True Ground State Research Articles

Ground state of the three-dimensional BCS d -wave superconductor

We determine the mean-field ground state of the three-dimensional rotationally symmetric $d$-wave $(\ensuremath{\ell}=2)$ superconductor at weak coupling. It is a noninert state, invariant under the symmetry ${C}_{2}$ only, which breaks time-reversal symmetry almost maximally, and features a high but again less-than-maximal average magnetization. The state obtained by minimization of the expanded sixth-order Ginzburg--Landau free energy is found to be an excellent approximation to the true ground state. The coupling to a parasitic $s$-wave component has only a minuscule quantitative and no qualitative effect on the ground state.

A Tight Lower Bound to the Ground-State Energy.

Ninety years ago Temple ( Proc. R. Soc. (London) 1928 , A119 , 276 ) derived a lower bound for the ground-state energy. The bound was tested and invariably found to be poor as compared to the upper bound obtained through the Rayleigh Ritz procedure due to the fact that it is based also on the second moment of the Hamiltonian. In this paper we (a) improve upon Temple's lower bound estimate for the overlap squared of the true ground-state wave function with the approximate one and (b) describe in detail and generalize our recent improvement on the Temple lower bound based on utilization of higher-order basis functions derived by the Arnoldi algorithm. Both improvements combined lead to a lower bound on the ground-state energy whose accuracy is better than that of the Temple lower bound. This is exemplified by considering the ground-state energy of a quartic potential where one finds that the improvements lead to a lower bound whose quality is comparable to that of the upper bound. The applicability of the method to atoms and molecules is discussed.

Thermal conductivity and diffusion mechanisms of noble gases in uranium dioxide: A DFT+U study

The bulk properties of uranium dioxide (UO2) have been investigated using Hubbard corrected density functional theory (DFT + U) calculations. Monitoring of the occupation matrix for 5f electrons of the uranium atoms is found to be crucial to avoid metastable state solutions and consequently to obtain the true ground state properties of bulk UO2. The lattice contribution to the thermal conductivity was obtained by the solution of the Boltzmann transport equation for phonons based on the interatomic force constants obtained from DFT + U calculations. Furthermore, the relative stabilities of noble gases (He, Ne, Ar, Kr, and Xe) in the octahedral interstitial site of bulk UO2 and their migration are revisited. The effect of the supercell approach for point defects is taken into account by considering the long-range elastic interactions. The computed incorporation energies and energy barriers indicate a size-dependent mechanism for the interstitial migration of noble gases.

Creating emergent phenomena in oxide superlattices

Complex oxides are record holder materials for many phenomena, including ferroelectricity, piezoelectricity, superconductivity and multiferroicity. Complex oxides often have competing ground states with energies slightly higher than that of the true ground state. This competition is fortuitous because thermodynamic variables (for example, temperature, electric field, magnetic field, stress and chemical potentials) can access these metastable phases that are usually hidden but emerge as the energetic landscape is reshaped by adjusting the thermodynamic variables. Epitaxial superlattices are a platform for imposing thermodynamic boundary conditions to unleash the properties of hidden phases by altering the delicate balance between competing spin, charge, orbital and lattice degrees of freedom. Additionally, a feature of complex oxides with large responses (large property coefficients) is the coexistence of phases on the nanoscale. New phases can emerge at the heterointerfaces of oxide superlattices, and X-ray, electron, neutron and proximal probes as well as ab initio theoretical studies can provide insights into these emergent phenomena. Oxide superlattices reveal emergent phenomena if the balance between competing degrees of freedom is altered. In this Review, synthetic approaches to tap the properties of competing ground states are described, focusing on two examples — one example yielding a room-temperature multiferroic and a second producing polarization skyrmions.

