Non-interacting Scalar Field Research Articles

Entanglement structures in quantum field theories: Negativity cores and bound entanglement in the vacuum

The many-body entanglement between two finite (size-$d$) disjoint vacuum regions of noninteracting lattice scalar field theory in one spatial dimension, i.e., a ${({d}_{A}\ifmmode\times\else\texttimes\fi{}{d}_{B})}_{\mathrm{mixed}}$ Gaussian continuous variable system, is locally transformed into a tensor-product core of ${({1}_{A}\ifmmode\times\else\texttimes\fi{}{1}_{B})}_{\mathrm{mixed}}$ entangled pairs. Accessible entanglement within these core pairs exhibits an exponential hierarchy and as such identifies the structure of dominant region modes from which vacuum entanglement could be extracted into a spatially separated pair of quantum detectors. Beyond the core, the remaining modes of the halo are determined to be $AB$ separable in isolation, as well as separable from the core. However, state preparation protocols that distribute entanglement in the form of ${({1}_{A}\ifmmode\times\else\texttimes\fi{}{1}_{B})}_{\mathrm{mixed}}$ core pairs are found to require additional entanglement in the halo that is obscured by classical correlations. This inaccessible (bound) halo entanglement is found to mirror the accessible entanglement, but with a step behavior as the continuum is approached. It remains possible that alternate initialization protocols that do not utilize the exponential hierarchy of core-pair entanglement may require less inaccessible entanglement. Entanglement consolidation is expected to persist in higher dimensions and may aid classical and quantum simulations of asymptotically free gauge field theories, such as quantum chromodynamics.

Sphaleron bound in some nonstandard cosmology scenarios

In the first scenario, we revise the upper bound of the cutoff scale of the dimension-six potential Higgs operator required for a successful electroweak baryogenesis in the case of a modified expansion history caused by the existence of a noninteracting scalar field at the time phase transition happens. The upper bound 860[Formula: see text]GeV of the cutoff scale in the conventional case can be improved to 1[Formula: see text]TeV in the modified expansion case under certain conditions. In the second scenario, we consider the Randall–Sundrum type II model. We show that the lower bound of the five-dimensional Planck scale in this model, which is determined from the validity of Newtonian gravitational potential at small distance, turns out to be crucial in eliminating this model as a viable candidate to satisfy the sphaleron bound; however, again modifying the expansion history by including a noninteracting scalar field at the electroweak scale can then make this model satisfy the sphaleron bound with a certain parameter space.

Cosmic inflation of generalized Starobinsky model in f(R,ϕ) gravity

In this paper, we investigate the inflationary cosmology in [Formula: see text] gravity by proposing different models of [Formula: see text], where [Formula: see text] is a noninteracting massive scalar field which is nonminimally coupled to gravity in the Jordan frame. In special cases of these models, we could reach the standard Starobinsky model. Further, we calculated the slow-roll parameters, scalar-to-tensor ratio, and spectral index for these models and compared them with observations. Our findings are located in the favorite area of Planck’s recent results. On the other hand, the discovery of the gravitational waves in the range of [Formula: see text] would rule out the Starobinsky model or even the nondiscovery of gravitational wave in this range [Formula: see text] by PICO. Our models, specifically the second one, might be the proper generalization for the Starobinsky model in this regard.

HKLL bulk reconstruction for small ∆

We discuss the extension of the HKLL (Hamilton, Kabat, Lifschytz, and Lowe) bulk reconstruction for non-interacting scalar fields corresponding to conformal weights ∆ smaller than the original condition ∆ > d − 1. We give explicit formulas for the cases d − 2 < ∆ ≤ d − 1 and ∆ = d − s with integer s. In the latter case we show that smearing CFT fields over a region of the boundary consisting of points light-like separated from the bulk point is sufficient for bulk reconstruction, whereas in general smearing over all light-like and space-like separated points is required.

