Twisted Boundary Research Articles

Continuum damping effects in nuclear collisions associated with twisted boundary conditions

The time-dependent Skyrme Hartree-Fock calculations have been performed to study $^{24}$Mg +$^{24}$Mg collisions. The twisted boundary conditions, which can avoid finite box-size effects of the employed 3D coordinate space, have been implemented. The prolate deformed $^{24}$Mg has been set to different orientations to study vibrations and rotations of the compound nucleus $^{48}$Cr. Our time evolution results show continuum damping effects associated with the twist-averaged boundary condition play a persistent role after the fusion stage. In particular, a rotational damping in continuum is presented in calculations of both twist-averaged and absorbing boundary conditions, in which damping widths can be clearly extracted. It is unusual that the rotating compound nucleus in continuum evolves towards spherical but still has a considerable angular momentum.

Fractional instanton of the SU(3) gauge theory in weak coupling regime

Motivated by recent studies on the resurgence structure of quantum field theories, we numerically study the nonperturbative phenomena of the SU(3) gauge theory in a weak coupling regime. We find that topological objects with a fractional charge emerge if the theory is regularized by an infrared (IR) cutoff via the twisted boundary conditions. Some configurations with nonzero instanton number are generated as a semi-classical configuration in the Monte Carlo simulation even in the weak coupling regime. Furthermore, some of them consist of multiple fractional-instantons. We also measure the Polyakov loop to investigate the center symmetry and confinement. The fractional-instanton corresponds to a solution linking two of degenerate ℤ3-broken vacua in the deconfinement phase.

Many-Body Chern Number without Integration.

The celebrated work of Niu, Thouless, and Wu demonstrated the quantization of Hall conductance in the presence of many-body interactions by revealing the many-body counterpart of the Chern number. The generalized Chern number is formulated in terms of the twisted angles of the boundary condition, instead of the single particle momentum, and involves an integration over all possible twisted angles. However, this formulation is physically unnatural, since topological invariants directly related to observables should be defined for each Hamiltonian under a fixed boundary condition. In this work, we show via numerical calculations that the integration is indeed unnecessary-the integrand itself is effectively quantized and the error decays exponentially with the system size. This implies that the numerical cost in computing the many-body Chern number could, in principle, be significantly reduced as it suffices to compute the Berry connection for a single value of the twisted boundary condition if the system size is sufficiently large.

Color structure of gluon field magnetic mass

The color structure of the gluon field magnetic mass is investigated in the lattice SU(2) gluodynamics. To realize that the interaction between a monopole–antimonopole string and external neutral Abelian chromomagnetic field flux is considered. The string is introduced in the way proposed by Srednicki and Susskind. The neutral Abelian field flux is introduced through the twisted boundary conditions. Monte Carlo simulations are performed on 4D lattices at finite temperature. It is shown that the presence of the Abelian field flux weakens the screening of the string field. That means decreasing the gluon magnetic mass for this environment. The contribution of the neutral Abelian field has the form of “enhancing” factor in the fitting functions. This behavior independently confirms the long-range nature of the neutral Abelian field reported already in the literature. The comparison with analytic calculations is given.

Improving the kinetic couplings in lattice nonrelativistic QCD

We improve the non-relativistic QCD (NRQCD) action by comparing the dispersion relation to that of the continuum through $\mathcal{O}(p^6)$ in perturbation theory. The one-loop matching coefficients of the $\mathcal{O}(p^4)$ kinetic operators are determined, as well as the scale at which to evaluate $\alpha_s$ in the $V$-scheme for each quantity. We utilise automated lattice perturbation theory using twisted boundary conditions as an infrared regulator. The one-loop radiative corrections to the mass renormalisation, zero-point energy and overall energy-shift of an NRQCD $b$-quark are also found. We also explore how a Fat$3$-smeared NRQCD action and changes of the stability parameter $n$ affect the coefficients. Finally, we use gluon field ensembles at multiple lattice spacing values, all of which include $u$, $d$, $s$ and $c$ quark vacuum polarisation, to test how the improvements affect the non-perturbatively determined $\Upsilon(1S)$ and $\eta_b(1S)$ kinetic masses, and the tuning of the $b$ quark mass.

