Single-particle Excitation Spectrum Research Articles

Matrix product study of spin fractionalization in the one-dimensional Kondo insulator

The Kondo lattice is one of the classic examples of strongly correlated electronic systems. We conduct a controlled study of the Kondo lattice in one dimension, highlighting the role of excitations created by the composite fermion operator. Using time-dependent matrix product state methods, we compute various correlation functions and contrast them with both large-N mean-field theory and the strong-coupling expansion. We show that the composite fermion operator creates long-lived, charge-e and spin-1/2 excitations, which cover the low-lying single-particle excitation spectrum of the system. Furthermore, spin excitations can be thought to be composed of such fractionalized quasiparticles with a residual interaction which tend to disappear at weak Kondo coupling. Published by the American Physical Society 2024

Single-particle excitations in the uniform electron gas by diagrammatic Monte Carlo

We calculate the single-particle excitation spectrum and the Landau liquid parameters for the archetypal model of solids, the three-dimensional uniform electron gas, with the variational diagrammatic Monte Carlo method, which gives numerically controlled results without systematic error. In the metallic range of density, we establish benchmark values for the wave-function renormalization factor Z, the effective mass m^*/m, and the Landau parameters F_0^s and F_0^a with unprecedented accuracy, and we resolve the long-standing puzzle of non-monotonic dependence of mass on density. We also exclude the possibility that experimentally measured large reduction of bandwidth in Na metal can originate from the charge and spin fluctuations contained in the model of the uniform electron gas.

Enhancement of superconductivity by electronic nematicity in cuprate superconductors

ABSTRACT The cuprate superconductors are characterised by numerous ordering tendencies, with the electronically nematic order being the most distinct form of order. Here the intertwinement of the electronic nematicity with superconductivity in cuprate superconductors is studied based on the kinetic-energy-driven superconductivity. It is shown that the optimised takes a dome-like shape with the weak and strong strength regions on each side of the optimal strength of the electronic nematicity, where the optimised reaches its maximum. This dome-like shape nematic-order strength dependence of thus indicates that the electronic nematicity enhances superconductivity. Moreover, this nematic order induces the anisotropy of the electron Fermi surface, where although the original electron Fermi surface contour with the four-fold rotation symmetry is broken up into that with a residual twofold rotation symmetry, this electron Fermi surface contour with the twofold rotation symmetry still is truncated to form the disconnected Fermi arcs with the most spectral weight that locates at around the tips of the Fermi arcs. Concomitantly, these tips of the Fermi arcs connected by the scattering wave vectors construct an octet scattering model, however, the partial scattering wave vectors and their respective symmetry-corresponding partners occur with unequal amplitudes, leading to these electronically ordered states being broken both rotation and translation symmetries. As a natural consequence, the electronic structure is inequivalent between the and directions in momentum space. These anisotropic features of the electronic structure are also confirmed via the result of the autocorrelation of the single-particle excitation spectra, where the breaking of the rotation symmetry is verified by the inequivalence on the average of the electronic structure at the two Bragg scattering sites. The theory also indicates that the order parameter of the electronic nematicity achieves its maximum in the characteristic energy and then decreases rapidly as the energy moves away from the characteristic energy.

Двумерные электроны низкой плотности в магнитном поле

The photoluminescence spectrum from the two-dimensional low density electrons with the localized valence-band holes in magnetic field is studied. The ground state is considered as Wigner crystal ore the strongly correlated electron system. For the quantum Wigner crystal the Landau levels for vacancions (quasiholes appearing in the process of photoluminescence) are calculated in the quasiclassical approximation. The spectrum of single-particle excitations for a triangular lattice in the nearest-neighbor approximation is used. It is found that Landau levels for vacancions depend unusually on magnetic field. For the electron system with strong Coulomb interaction the Mahan exciton effect in the photoluminescence for the two-dimensional electrons in magnetic field is considered.