Revisiting dynamics of interacting quintessence

We apply the tools of the dynamical system theory in order to revisit and uncover the structure of a nongravitational interaction between pressureless dark matter and dark energy described by a scalar field phi . For a coupling function Q = -(alpha drho _m/dt + beta drho _phi /dt ), where t is the cosmic time, we have found that it can be rewritten in the form Q = 3H (alpha rho _m + beta (dphi /dt)^2 )/(1-alpha +beta ), so that its dependence on the dark matter density and on the kinetic term of the scalar field is linear and proportional to the Hubble parameter. We analyze the scenarios alpha =0, alpha = beta and alpha = -beta , separately and in order to describe the cosmological evolution we have calculated various observables. A notable result of this work is that, unlike for the noninteracting scalar field with exponential potential where five critical points appear, in the case studied here, with the exception of the matter dominated solution, the remaining singular points are transformed into scaling solutions enriching the phase space. It is shown that for alpha ne 0, a separatrix arises modifying prominently the structure of the phase space. This represents a novel feature no mentioned before in the literature.

Self-gravitating vector dark matter

We derive the non-relativistic limit of a massive vector field. We show that the Cartesian spatial components of the vector behave as three identical, non-interacting scalar fields. We find classes of spherical, cylindrical, and planar self-gravitating vector solitons in the Newtonian limit. The gravitational properties of the lowest-energy vector solitons$\mathrm{-}$the gravitational potential and density field$\mathrm{-}$depend only on the net mass of the soliton and the vector particle mass. In particular, these self-gravitating, ground-state vector solitons are independent of the distribution of energy across the vector field components, and are indistinguishable from their scalar-field counterparts. Fuzzy Vector Dark Matter models can therefore give rise to halo cores with identical observational properties to the ones in scalar Fuzzy Dark Matter models. We also provide novel hedgehog vector soliton solutions, which cannot be observed in scalar-field theories. The gravitational binding of the lowest-energy hedgehog halo is about three times weaker than the ground-state vector soliton. Finally, we show that no spherically symmetric solitons exist with a divergence-free vector field.

Geometric quantum information structure in quantum fields and their lattice simulation

An upper limit to distillable entanglement between two disconnected regions of massless non-interacting scalar field theory has an exponential decay defined by a geometric decay constant. When regulated at short distances with a spatial lattice, this entanglement abruptly vanishes beyond a dimensionless separation, defining a negativity sphere. In two spatial dimensions, we determine this geometric decay constant between a pair of disks and the growth of the negativity sphere toward the continuum through a series of lattice calculations. Making the connection to quantum field theories in three-spatial dimensions, assuming such quantum information scales appear also in quantum chromodynamics (QCD), a new relative scale may be present in effective field theories describing the low-energy dynamics of nucleons and nuclei. We highlight potential impacts of the distillable entanglement structure on effective field theories, lattice QCD calculations and future quantum simulations.

Geometrically confined thermal field theory: Finite size corrections and phase transitions

Motivated by evidence for quark-gluon plasma signatures in small systems, we study a simple model of a massless, noninteracting scalar field confined with Dirichlet boundary conditions. We use this system to investigate the finite size corrections to thermal field--theoretically derived quantities compared to the usual Stefan-Boltzmann limit of an ideal gas not confined in any direction. Two equivalent expressions with different numerical convergence properties are found for the free energy in $D$ rectilinear spacetime dimensions with $c\ensuremath{\le}D\ensuremath{-}1$ spatial dimensions of finite extent. We find that the first law of thermodynamics generalizes such that the pressure depends on direction. For systems with finite dimension(s) but infinite volumes, such as a field constrained between two parallel plates or a rectangular tube, the relative fluctuations in energy are zero, and hence the canonical and microcanonical ensembles are equivalent. We present precise numerical results for the free energy, total internal energy, pressure, entropy, and heat capacity of our field between parallel plates, in a tube, and in finite volume boxes of various sizes in four spacetime dimensions. For temperatures and system sizes relevant for heavy ion phenomenology, we find large deviations from the Stefan-Boltzmann limit for these quantities, especially for the pressure. Our main result is the discovery that an isolated system of fields constrained between parallel plates reveals a divergent isoenergetic compressibility at a critical length ${L}_{c}\ensuremath{\sim}1/T$. This divergence constitutes a novel phase transition, which, unlike the usual temperature-driven phase transition, is driven solely by the size of the system.