The twisted gradient flow coupling at one loop

We compute the one-loop running of the SU(N) ’t Hooft coupof twelve-flavor SU(3) gauge theoryling in a finite volume gradient flow scheme using twisted boundary conditions. The coupling is defined in terms of the energy density of the gradient flow fields at a scale tilde{l} given by an adequate combination of the torus size and the rank of the gauge group, and is computed in the continuum using dimensional regularization. We present the strategy to regulate the divergences for a generic twist tensor, and determine the matching to the overline{mathrm{MS}} scheme at one-loop order. For the particular case in which the twist tensor is non-trivial in a single plane, we evaluate the matching coefficient numerically and determine the ratio of Λ parameters between the two schemes. We analyze the N dependence of the results and the possible implications for non-commutative gauge theories and volume independence.

Deformation and recrystallization mechanisms inferred from microstructures of naturally deformed rock salt from the diapiric stem and surface glaciers of a salt diapir in Southern Iran

Microstructures of three naturally deformed rocksalt samples, from the Deh Kuyeh salt fountain in South Iran, were studied by electron backscatter diffraction to constrain deformation and recrystallization processes. Two samples came from the upper salt fountain glaciers and one from the diapiric stem. Lattice distortion and low-angle boundaries in salt grains have intra-crystalline misorientations described by rotations around low-order crystallographic axes and are inferred to relate to dislocation creep and recovery. Misorientation analysis suggests that both easy and hard slip systems are responsible for grain distortions. Small grains have similar dimensions to subgrains, which we interpret to mean that subgrain rotation recrystallization (SGR) is important. Many boundaries are quite lobate, consistent with grain boundary migration (GBM) also being active. Bulges off of some large grains are related to the host by a tilt or twist boundary suggesting that GBM and SGR interacted to facilitate a bulge nucleation process. Idiomorphic grains occur, particularly in the upper fountain (surface glaciers) samples and are less deformed internally than neighboring grains. The grain and subgrain sizes in the sample from the diapiric stem are smaller than those in the upper salt fountain. Subgrain sizes suggest differential stresses were twice as large (2 MPa) during deformation in the diapiric stem compared to the upper fountain. The diapiric stem sample has greater intragranular distortion compared to the fountain samples. Furthermore, the diapiric stem sample has a continuous grain-boundary hierarchy, suggesting a dominance of SGR, whereas the upper fountain samples have different boundary hierarchy characteristics for boundary misorientations above and below ∼7° suggesting that GBM is limiting the SGR process: grains are consumed by GBM before boundaries with misorientations >7° developed by SGR. The increased importance of GBM relative to SGR in the upper fountain compared to the diapiric stem is consistent with the change in balance of the different recrystallization mechanisms expected as a function of lower stress magnitude in the upper fountain.

Bion non-perturbative contributions versus infrared renormalons in two-dimensional \u2102PN \u2212 1 models

We derive the semiclassical contributions from the real and complex bions in the two-dimensional ℂPN − 1 sigma model on ℝ×S1 with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the ℂPN − 1 quantum mechanics. The bion solutions have quasi-moduli parameters corresponding to the relative distance and phase between the constituent fractional instantons. By summing over the Kaluza-Klein modes of the quantum fluctuations around the bion backgrounds, we find that the effective action for the quasi-moduli parameters is renormalized and becomes a function of the dynamical scale (or the renormalized coupling constant). Based on the renormalized effective action, we obtain the semiclassical bion contribution in a weak coupling limit by making use of the Lefschetz thimble method. We find in the supersymmetric case that the bion contribution vanishes as expected from supersymmetry. In non-supersymmetric cases, the non-perturbative contribution has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity. Our results explicitly demonstrate that the complex bion can explain the infrared renormalon.

⟨x⟩ and ⟨x2⟩ of the pion PDF from lattice QCD with Nf=2+1+1 dynamical quark flavors

Using Nf=2+1+1 lattice QCD, we determine the fermionic connected contributions to the second and third moment of the pion PDF. Based on gauge configurations from the European Twisted Mass Collaboration, chiral and continuum extrapolations are performed using pion masses in the range of 230 to 500 MeV and three values of the lattice spacing. Finite volume effects are investigated using different volumes. In order to avoid mixing under renormalisation for the third moment, we use an operator with two non-zero spatial components of momentum. Momenta are injected using twisted boundary conditions. Our final values read $\langle x\rangle=0.2075(106)$ and $\langle x^2\rangle=0.163(33)$, determined at 2 GeV in the $\overline{MS}$-scheme and with systematic and statistical uncertainties summend in quadrature.