Role of defects in determining the magnetic ground state of ytterbium titanate

Pyrochlore systems are ideally suited to the exploration of geometrical frustration in three dimensions, and their rich phenomenology encompasses topological order and fractional excitations. Classical spin ices provide the first context in which it is possible to control emergent magnetic monopoles, and anisotropic exchange leads to even richer behaviour associated with large quantum fluctuations. Whether the magnetic ground state of Yb2Ti2O7 is a quantum spin liquid or a ferromagnetic phase induced by a Higgs transition appears to be sample dependent. Here we have determined the role of structural defects on the magnetic ground state via the diffuse scattering of neutrons. We find that oxygen vacancies stabilise the spin liquid phase and the stuffing of Ti sites by Yb suppresses it. Samples in which the oxygen vacancies have been eliminated by annealing in oxygen exhibit a transition to a ferromagnetic phase, and this is the true magnetic ground state.

DFT+ <i>U</i> Study of the Thermal Conductivity and Noble Gas Impurities in Uranium Dioxide

The bulk properties of uranium dioxide (UO2) have been investigated using Hubbard corrected density functional theory (DFT+U) calculations. Monitoring of the occupation matrix for 5f electrons of the uranium atoms is found to be crucial to avoid metastable state solutions and consequently to obtain the true ground state properties of bulk UO2. The lattice contribution to the thermal conductivity was obtained by the solution of the Boltzmann transport equation for phonons based on the interatomic force constants obtained from DFT+U calculations. Furthermore, the relative stabilities of noble gases (He, Ne, Ar, Kr, and Xe) in the octahedral interstitial site of bulk UO2 and their migration are revisited. The effect of the supercell approach for point defects is taken into account by considering the long-range elastic interactions. The computed incorporation energy and energy barriers indicate a size-dependent mechanism for the interstitial migration of noble gases.

Exact solutions of a model for strange stars with interacting quarks

The search for the true ground state of dense matter has remained open since Edward Witten proposed the strange matter hypothesis in 1984. In this hypothesis, the strange matter is assumed to be composed of u, d, and s quarks, having an energy per baryon lower than that of quark matter (only u and d), and even lower than that of the nuclear matter. In this sense, neutron stars would be strange stars. Later work showed that a color‐flavor‐locked (CFL) state would be preferred to the one without any pairing for a wide range of the parameters (gap Δ, strange quark mass ms, and bag constant B). We use an approximate, yet very accurate, CFL equation of state (EoS) to obtain exact solutions for the static Einstein field equations that describe a compact relativistic object, providing the first solution directly connected with microphysics.

Dark matter axion clump resonance of photons

Recently there has been interest in the physical properties of dark matter axion condensates. Due to gravitational attraction and self-interactions, they can organize into spatial localized clumps, whose properties were examined by us in refs. [1, 2]. Since the axion condensate is coherently oscillating, it can conceivably lead to parametric resonance of photons, leading to exponential growth in photon occupancy number and subsequent radio wave emission. We show that while resonance always exists for spatially homogeneous condensates, its existence for a spatially localized clump condensate depends sensitively on the size of clump, strength of axion-photon coupling, and field amplitude. By decomposing the electromagnetic field into vector spherical harmonics, we are able to numerically compute the resonance from clumps for arbitrary parameters. We find that for spherically symmetric clumps, which are the true BEC ground states, the resonance is absent for conventional values of the QCD axion-photon coupling, but it is present for axions with moderately large couplings, or into hidden sector photons, or from scalar dark matter with repulsive interactions. We extend these results to non-spherically symmetric clumps, organized by finite angular momentum, and find that even QCD axion clumps with conventional couplings can undergo resonant decay for sufficiently large angular momentum. We discuss possible astrophysical consequences of these results, including the idea of a pile-up of clump masses and rapid electromagnetic emission in the sky from mergers.

Gribov copies, avalanches and dynamic generation of a gluon mass

Analytic calculations in the infrared regime of nonabelian gauge theories are hampered by the presence of Gribov copies which results in some ambiguity in the gauge-fixing procedure. This problem shares strong similarities with the issue of finding the true ground state among a large number of metastable states, a typical situation in the field of statistical physics of disordered systems. Building on this analogy, we propose a new gauge-fixing procedure which, we argue, makes more explicit the influence of the Gribov copies. A 1-loop calculation shows that the dynamics of these copies can lead to the spontaneous generation of a gauge-dependent gluon mass.