Fixed-point quantum circuits for quantum field theories

Renormalization group ideas and effective operators are used to efficiently determine localized unitaries for preparing the ground states of non-interacting scalar field theories on digital quantum devices. With these methods, classically computed ground states in a small spatial volume can be used to determine operators for preparing the ground state in a beyond-classical quantum register, even for interacting scalar field theories. Due to the exponential decay of correlation functions and the double exponential suppression of digitization artifacts, the derived quantum circuits are expected to be relevant already for near-term quantum devices.

Boson stars in f(T) extended theory of gravity

Spherically symmetric configurations of the non-interacting massive complex scalar field, representing non-rotating boson stars, are considered within the framework of the modified torsion based $f(T)$ gravity, with $f(T) = T + \alpha \, T^2/2$. We find that with sufficiently large negative value of $\alpha$ the mass of the boson stars can be made arbitrarily large. This is in contrast to General Relativity where an upper bound, $M_{max} \sim M_{Planck}^2/m$, to the mass of the boson stars built from the non-interacting scalar field exists and where the masses of boson stars in the astrophysical regime can be obtained only with the introduction of the scalar field self-interaction. With sufficiently large negative $\alpha$ we also find negative gravitational binding energy for all masses, which can be seen as an indication of the stability of such configurations. In its positive regime, $\alpha$ can not be made arbitrarily large as a phase transition in the stress--energy components of the $f(T)$-fluid develops. This phenomenon has already been reported to occur in polytropic stars constructed within the $f(T)$ gravity theory.

Minimally entangled state preparation of localized wave functions on quantum computers

Initializing a single site of a lattice scalar field theory into an arbitrary state with support throughout the quantum register requires $O({2}^{{n}_{Q}})$ entangling gates on a quantum computer with ${n}_{Q}$ qubits per site. It is conceivable that instead initializing to functions that are good approximations to states may have utility in reducing the number of required entangling gates. In the case of a single site of a noninteracting scalar field theory, initializing to a symmetric exponential wave function requires ${n}_{Q}\ensuremath{-}1$ entangling gates, the minimal number necessary to create an entangled state of all ${n}_{Q}$ qubits. This is compared with the ${2}^{{n}_{Q}\ensuremath{-}1}+{n}_{Q}\ensuremath{-}3+{\ensuremath{\delta}}_{{n}_{Q},1}$ required for a symmetric Gaussian wave function. In this work, we explore the initialization of one-site (${n}_{Q}=4$), two-site (${n}_{Q}=3$), and three-site (${n}_{Q}=3$) noninteracting scalar field theories with symmetric exponential wave functions using IBM's quantum simulators and quantum devices (Poughkeepsie and Tokyo). With the digitizations attainable with ${n}_{Q}=3,4$, these tensor-product wave functions are found to have large overlap with a Gaussian wave function and provide a suitable low-noise initialization for improvement and Somma inflation. In performing these simulations, we have employed a workflow that interleaves calibrations to mitigate systematic errors in production. The calibrations allow tolerance cuts on gate performance including the fidelity of the symmetrizing Hadamard gate, both in vacuum (${|\mathbf{0}\ensuremath{\rangle}}^{\ensuremath{\bigotimes}{n}_{Q}}$) and in medium (${n}_{Q}\ensuremath{-}1$ qubits initialized to an exponential function). The results obtained in this work are relevant to systems beyond scalar field theories, such as the deuteron radial wave function, two- and three-dimensional Cartesian-space wave functions, and nonrelativistic multinucleon systems built on a localized eigenbasis.