Two-dimensional low density electrons in high magnetic field

The photoluminescence spectrum from the two-dimensional low density electrons with the localized valence-band holes in magnetic field is studied. The ground state is considered as Wigner crystal ore the strongly correlated electron system. For the quantum Wigner crystal the Landau levels for vacancions (quasiholes appearing in the process of photoluminescence) are calculated in the quasiclassical approximation. The spectrum of single-particle excitations for a triangular lattice in the nearest-neighbor approximation is used. It is found that Landau levels for vacancions depend unusually on magnetic field. For the electron system with strong Coulomb interaction the Mahan exciton effect in the photoluminescence for the two-dimensional electrons in magnetic field is considered. Keywords: Wigner crystal, magnetic field, Mahan exciton, correlated electrons.

Magnetic phases and phase diagram of spin-1 condensate with quadrupole degrees of freedom

We obtain and justify a many-body Hamiltonian of pairwise interacting spin-1 atoms, which includes eight generators of the SU(3) group associated with spin and quadrupole degrees of freedom. It is shown that this Hamiltonian is valid for non-local interaction potential, whereas for local interaction specified by s-wave scattering length, the Hamiltonian should be bilinear in spin operators only (of the Heisenberg type). We apply the obtained Hamiltonian to study the ground-state properties and single-particle excitations of a weakly interacting gas of spin-1 atoms with Bose–Einstein condensate (BEC) taking into account the quadrupole degrees of freedom. It is shown that the system under consideration can be in ferromagnetic, quadrupole, and paramagnetic phases. The corresponding phase diagram is constructed and discussed. The main characteristics such as the density of the grand thermodynamic potential, condensate density, and single-particle excitation spectra modified by quadrupole degrees of freedom are determined in different phases.

Peak structure in the self-energy of cuprate superconductors

The recently deduced normal and anomalous self-energies from photoemission spectra of cuprate superconductors via the machine learning technique are calling for an explanation. Here the normal and anomalous self-energies in cuprate superconductors are analyzed within the framework of the kinetic-energy-driven superconductivity. It is shown that the exchanged spin excitations give rise to the well-pronounced low-energy peak-structures in both the normal and anomalous self-energies, however, they do not cancel in the total self-energy. In particular, the peak-structure in the normal self-energy is mainly responsible for the peak-dip-hump structure in the single-particle excitation spectrum, and can persist into the normal-state, while the sharp peak in the anomalous self-energy gives rise to a crucial contribution to the superconducting gap, and vanishes in the normal state. Moreover, the evolution of the peak structure with doping and momentum are also analyzed.

Combined spontaneous symmetry-breaking and symmetry-protected topological order from cluster charge interactions

The study of symmetry-protected topological states in presence of electron correlations has recently aroused great interest as rich and exotic phenomena can emerge. Here, we report a concrete example by employing large-scale unbiased quantum Monte Carlo study of the Kane-Mele model with cluster charge interactions. The ground-state phase diagram for the model at half filling is established. Our simulation identifies the coexistence of a symmetry-protected topological order with a symmetry-breaking Kekul$\acute{e}$ valence bond order and shows that the spontaneous symmetry-breaking is accompanied by an interaction-driven topological phase transition (TPT). This TPT features appearance of zeros of single-particle Green's function and gap closing in spin channel rather than single-particle excitation spectrum, and thus has no mean-field correspondence.

SU(3) symmetry in theory of a weakly interacting gas of spin-1 atoms with Bose-Einstein condensate

We study a many-body system of interacting spin-1 particles in the context of homogeneous gases of ultracold atoms. In general, its description requires eight parameters among which there are three components of magnetization and five parameters associated with quadrupole degrees of freedom. Based on the symmetry considerations, we construct a many-body interaction Hamiltonian that includes eight generators of the SU(3) group related to the above description parameters. The SU(3) symmetric Hamiltonian is applied to study the ferromagnetic and quadrupolar phases of a homogeneous weakly interacting gas of spin-1 atoms with Bose-Einstein condensate. It is shown how the quadrupole degrees of freedom entering the Hamiltonian modify the ground state and single-particle excitation spectra in comparison with those obtained from the Hamiltonian bilinear in spin operators and not including quadrupole degrees of freedom. We discuss the issue of taking into account the local character of interaction to obtain the correct spectra of single-particle excitations.