Effects of stuffing on the atomic and electronic structure of the pyrochlore Yb2Ti2O7

There are reasons to believe that the ground state of the magnetic rare earth pyrochlore Yb$_2$Ti$_2$O$_7$ is on the boundary between competing ground states. We have carried out $\mathrm{\textit{ab initio}}$ density functional calculations to determine the most stable chemical formula as a function of the oxygen chemical potential and the likely location of the oxygen atoms in the unit cell of the "stuffed" system. We find that it is energetically favorable in the "stuffed" crystal (with an Yb replacement on a Ti site) to contain oxygen vacancies which dope the Yb 4$\mathrm{\textit{f}}$ orbitals and qualitatively change the electronic properties of the system. In addition, with the inclusion of the contribution of spin-orbit-coupling (SOC) on top of the GGA+U approach, we investigated the electronic structure and the magnetic moments of the most stable "stuffed" system. In our determined "stuffed" structure the valence bands as compared to those of the pure system are pushed down and a change in hybridization between the O 2$\mathrm{\textit{p}}$ orbitals and the metal ion states is found. Our first-principle findings should form a foundation for effective models describing the low-temperature properties of this material whose true ground state remains controversial.

What can one learn about material structure given a single first-principles calculation?

We extract a variable $X$ from electron orbitals ${\mathrm{\ensuremath{\Psi}}}_{n\mathbf{k}}$ and energies ${E}_{n\mathbf{k}}$ in the parent high-symmetry structure of a wide range of complex oxides: perovskites, rutiles, pyrochlores, and cristobalites. Even though calculation was done only in the parent structure, with no distortions, we show that $X$ dictates material's true ground-state structure. We propose using Wannier functions to extract concealed variables such as $X$ both for material structure prediction and for high-throughput approaches.

Solid Parahydrogen Infrared Matrix Isolation and Computational Studies of Lin-(C2H4)m Complexes.

Complexes of lithium atoms with ethylene have been identified as potential hydrogen storage materials. As a Li atom approaches an ethylene molecule, two distinct low-lying electronic states are established; one is the 2A1 electronic state (for C2v geometries) that is repulsive but supports a shallow van der Waals well and correlates with the Li 2s atomic state, and the second is a 2B2 electronic state that correlates with the Li 2p atomic orbital and is a strongly bound charge-transfer state. Only the 2B2 charge-transfer state would be advantageous for hydrogen storage because the strong electric dipole created in the Li-(C2H4) complex due to charge transfer can bind molecular hydrogen through dipole-induced dipole and dipole-quadrupole electrostatic interactions. Ab initio studies have produced conflicting results for which electronic state is the true ground state for the Li-(C2H4) complex. The most accurate ab initio calculations indicate that the 2A1 van der Waals state is slightly more stable. In contrast, argon matrix isolation experiments have clearly identified the Li-(C2H4) complex exists in the 2B2 state. Some have suggested that argon matrix effects shift the equilibrium toward the 2B2 state. We report the low-temperature synthesis and IR characterization of Lin-(C2H4)m (n = 1, m = 1 and 2) complexes in solid parahydrogen which are observed using the C═C stretching vibration of ethylene in the complex. These results show that under cryogenic hydrogen storage conditions the Li-(C2H4) complex is more stable in the 2B2 electronic state and thus constitutes a potential hydrogen storage material with desirable characteristics.