Early-time and late-time quantum chaos

We show the relation between the Heisenberg averaging of regularized 2-point out-of-time ordered correlation function and the 2-point spectral form factor in bosonic quantum mechanics. The generalization to all even-point is also discussed. We also do the direct extension from the bosonic quantum mechanics to the noninteracting scalar field theory. Finally, we find that the coherent state and large-[Formula: see text] approaches are useful in the late-time study. We find that the computation of the coherent state can be simplified by the Heisenberg averaging. Therefore, this provides a simplified way to probe the late-time quantum chaos through a coherent state. The large-[Formula: see text] result is also comparable to the [Formula: see text] numerical result in the large-[Formula: see text] quantum mechanics. This can justify that large-[Formula: see text] technique in bosonic quantum mechanics can probe the late time, not the early time. Because the quantitative behavior of large-[Formula: see text] can be captured from the [Formula: see text] numerical result, the realization in experiments should be possible.

Free energy and entropy for finite temperature quantum field theory under the influence of periodic backgrounds

The basic thermodynamic quantities for a non-interacting scalar field in a periodic potential composed of either a one-dimensional chain of Dirac delta -delta ^prime functions or a specific potential with extended compact support are calculated. First, we consider the representation in terms of real frequencies (or one-particle energies). Then we turn the axis of frequency integration towards the imaginary axis by a finite angle, which allows for easy numerical evaluation, and finally turn completely to the imaginary frequencies and derive the corresponding Matsubara representation, which this way appears also for systems with band structure. In the limit case T rightarrow 0 we confirm earlier results on the vacuum energy. We calculate for the mentioned examples the free energy and the entropy and generalize earlier results on negative entropy.

The probe of curvature in the Lorentzian AdS2/CFT1 correspondence

We establish the Lorentzian AdS2/CFT1 correspondence from a reconstruction of all bulk points through the kinematic-space approach. The OPE block is exactly a bulk local operator. We formulate the correspondence between the bulk propagator in the non-interacting scalar field theory and the conformal block in CFT1. When we consider the stress tensor, the variation probes the variation of AdS2 metric. The reparameterization provides the asymptotic boundary of the bulk spacetime as in the derivation of the Schwarzian theory from two-dimensional dilaton gravity theory. Finally, we find the AdS2 Riemann curvature tensor based on the above consistent check.

Model-independent constraints on dark energy evolution from low-redshift observations

Knowing the late time evolution of the Universe and finding out the causes for this evolution are the important challenges of modern cosmology. In this work, we adopt a model-independent cosmographic approach and approximate the Hubble parameter considering the Pade approximation which works better than the standard Taylor series approximation for $z>1$. With this, we constrain the late time evolution of the Universe considering low-redshift observations coming from SNIa, BAO, $H(z)$, $H_{0}$ , strong-lensing time-delay as well as the Megamaser observations for angular diameter distances. We confirm the tensions with $\Lambda$CDM model for low-redshifts observations. The present value of the equation of state for the dark energy has to be phantom-like and for other redshifts, it has to be either phantom or should have a phantom crossing. For lower values of $\Omega_{m0}$, multiple phantom crossings are expected. This poses serious challenges for single, non-interacting scalar field models for dark energy. We derive constraints on the {\it statefinders} $(r,s)$ and these constraints show that a single dark energy model cannot fit data for the whole redshift range $0\leq z\leq 2$: in other words, we need multiple dark energy behaviors for different redshift ranges. Moreover, the constraint on sound speed for the total fluid of the Universe, and for the dark energy fluid (assuming them being barotropic), rules out the possibility of a barotropic fluid model for unified dark sector and barotropic fluid model for dark energy, as fluctuations in these fluids are unstable as $c_{s}^2 < 0$ due to constraints from low-redshift observations.

