Ground State Pair Research Articles

Absence of the FFLO/BCS hybrid paired ground state in superconducting Weyl semimetals

Absence of the FFLO/BCS hybrid paired ground state in superconducting Weyl semimetals

Neutron-proton pairing in the N=Z radioactive fp-shell nuclei 56Ni and 52Fe probed by pair transfer

The isovector and isoscalar components of neutron-proton pairing are investigated in the N=Z unstable nuclei of the fp-shell through the two-nucleon transfer reaction (p,3He) in inverse kinematics. The combination of particle and gamma-ray detection with radioactive beams of 56Ni and 52Fe, produced by fragmentation at the GANIL/LISE facility, made it possible to carry out this study for the first time in a closed and an open-shell nucleus in the fp-shell. The transfer cross-sections for ground-state to ground-state (J=0+, T=1) and to the first (J=1+, T=0) state were extracted for both cases together with the transfer cross-section ratios σ(0+,T=1)/σ(1+,T=0). They are compared with second-order distorted-wave born approximation (DWBA) calculations. The enhancement of the ground-state to ground-state pair transfer cross-section close to mid-shell, in 52Fe, points towards a superfluid phase in the isovector channel. For the “deuteron-like” transfer, very low cross-sections to the first (J=1+, T=0) state were observed both for 56Ni(p,3He) and 52Fe(p,3He) and are related to a strong hindrance of this channel due to spin-orbit effect. No evidence for an isoscalar deuteron-like condensate is observed.

Locally equivalent quasifree states and index theory

We consider quasifree ground states of Araki’s self-dual canonical anti-commutation relation algebra from the viewpoint of index theory and symmetry protected topological (SPT) phases. We first review how Clifford module indices characterise a topological obstruction to connect pairs of symmetric gapped ground states. This construction is then generalised to give invariants in with A a -algebra of allowed deformations. When A = C*(X), the Roe algebra of a coarse space X, and we restrict to gapped ground states that are locally equivalent with respect X, a K-homology class is also constructed. The coarse assembly map relates these two classes and clarifies the relevance of K-homology to free-fermionic SPT phases.

η -pairing ground states in the non-Hermitian Hubbard model

The introduction of non-Hermiticity has greatly enriched the research field of traditional condensed matter physics and eventually led to a series of discoveries of exotic phenomena. We investigate the effect of non-Hermitian imaginary hoppings on the Hubbard model. The exact bound-pair solution shows that the electron-electron correlation suppresses the non-Hermiticity, resulting in off-diagonal long-range order (ODLRO) ground state in the attractive Hubbard model. In a large $U$ limit, such non-Hermiticity contributes an extra minus sign in the virtual exchange of the particles. As a consequence, the energy of the effective spin model describing the behavior of the ground state and low energy excitations will be reversed. The corresponding ground state experiences a transition from antiferromagnetism to ferromagnetism characterized by the appearance of a non-decaying correlation function. The numerical result indicates that the $\ensuremath{\eta}$-pairing ground state exits in 1D and 2D systems and is insensitive to the disorder. We further propose a protocol to adiabatically generate the $\ensuremath{\eta}$-pairing state. Our results provide a promising approach for the non-Hermitian strongly correlated system.

Variational theory combining number-projected BCS and coupled-cluster doubles

The ground state pairing correlations in finite fermionic systems are described with a high degree of accuracy within a variational approach based on a combined coupled-cluster and particle-number-projected BCS ansatz. The flexibility of this symmetry-preserving wavefunction enables a unified picture valid from weak to strong coupling, both in small and large systems. The present variational approach consistently yields an energy upper bound while operating at the same level of precision of the non-variational particle-number projected Bogoliubov-coupled-cluster theory [Phys. Rev. C 99, 044301 (2019)].

Dispersion without Many-Body Density Distortion: Assessment on Atoms and Small Molecules.

The “fixed diagonal matrices” (FDM) dispersion formalism [Kooi, D. P.; et al. J. Phys. Chem. Lett.2019, 10, 153730865464] is based on a supramolecular wave function constrained to leave the diagonal of the many-body density matrix of each monomer unchanged, reducing dispersion to a balance between kinetic energy and monomer–monomer interaction. The corresponding variational optimization leads to expressions for the dispersion energy in terms of the ground-state pair densities of the isolated monomers only, providing a framework to build new approximations without the need for polarizabilities or virtual orbitals. Despite the underlying microscopic real space mechanism being incorrect, as in the exact case there is density relaxation, the formalism has been shown to give extremely accurate (or even exact) dispersion coefficients for H and He. The question we answer in this work is how accurate the FDM expressions can be for isotropic and anisotropic C6 dispersion coefficients when monomer pair densities are used from different levels of theory, namely Hartree–Fock, MP2, and CCSD. For closed-shell systems, FDM with CCSD monomer pair densities yield a mean average percent error for isotropic C6 dispersion coefficients of about 7% and a maximum absolute error within 18%, with a similar accuracy for anisotropies. The performance for open-shell systems is less satisfactory, with CCSD pair densities performing sometimes worse than Hartree–Fock or MP2. In the present implementation, the computational cost on top of the monomer’s ground-state calculations is O(N4). The results show little sensitivity to the basis set used in the monomer’s calculations.