Inspecting Non-Perturbative Contributions to the Entanglement Entropy via Wavefunctions

In this paper, we would like to systematically explore the implications of non-perturbative effects on entanglement in a many body system. Instead of pursuing the usual path-integral method in a singular space, we attempt to study the wavefunctions in detail. We begin with a toy model of multiple particles whose interaction potential admits multiple minima. We study the entanglement of the true ground state after taking the tunneling effects into account and find some simple patterns. Notably, in the case of multiple particle interactions, entanglement entropy generically decreases with increasing number of minima. The knowledge of the subsystem actually increases with the number of minima. The reduced density matrix can also be seen to have close connections with graph spectra. In a more careful study of the two-well tunneling system, we also extract the exponentially-suppressed tail contribution, the analogue of instantons. To understand the effects of multiple minima in a field theory, we are inspired to inspect wavefunctions in a toy model of a bosonic field describing quasi-particles of two different condensates related by Bogoliubov transformations. We find that the area law is naturally preserved. This is probably a useful set of perspectives that promise wider applications.

Searching for Strange Quark Matter Objects in Exoplanets

Abstract The true ground state of hadronic matter may be strange quark matter (SQM). Consequently, observed pulsars may actually be strange quark stars, but not neutron stars. However, proving or disproving the SQM hypothesis still remains a difficult problem to solve due to the similarity between the macroscopical characteristics of strange quark stars and neutron stars. Here, we propose a hopeful method to probe the existence of SQM. In the framework of the SQM hypothesis, strange quark dwarfs and even strange quark planets can also stably exist. Noting that SQM planets will not be tidally disrupted even when they get very close to their host stars due to their extreme compactness, we argue that we could identify SQM planets by searching for very close-in planets among extrasolar planetary systems. Especially, we should keep our eyes on possible pulsar planets with orbital radius less than ∼5.6 × 1010 cm and period less than ∼6100 s. A thorough search in the currently detected ∼2950 exoplanets around normal main-sequence stars has failed to identify any stable close-in objects that meet the SQM criteria, i.e., lying in the tidal disruption region for normal matter planets. However, the pulsar planet PSR J1719-1438B, with an orbital radius of ∼6 × 1010 cm and orbital period of 7837 s, is, encouragingly, found to be a good candidate.

Simple variational ground state and pure-cat-state generation in the quantum Rabi model

We introduce a simple, physically-motivated variational ground state for the quantum Rabi model, and demonstrate that it provides a high-fidelity approximation of the true ground state in all parameter regimes (including intermediate and strong coupling regimes). Our variational state is constructed using Gaussian cavity states and nonorthogonal qubit pointer states, and contains only three variational parameters. We use our state to develop a heuristic understanding of how the ground state evolves with increasing coupling, and find a previously unexplored regime where the ground state corresponds to the cavity being in a nearly pure Schr\"odinger cat state.

First-Principles Chemical Bonding Study of Manganese Carbodiimide, MnNCN, As Compared to Manganese Oxide, MnO.

We have performed an in-depth study of the chemical bonding in manganese oxide (MnO) and carbodiimide (MnNCN) from correlated spin-polarized density functional calculations. The chemical-bonding data were produced using the LOBSTER package, which has recently been enabled to process PAW-based output from Quantum ESPRESSO. Our results show that the ground states of MnO and MnNCN are similar, namely, antiferromagnetic structures whose axes are the MnO cubic [111] and the MnNCN hexagonal [001] axes, in agreement with experimental results. The results also evidence MnNCN being more covalent than MnO, in harmony with chemical intuition and spectroscopic data. In addition, the crystal orbital Hamilton population (COHP) analysis evidences that adopting the ground-state magnetic structures by MnO and MnNCN makes the cation-anion bonds optimized and annihilates obvious instability issues, that is, the existence of antibonding states in the vicinity of the Fermi level. We also detail the interactions involved in the systems using the recently introduced density-of-energy analysis and by partitioning the total and band-structure energies. While it is trivial that the total energy points toward the true magnetic ground state taken, the COHP integral of the metal-nonmetal bond is also capable of correctly delivering that particular information.