Non-relativistic limit of thermodynamics of Bose field in a static space-time and Bose–Einstein condensation

We consider the grand canonical thermodynamics of a noninteracting scalar field in a static spacetime. We take the nonrelativistic limit of thermodynamic quantities in a way that leaves the curved structure of the background geometry intact. Using Mellin transform and heat kernel techniques we obtain asymptotic expansions of thermodynamic quantities appropriate for the analysis of Bose–Einstein condensation. We apply our results to investigate gravitational effects on the Bose–Einstein condensation for a scalar field in a finite volume. We also analyze the boundary effects on the depletion coefficient of the scalar field.

Rotation curves of high-resolution LSB and SPARC galaxies with fuzzy and multistate (ultralight boson) scalar field dark matter

Cold dark matter (CDM) has shown to be an excellent candidate for the dark matter (DM) of the Universe at large scales, however it presents some challenges at the galactic level. The scalar field dark matter (SFDM), also called fuzzy, wave, Bose-Einstein condensate or ultra-light axion DM, is identical to CDM at cosmological scales but different at the galactic ones. SFDM forms core halos, it has a natural cut-off in its matter power spectrum and it predicts well-formed galaxies at high redshifts. In this work we reproduce the rotation curves of high-resolution low surface brightness (LSB) and SPARC galaxies with two SFDM profiles: (1)~The soliton+NFW profile in the fuzzy DM (FDM) model, arising empirically from cosmological simulations of real, non-interacting scalar field (SF) at zero temperature, and (2)~the multistate SFDM (mSFDM) profile, an exact solution to the Einstein-Klein-Gordon equations for a real, self-interacting SF, with finite temperature into the SF potential, introducing several quantum states as a realistic model for a SFDM halo. From the fits with the soliton+NFW profile, we obtained for the boson mass $0.212< m_\psi/(10^{-23} \mathrm{eV}/c^2)<27.0$ and for the core radius $0.326< r_c/\mathrm{kpc}<8.96$. From the combined analysis with the LSB galaxies, we obtained $m_\psi = 0.554 \times10^{-23}\mathrm{eV}$, a result in tension with the severe cosmological constraints. Also, we show the analytical mSFDM model fits the observations as well as or better than the empirical soliton+NFW profile, and it reproduces naturally the wiggles present in some galaxies, being a theoretically motivated framework additional or alternative to the FDM profile.

Thermal Field Theory in Small Systems

We compute the finite size corrections to the partition function in a Cartesian space of finite extent in M directions and of infinite extent in D – M directions for a massless, non-interacting scalar field theory. We then use this partition function to compute numerically the energy density, pressure, entropy density, and speed of sound for this theory for M = 1, 2, and 3 for D = 3 total spatial dimensions. The finite size corrections for the speed of sound are ∼ 600%, which indicates the need to consider these corrections in hydrodynamic simulations of small collision systems in high energy nuclear physics.

Towards an analytic construction of the wavefunction of boson stars

Light scalar fields can form gravitationally bound compact objects called boson stars. The profile of boson stars in the Newtonian limit is described by the Gross-Pitaevskii-Poisson equations. We present a semi-analytic solution to these equations and construct the profile of boson stars formed by a non-interacting scalar field. Our solution is stable with respect to numerical errors and has accuracy better than $10^{-6}$ over the entire range.

Wormholes without exotic matter in Einstein–Cartan theory

We study the possible existence of static traversable wormholes without invoking exotic matter in the framework of the Einstein--Cartan theory. A family of exact static, spherically symmetric wormhole solutions with an arbitrary throat radius, with flat or AdS asymptotic behavior, has been obtained with sources in the form of two noninteracting scalar fields with nonzero potentials. Both scalar fields are canonical (that is, satisfy the weak energy condition), one is minimally and the other nonminimally coupled to gravity, and the latter is a source of torsion.