Ground state wave function overlap in superconductors and superfluids

Abstract In order to elucidate the quantum ground state structure of nonrelativistic condensates, we explicitly construct the ground state wave function for multiple species of bosons, describing either superconductivity or superfluidity. Since each field Ψ j carries a phase θ j and the Lagrangian is invariant under rotations θ j → θ j + α j for independent α j , one can investigate the corresponding wave function overlap between a pair of ground states 〈 G | G ′ 〉 $\langle G\vert {G}^{\prime }\rangle $ differing by these phases. We operate in the infinite volume limit and use a particular prescription to define these states by utilizing the position space kernel and regulating the UV modes. We show that this overlap vanishes for most pairs of rotations, including θ j → θ j + m j ϵ, where m j is the mass of each species, while it is unchanged under the transformation θ j → θ j + q j ϵ, where q j is the charge of each species. We explain that this is consistent with the distinction between a superfluid, in which there is a nontrivial conserved number, and the superconductor, in which the electric field and conserved charge is screened, while it is compatible with a nonzero order parameter in both cases. Moreover, we find that this bulk ground state wave function overlap directly reflects the Goldstone boson structure of the effective theory and provides a useful diagnostic of its physical phase.

η -pairing in correlated fermion models with spin-orbit coupling

We generalize the $\eta$-pairing theory in Hubbard models to the ones with spin-orbit coupling (SOC) and obtain the conditions under which the $\eta$-pairing operator is an eigenoperator of the Hamiltonian. The $\eta$ pairing thus reveals an exact $SU(2)$ pseudospin symmetry in our spin-orbit coupled Hubbard model, even though the $SU(2)$ spin symmetry is explicitly broken by the SOC. In particular, these exact results can be applied to a variety of Hubbard models with SOC on either bipartite or non-bipartite lattices, whose noninteracting limit can be a Dirac semimetal, a Weyl semimetal, a nodal-line semimetal, and a Chern insulator. The $\eta$ pairing conditions also impose constraints on the band topology of these systems. We then construct and focus on an interacting Dirac-semimetal model, which exhibits an exact pseudospin symmetry with fine-tuned parameters. The stability regions for the exact $\eta$-pairing ground states (with momentum $\bm{\pi}$ or $\bm{0}$) and the exact charge-density-wave ground states are established. Between these distinct symmetry-breaking phases, there exists an exactly solvable multicritical line. In the end, we discuss possible experimental realizations of our results.

Minimal-size real-space d -wave pairing operator in CuO2 planes

A novel minimal-size pairing operator $\Delta^{\dagger}_{D0}$ with $d$-wave symmetry in CuO$_2$ planes is introduced. This pairing operator creates on-site Cooper pairs at the four oxygens that surround a copper atom. Via the time evolution of $\Delta^{\dagger}_{D0}$, an additional inter-orbital pairing operator $\Delta^{\dagger}_{Dpd}$ with $d$-wave symmetry is generated that pairs fermions located in a Cu and its four surrounding O's. The subsequent time evolution of $\Delta^{\dagger}_{Dpd}$ generates an intra-orbital $d$-wave pairing operator $\Delta^{\dagger}_{Dpp}$ involving the four O atoms that surround a Cu, as well as the $d$-wave operator $\Delta^{\dagger}_D$ traditionally used in single-band models for cuprates. Because we recover the larger size operators extensively used in the three-orbital Hubbard model, we suggest that long-range order using the canonical extended operators occurs together with long-range order in the new minimal operators. However, our minimal $d$-wave operators could be more practical to study $d$-wave superconductivity because in the finite-size relatively small systems accessible to computational techniques it is easier to observe long-range order using local operators. Moreover, an effective model with the usual tight-binding hopping of the CuO$_2$ planes supplemented by an attractive potential $V$ in the $d$-wave channel is introduced. Using mean-field techniques we show that a paired ground state is stabilized for any finite value of $V$.

