of disorder in the study of the system. It has been shown previously that disorder may drive a quantum phase transition in the Hall ferromagnet. However, such studies have been either carried out in the framework of nonlinear sigma model, as an effective low-energy theory, or included the long-range Coulomb interaction in a quantum description only up to the Hartree-Fock level. Here, we establish the occurrence of a disorder-driven quantum phase transition from a ferromagnetic 2DEG to a spin glass phase by taking into account interactions between electrons up to the random phase approximation level in a fully quantum description.

Spin 3/2 fermions with attractive interactions in a one-dimensional optical lattice: phase diagrams, entanglement entropy, and the effect of the trap

We study spin 3/2 fermionic cold atoms with attractive interactions confined in a one-dimensional optical lattice. Using numerical techniques, we determine the phase diagram for a generic density. For the chosen parameters, one-particle excitations are gapped and the phase diagram is separated into two regions: one where the two-particle excitation gap is zero, and one where it is finite. In the first region, the two-body pairing fluctuations (BCS) compete with the density ones. In the other one, a molecular superfluid (MS) phase, in which bound-states of four particles form, competes with the density fluctuations. The properties of the transition line between these two regions is studied through the behavior of the entanglement entropy. The physical features of the various phases, comprising leading correlations, Friedel oscillations, and excitation spectra, are presented. To make the connection with experiments, the effect of a harmonic trap is taken into account. In particular, we emphasize the conditions under which the appealing MS phase can be realized, and how the phases could be probed by using the density profiles and the associated structure factor. Lastly, the consequences on the flux quantization of the different nature of the pairing in the BCS and MS phases are studied in a situation where the condensate is in a ring geometry.

Single- and two-particle excitations in a 1D aperiodic sequence of quantum dots

The energy spectrum of single- and two-particle excitations for a one-dimensional aperiodic Fibonacci sequence of quantum dots (QDs) was determined within the pair interaction approximation. The critical behaviour of the energy spectrum and wave functions were obtained. The energy spectrum is a Cantor set of zero Lebesgue measure. The perturbation theory was used to obtain the critical value of the distance between the centres of the neighboring QDs when the first-order corrections to the energy of the excitations were neglected. The contribution of the external transverse magnetic field to particle localization was also considered and the influence of the external field on the first-order corrections to the energy was analyzed. The transmission coefficient was determined using the quasi-classical approximation and the energy level splitting versus the distance between the QDs was obtained. The effect of resonance tunneling of the excitations between QD pairs was studied. Localization occurs at finite values of the perturbations, in contrast to periodic one-dimensional sequences.