Emergence of anomalous dynamics from the underlying singular continuous spectrum in interacting many-body systems

We investigate the dynamical properties of an interacting many-body system with a non-trivial energy potential landscape that may induce a singular continuous single-particle energy spectrum. Focusing on the Aubry-Andr\'e model, whose anomalous transport properties in presence of interaction has recently been demonstrated experimentally in an ultracold gas setup, we discuss the anomalous slowing down of the dynamics it exhibits and show that it emerges from the singular-continuous nature of the single-particle excitation spectrum. Our study demonstrates that singular-continuous spectra can be found in interacting systems, unlike previously conjectured by treating the interactions in the mean-field approximation. This, in turns, also highlights the importance of the many-body correlations in giving rise to anomalous dynamics, which, in many-body systems, can result from a non-trivial interplay between geometry and interactions.

Colloquium : Heavy-electron quantum criticality and single-particle spectroscopy

Angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) have become indispensable tools in the study of correlated quantum materials. Both probe complementary aspects of the single-particle excitation spectrum. Taken together, ARPES and STM have the potential to explore properties of the electronic Green's function, a central object of many-body theory. This review explicates this potential with a focus on heavy-electron quantum criticality, especially the role of Kondo destruction. A discussion on how to probe the Kondo destruction effect across the quantum-critical point using ARPES and STM measurements is presented. Particular emphasis is placed on the question of how to distinguish between the signatures of the initial onset of hybridization-gap formation, which is the "high-energy" physics to be expected in all heavy-electron systems, and those of Kondo destruction, which characterizes the low-energy physics and, hence, the nature of quantum criticality. Recent progress and possible challenges in the experimental investigations are surveyed, the STM and ARPES spectra for several quantum-critical heavy-electron compounds are compared, and the prospects for further advances are outlined.

Fermion Condensation: Theory and Experiment

Fundamentals of fermion-condensation physics are outlined. Fermion condensation is a phase transition occurring in a strongly correlated Fermi system upon a topological reconstruction of the Landau ground state and leading to the formation of a fermion condensate that possesses the dispersionless single-particle spectrum $$\epsilon({\mathbf{p}})=0$$ in the momentum-space region adjacent to the Fermi surface and, accordingly, an anomalously enhanced density of single-particle states. A original method is developed for solving the set of nonlinear integral equations of fermion-condensation theory. This method makes it possible to analyze the problem of quantum chaos in strongly interacting multifermion systems. The computational technique used is demonstrated by applying it to superdense quark–gluon plasma, where the structure of exchange quark–quark interaction is well known. In electron systems featuring a fermion condensate, the magnitude of the gap appearing in the single-particle spectrum owing to Cooper pairing is shown to be much larger than that in Bardeen–Cooper–Schrieffer (BCS) theory. This explains both a high superconducting-transition temperature $$T_{c}$$ and, with allowance for $$C_{4}$$ crystal-lattice symmetry, the $$D$$ -wave pairing-gap structure observed in cuprates. It is found that, in addition to the BCS gap $$\Delta$$ , the spectrum of single-particle excitations of superconducting systems where a fermion condensate is present develops a nonsuperconducting gap $$\Upsilon$$ that owes its existence to the interaction of condensate particles with normal quasiparticles residing outside the condensate region in momentum space. The question of whether these results are pertinent to the two-gap structure recently unearthed in the excitation spectrum of cuprates upon analyzing ARPES data is addressed.

Typicality-Based Variational Cluster Approach to Thermodynamic Properties of the Hubbard Model

We develop the variational-cluster-approximation method based on the thermal-pure-quantum-state approach and apply the method to the calculations of the thermodynamic properties of the Hubbard model, thereby obtaining the temperature dependence of the single-particle excitation spectra, entropy and specific heat, and order parameter of the antiferromagnetic phase efficiently. We thus demonstrate that the method developed here has a potential power for elucidating finite-temperature properties of strongly correlated electron systems.