Spontaneous rotational symmetry breaking in a Kramers two-level system

Here, I develop a model for a two-level system that respects the time-reversal symmetry of the atom Hamiltonian and the Kramers theorem. The two-level system is formed by two Kramers pairs of excited and ground states. It is shown that due to the spin-orbit interaction it is in general impossible to find a basis of atomic states for which the crossed transition dipole moment vanishes. The parametric electric polarizability of the Kramers two-level system for a definite ground-state is generically nonreciprocal. I apply the developed formalism to study Casimir-Polder forces and torques when the two-level system is placed nearby either a reciprocal or a nonreciprocal substrate. In particular, I investigate the stable equilibrium orientation of the two-level system when both the atom and the reciprocal substrate have symmetry of revolution about some axis. Surprisingly, it is found that when chiral-type dipole transitions are dominant the stable ground state is not the one in which the symmetry axes of the atom and substrate are aligned. The reason is that the rotational symmetry may be spontaneously broken by the quantum vacuum fluctuations, so that the ground state has less symmetry than the system itself.

Phase stiffness in an antiferromagnetic superconductor

We analyze the suppression of the phase stiffness in a superconductor by antiferromagnetic order. The analysis is based on a general expression for the phase stiffness in a mean-field state with coexisting spin-singlet superconductivity and spiral magnetism. Neel order is included as a special case. Close to half-filling, where the pairing gap is much smaller than the magnetic gap, a simple formula for the phase stiffness in terms of magnetic quasi-particle bands is derived. The phase stiffness is determined by charge carriers in small electron or hole pockets in this regime. The general analysis is complemented by a numerical calculation for the two-dimensional Hubbard model with nearest and next-to-nearest neighbor hopping amplitudes at a moderate interaction strength. The resulting phase stiffness exhibits a striking electron-hole asymmetry. In the ground state, it is larger than the pairing gap on the hole-doped side, and smaller for electron doping. Hence, in the hole-doped regime near half-filling the ground state pairing gap sets the scale for the Kosterlitz-Thouless temperature T_c^{KT}, while in the slightly electron-doped regime T_c^{KT} is determined essentially by the ground state phase stiffness.

A Variational Approach to London Dispersion Interactions without Density Distortion.

We introduce a class of variational wave functions that captures the long-range interaction between neutral systems (atoms and molecules) without changing the diagonal of the density matrix of each monomer. The corresponding energy optimization yields explicit expressions for the dispersion coefficients in terms of the ground-state pair densities of the isolated systems, providing a clean theoretical framework to build new approximations in several contexts. As the individual monomer densities are kept fixed, we can also unambiguously assess the effect of the density distortion on London dispersion interactions; for example, we obtain virtually exact dispersion coefficients between two hydrogen atoms up to C10 and relative errors below 0.2% in other simple cases.

A near-linear scaling equation of motion coupled cluster method for ionized states.

In this work, a domain-based local pair natural orbital (DLPNO) version of the equation of motion coupled cluster theory with single and double excitations for ionization potentials (IP-EOM-CCSD) equations has been formulated and implemented. The method uses ground state localized occupied and pair natural virtual orbitals and applies the DLPNO machinery to arrive at a linear scaling implementation of the IP-EOM-CCSD method. The accuracy of the method is controllable using ground state truncation parameters. Using default thresholds, the method predicts ionization potential (IP) values with good accuracy (mean absolute error of 0.08 eV). We demonstrate that our code can be used to compute IP values for systems with more than 1000 atoms and 10 000 basis functions.

Electron\u2013electron interactions and the paired-to-nematic quantum phase transition in the second Landau level

In spite of its ubiquity in strongly correlated systems, the competition of paired and nematic ground states remains poorly understood. Recently such a competition was reported in the two-dimensional electron gas at filling factor ν = 5/2. At this filling factor a pressure-induced quantum phase transition was observed from the paired fractional quantum Hall state to the quantum Hall nematic. Here we show that the pressure-induced paired-to-nematic transition also develops at ν = 7/2, demonstrating therefore this transition in both spin branches of the second orbital Landau level. However, we find that pressure is not the only parameter controlling this transition. Indeed, ground states consistent with those observed under pressure also develop in a sample measured at ambient pressure, but in which the electron–electron interaction was tuned close to its value at the quantum critical point. Our experiments suggest that electron–electron interactions play a critical role in driving the paired-to-nematic transition.

Subpicosecond X rotations of atomic clock states

We demonstrate subpicosecond-timescale population transfer between the pair of hyperfine ground states of atomic rubidium using a single laser-pulse. Our scheme utilizes the geometric and dynamic phases induced during Rabi oscillation through the fine-structure excited state to construct an $X$ rotation gate for the hyperfine-state qubit system. The experiment performed with a femtosecond laser and cold rubidium atoms, in a magnetooptical trap, shows over 98% maximal population transfer between the clock states.