Non-Linear Stationary Solutions in Realistic Models for Analog Black-Hole Lasers

From both a theoretical and an experimental point of view, Bose–Einstein condensates are good candidates for studying gravitational analogues of black holes and black-hole lasers. In particular, a recent experiment has shown that a black-hole laser configuration can be created in the laboratory. However, the most considered theoretical models for analog black-hole lasers are quite difficult to implement experimentally. In order to fill this gap, we devote this work to present more realistic models for black-hole lasers. For that purpose, we first prove that, by symmetrically extending every black-hole configuration, one can obtain a black-hole laser configuration with an arbitrarily large supersonic region. Based on this result, we propose the use of an attractive square well and a double delta-barrier, which can be implemented using standard experimental tools, for studying black-hole lasers. We also compute the different stationary states of these setups, identifying the true ground state of the system and discussing the relation between the obtained solutions and the appearance of dynamical instabilities.

Pairing in doped inversion-symmetric Weyl semimetals: a finite temperature analysis from Thouless criterion

In doped Weyl semimetal with inversion symmetry, the two pairing states, i.e., the zero momentum BCS pairing and the finite momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing are possible in principle. In this paper we use the standard Thouless criterion for the onset of pairings to investigate the leading pairing instability at the finite temperature. Our results suggest that both BCS and FFLO instabilities are possible depending on the on-site attractive interaction. The competition between the BCS pairing and FFLO pairing is driven by the mutual suppression between density of state near the Fermi surface and finite energy band structure in the whole Brillouin zone. For small and intermediate interaction, the former dominates and supports BCS pairing, while for strong interaction, the latter wins and favors FFLO pairing. We expect our results at the finite temperature can provide some important message to identify the true ground state.

Strangeon and Strangeon Star

The nature of pulsar-like compact stars is essentially a central question of the fundamental strong interaction (explained in quantum chromo-dynamics) at low energy scale, the solution of which still remains a challenge though tremendous efforts have been tried. This kind of compact objects could actually be strange quark stars if strange quark matter in bulk may constitute the true ground state of the strong-interaction matter rather than 56Fe (the so-called Witten’s conjecture). From astrophysical points of view, however, it is proposed that strange cluster matter could be absolutely stable and thus those compact stars could be strange cluster stars in fact. This proposal could be regarded as a general Witten’s conjecture: strange matter in bulk could be absolutely stable, in which quarks are either free (for strange quark matter) or localized (for strange cluster matter). Strange cluster with three-light-flavor symmetry is renamed strangeon, being coined by combining “strange nucleon” for the sake of simplicity. A strangeon star can then be thought as a 3-flavored gigantic nucleus, and strangeons are its constituent as an analogy of nucleons which are the constituent of a normal (micro) nucleus. The observational consequences of strangeon stars show that different manifestations of pulsarlike compact stars could be understood in the regime of strangeon stars, and we are expecting more evidence for strangeon star by advanced facilities (e.g., FAST, SKA, and eXTP).

Relation between quantum fluctuations and the performance enhancement of quantum annealing in a nonstoquastic Hamiltonian

We study the relation between quantum fluctuations and the significant enhancement of the performance of quantum annealing in a mean-field Hamiltonian. First-order quantum phase transitions were shown to be reduced to second order by antiferromagnetic transverse interactions in a mean-field-type many-body-interacting Ising spin system in a transverse field, which means an exponential speedup of quantum annealing by adiabatic quantum computation. We investigate if and how quantum effects manifest themselves around these first- and second-order phase transitions to understand if the antiferromagnetic transverse interactions appended to the conventional transverse-field Ising model induce notable quantum effects. By measuring the proximity of the semiclassical spin-coherent state to the true ground state as well as the magnitude of the concurrence representing entanglement, we conclude that significant quantum fluctuations exist around second-order transitions, whereas quantum effects are much less prominent at first-order transitions. Although the location of the transition point can be predicted by the classical picture, system properties near the transition need quantum-mechanical descriptions for a second-order transition but not necessarily for first order. It is also found that quantum fluctuations are large within the ferromagnetic phase after a second-order transition from the paramagnetic phase. These results suggest that the antiferromagnetic transverse interactions induce marked quantum effects, and this fact would be related to closely to the significant enhancement of the performance of quantum annealing.