SpM: Sparse modeling tool for analytic continuation of imaginary-time Green’s function

We present SpM, a sparse modeling tool for the analytic continuation of imaginary-time Green’s function, licensed under GNU General Public License version 3. In quantum Monte Carlo simulation, dynamic physical quantities such as single-particle and magnetic excitation spectra can be obtained by applying analytic continuation to imaginary-time data. However, analytic continuation is an ill-conditioned inverse problem and thus sensitive to noise and statistical errors. SpM provides stable analytic continuation against noise by means of a modern regularization technique, which automatically selects bases that contain relevant information unaffected by noise. This paper details the use of this program and shows some applications. Program summaryProgram Title: SpMProgram Files doi:http://dx.doi.org/10.17632/ycmpsnv5yx.1Licensing provisions: GNU General Public License version 3Programming language: C++.External routines/libraries: BLAS, LAPACK, and CPPLapack libraries.Nature of problem: The analytic continuation of imaginary-time input data to real-frequency spectra is known to be an ill-conditioned inverse problem and very sensitive to noise and the statistic errors.Solution method: By using a modern regularization technique, analytic continuation is made robust against noise since the basis that is unaffected by the noise is automatically selected.

Nonperturbative Extraction of the Effective Mass in Neutron Matter.

We carry out nonperturbative calculations of the single-particle excitation spectrum in strongly interacting neutron matter. These are microscopic quantum MonteCarlo computations of many-neutron energies at different densities as well as several distinct excited states. As input, we employ both phenomenological and chiral two- and three-nucleon interactions. We use the single-particle spectrum to extract the effective mass in neutron matter. With a view to systematizing the error involved in this extraction, we carefully assess the impact of finite-size effects on the quasiparticle dispersion relation. We find an effective-mass ratio that drops from 1 as the density is increased. We conclude by connecting our results with the physics of ultracold gases as well as with energy-density functional theories of nuclei and neutron-star matter.

Perturbation calculations of nucleon–nucleon effective interactions in the Hartree–Fock basis

We prove that the Hartree–Fock (HF) basis provides good convergences for many-body perturbation calculations with renormalized realistic nuclear forces. Two types of ab initio perturbation calculations of effective interactions have been performed in the HF basis instead of the harmonic oscillator basis. One is called the Brillouin–Wigner (BW) perturbation and another is the Rayleigh–Schrödinger (RS) perturbation. The results show that ab initio perturbation calculations within the HF basis have comparably good convergences as the nonperturbative in-medium similarity renormalization group. In the HF basis some types of perturbation diagrams can be cancelled out, while the cancellation does not happen in the harmonic oscillator basis. We have investigated the sd shell with the chiral N3LO potential softened by . With the low-momentum N3LO potential, we first perform the spherical HF calculation for the 16O core, and use the perturbations to derive the sd-shelleffective two-body interactions in the HF basis. The calculations give simultaneously single-particle energies and excitation spectra of two-valence-particle systems (i.e. 18O, 18F, and 18Ne in the sd shell). Convergences have been analyzed order by order. We find that the HF RS perturbation gives even better results than the HF BW approximation. The HF effective interactions derived by the perturbations can be used for further many-body calculations.

Variational cluster approach to thermodynamic properties of interacting fermions at finite temperatures: A case study of the two-dimensional single-band Hubbard model at half filling