Hole pairing and ground state properties of high-T c superconductivity within the t–t′–J–V model

The t–t′–J–V model, one of the realistic models for studying high-T c cuprates, has been investigated to explore the hole pairing and other ground state properties using exact diagonalization (ED) technique with 2 holes in a small 8-site cluster. The role of next-nearest-neighbor (NNN) hopping and nearest-neighbor (NN) Coulomb repulsion has been considered. It appears that qualitative behavior of the ground state energies of an 8-site and 16- or 18-site cluster is similar. Results show that a small short-ranged antiferromagnetic (AF) correlation exists in the 2 hole case which is favored by large V∕t. A superconducting phase emerges at 0 ≤ V∕t ≤ 4J. Hole–hole correlation calculation also suggests that the two holes of the pair are either at |i − j| = 1 or √2. Negative t′∕t suppresses the possibility of pairing of holes. Though s-wave pairing susceptibility is dominant, pairing correlation length calculation indicates that the long range pairing, which is suitable for superconductivity, is in the d-wave channel. Both s- and d-wave pairing susceptibility gets suppressed by V∕t while d-(s-) wave susceptibility gets favored (suppressed) by t′∕t. The charge gap shows a gapped behavior while a spin-gapless region exists at small V∕t for finite t ′ ∕t.

Density–wave-function mapping in degenerate current-density-functional theory

We show that the particle density $\ensuremath{\rho}(\mathbf{r})$ and the paramagnetic current density ${\mathbf{j}}^{p}(\mathbf{r})$ are not sufficient to determine the set of degenerate ground-state wave functions. This is a general feature of degenerate systems where the degenerate states have different angular momenta. We provide a general strategy for constructing Hamiltonians that share the same ground-state density pair yet differ in degree of degeneracy. We then provide a fully analytical example for a noninteracting system subject to electrostatic potentials and uniform magnetic fields. Moreover, we prove that when $(\ensuremath{\rho},{\mathbf{j}}^{p})$ is ensemble $(v,\mathbf{A})$-representable by a mixed state formed from $r$ degenerate ground states, then any Hamiltonian $H({v}^{\ensuremath{'}},{\mathbf{A}}^{\ensuremath{'}})$ that shares this ground-state density pair must have at least $r$ degenerate ground states in common with $H(v,\mathbf{A})$. Thus, any set of Hamiltonians that shares a ground-state density pair $(\ensuremath{\rho},{\mathbf{j}}^{p})$ by necessity has to have at least one joint ground state.

Transport and excitations in a negative-U quantum dot at the LaAlO3/SrTiO3 interface

In a solid-state host, attractive electron–electron interactions can lead to the formation of local electron pairs which play an important role in the understanding of prominent phenomena such as high Tc superconductivity and the pseudogap phase. Recently, evidence of a paired ground state without superconductivity was demonstrated at the level of single electrons in quantum dots at the interface of LaAlO3 and SrTiO3. Here, we present a detailed study of the excitation spectrum and transport processes of a gate-defined LaAlO3/SrTiO3 quantum dot exhibiting pairing at low temperatures. For weak tunneling, the spectrum agrees with calculations based on the Anderson model with a negative effective charging energy U, and exhibits an energy gap corresponding to the Zeeman energy of the magnetic pair-breaking field. In contrast, for strong coupling, low-bias conductance is enhanced with a characteristic dependence on temperature, magnetic field and chemical potential consistent with the charge Kondo effect.

Paired states in half-filled Landau levels

We discuss monolayer and bilayer quantum Hall systems in which each layer is a half-filled Landau level (LL) system. In the mean field approximation of the Son's formalism there is a common pairing structure that underlines the possibilities for paired ground states in both systems. We argue that the particle-hole (PH) Pfaffian state in the (particle-hole symmetric) half-filled LL of a monolayer, and analogous state in the PH symmetric bilayer (in which each layer is half-filled LL) can be considered as {\em critical states} i.e. states that cannot describe a phase under PH symmetry. We point out that the inclusion of a PH symmetry breaking (like LL mixing) may stabilize the PH Pfaffian in a monolayer. In the bilayer case, in numerical experiments on a sphere, by choosing the PH symmetric shift, we can stabilize the interlayer correlated (111) excitonic state or critical state, for any distance between the layers, but in general, with no bias, the evolution of the bilayer includes other phases.

Supersolid phases in Bose gases with three-dimensional spin–orbit coupling

We investigate the ground state phases of the two-component Bose–Einstein condensates with three-dimensional Weyl-type spin–orbit coupling (SOC) loaded in a cubic optical lattice. The single-particle lowest energy band exhibits one, two or four pairs of degenerate ground states depending on the configuration of the SOC. We find two types of the supersolid (SS) phases with the isotropic SOC, and the SS phases are signaled by the momentum peaks distribution. We also discuss the spin textures of the SS phases, the spin vectors consist alternatively of two sets of continuous textures at the even and the odd lattice sites.