We formulate a finite-temperature scheme of the variational cluster approximation (VCA) particularly suitable for an exact-diagonalization cluster solver. Based on the analytical properties of the single-particle Green's function matrices, we explicitly show the branch-cut structure of logarithm of the complex determinant functions appearing in the self-energy-functional theory (SFT) and whereby construct an efficient scheme for the finite-temperature VCA. We first apply the method to explore the antiferromagnetic order in a half-filled Hubbard model by calculating the entropy, specific heat, and single-particle excitation spectrum for different values of on-site Coulomb repulsion $U$ and temperature $T$. We also calculate the $T$ dependence of the single-particle excitation spectrum in the strong coupling region, and discuss the overall similarities to and the fine differences from the spectrum obtained by the spin-density-wave mean-field theory at low temperatures and the Hubbard-I approximation at high temperatures. On the basis of the thermodynamic properties, we obtain a crossover diagram in the $(U,T)$-plane which separates a Slater-type insulator and a Mott-type insulator. Next, we demonstrate the finite-temperature scheme in the cluster-dynamical-impurity approximation (CDIA) and study the paramagnetic Mott metal-insulator transition in the half-filled Hubbard model. Formulating the finite-temperature CDIA, we first address a subtle issue regarding the treatment of the artificially introduced bath degrees of freedom which are absent in the originally considered Hubbard model. We then apply the finite-temperature CDIA to calculate the finite-temperature phase diagram in the $(U,T)$-plane. We find that the Mott transition at low temperatures is discontinuous, and the coexistence region of the metallic and insulating states persists down to zero temperature.

Re-examining the quadratic approximation in theory of a weakly interacting Bose gas with condensate: the role of nonlocal interaction potentials

We derive and analyze the coupled equations of quadratic approximation of the Bogoliubov model for a weakly interacting Bose gas. The first equation determines the condensate density as a variational parameter and ensures the minimum of the grand thermodynamic potential. The second one provides a relation between the total number of particles and chemical potential. Their consistent theoretical analysis is performed for a number of model interaction potentials including contact (local) and nonlocal interactions, where the latter provide nontrivial dependencies in momentum space. We demonstrate that the derived equations have no solutions for the local potential, although they formally reproduce the well-known results of the Bogoliubov approach. At the same time, it is shown that these equations have the solutions for physically relevant nonlocal potentials. We show that in the regimes close to experimental realizations with ultracold atoms, the contribution of the terms originating from the quadratic part of the truncated Hamiltonian to the chemical potential can be of the same order of magnitude as from its c-number part. Due to this fact, in particular, the spectrum of single-particle excitations in the quadratic approximation acquires a gap. The issue of the gap is also discussed.

Theory of Fermi Liquid with Flat Bands

A self-consistent theory of Fermi systems hosting flat bands is developed. Compared with an original model of fermion condensation, its key point consists in proper accounting for mixing between condensate and non-condensate degrees of freedom that leads to formation of a non-BCS gap \(\Upsilon (\mathbf{p})\) in the single-particle spectrum. The results obtained explain: (1) the two-gap structure of spectra of single-particle excitations of electron systems of copper oxides, revealed in ARPES studies, (2) the role of violation of the topological stability of the Landau state in the arrangement of the \(T-x\) phase diagram of this family of high-\(T_\mathrm{c}\) superconductors, (3) the topological nature of a metal–insulator transition, discovered in homogeneous two-dimensional low-density electron liquid of MOSFETs more than 20 years ago.

Bose–Einstein condensation of heteronuclear bound states formed in a Fermi gas of two atomic species: a microscopic approach

We study a many-body system of interacting fermionic atoms of two species that are in thermodynamic equilibrium with their condensed heteronuclear bound states (molecules). In order to describe such an equilibrium state, we use a microscopic approach that involves the Bogoliubov model for a weakly interacting Bose gas and approximate formulation of the second quantization method in the presence of bound states of particles elaborated earlier by the authors. This microscopic approach is valid at low temperatures, when the average kinetic energy of all the components in the system is small in comparison with the bound state energy. The coupled equations, which relate the chemical potentials of fermionic components and molecular condensate density, are obtained within the proposed theory. At zero temperature, these equations are analyzed both analytically and numerically, attracting the relevant experimental data. We find the conditions at which a condensate of heteronuclear molecules coexists in equilibrium with degenerate components of a Fermi gas. The ground state energy and single-particle excitation spectrum are found. The boundaries of the applicability of the developed microscopic approach are analyzed.