Majorana edge state in a number-conserving Fermi gas with tunable p-wave interaction

The remarkable properties and potential applications of Majorana fermions have led to considerable efforts in recent years to realize topological matters that host these excitations. For a number conserving system, there have been a few proposals, using either coupled chain models or a multi-component system with spin–orbit coupling (SOC), to create number fluctuation of fermion pairs in achieving Majorana fermions. In this work, we show that Majorana edge states can occur in a spinless Fermi gas in 1D lattices with tunable p-wave interaction. This is facilitated by the conversion between a pair of (open-channel) fermions and a (close channel) boson, thereby allowing the number fluctuation of fermion pairs in a single chain. This scheme requires neither SOC nor a multi-chain setup and can be implemented easily. Using the density-matrix-renormalization-group method, we have identified the Majorana phase in a wide range of parameter regimes as well as its associated phase transitions. The topological nature of the Majorana phase manifests itself in a strong edge–edge correlation in an open chain that is robust against disorder, as well as in a non-trivial winding number in the bulk generated by using twisted boundary condition. It is also shown that the Majorana phase in this system can be stable against atom losses due to few-body collisions on the same site, and can be easily identified from the fermion momentum distribution. These results pave the way for probing the intriguing Majorana physics in a simple and stable cold atoms system.

Exact half-BPS black hole entropies in CHL models from Rademacher series

The microscopic spectrum of half-BPS excitations in toroidally compactified heterotic string theory has been computed exactly through the use of results from analytic number theory. Recently, similar quantities have been understood macroscopically by evaluating the gravitational path integral on the M-theory lift of the AdS2 near-horizon geometry of the corresponding black hole. In this paper, we generalize these results to a subset of the CHL models, which include the standard compactification of IIA on K3 × T2 as a special case. We begin by developing a Rademacher-like expansion for the Fourier coefficients of the partition functions for these theories, which are modular forms for congruence subgroups. We then describe a possible macroscopic interpretation of these results, emphasizing the role of twisted boundary conditions.

Magnetized orbifolds and localized flux

Magnetized orbifolds play an important role in compactifications of string theories and higher-dimensional field theories to four dimensions. Magnetic flux leads to chiral fermions, it can be a source of supersymmetry breaking and it is an important ingredient of moduli stabilization. Flux quantization on orbifolds is subtle due to the orbifold singularities. Generically, Wilson line integrals around these singularities are non-trivial, which can be interpreted as localized flux. As a consequence, flux densities on orbifolds can take the same values as on tori. We determine the transition functions for the flux vector bundle on the orbifold T2∕Z2 and the related twisted boundary conditions of zero-mode wave functions. We also construct “untwisted” zero-mode functions that are obtained for singular vector fields related to the Green’s function on a torus, and we discuss the connection between zeros of the wave functions and localized flux. Twisted and untwisted zero-mode functions are related by a singular gauge transformation.

Lattice study of $J/\Psi$J/Ψ form factors with twisted boundary conditions

We present a lattice calculation for the electromagnetic form factors of $J/\Psi$ by using $N_{f}=2$ twisted mass gauge field configurations. We apply twisted boundary conditions to compute correlation functions at small values of momentum transfer that are difficult to access with periodic boundary conditions. The electromagnetic form factors with more small four-momentum transfer are determined, and further the charge radius and the quadrupole moment for $J/\Psi$ are fitted, respectively.

Large-order NSPT for lattice gauge theories with fermions: the plaquette in massless QCD

Numerical Stochastic Perturbation Theory (NSPT) allows for perturbative computations in quantum field theory. We present an implementation of NSPT that yields results for high orders in the perturbative expansion of lattice gauge theories coupled to fermions. The zero-momentum mode is removed by imposing twisted boundary conditions; in turn, twisted boundary conditions require us to introduce a smell degree of freedom in order to include fermions in the fundamental representation. As a first application, we compute the critical mass of two flavours of Wilson fermions up to order O(beta ^{-7}) in a {{mathrm{{mathrm {SU}}}}}(3) gauge theory. We also implement, for the first time, staggered fermions in NSPT. The residual chiral symmetry of staggered fermions protects the theory from an additive mass renormalisation. We compute the perturbative expansion of the plaquette with two flavours of massless staggered fermions up to order O(beta ^{-35}) in a {{mathrm{{mathrm {SU}}}}}(3) gauge theory, and investigate the renormalon behaviour of such series. We are able to subtract the power divergence in the Operator Product Expansion (OPE) for the plaquette and estimate the gluon condensate in massless QCD. Our results confirm that NSPT provides a viable way to probe systematically the asymptotic behaviour of perturbative series in QCD and, eventually, gauge theories with fermions in higher representations.

Insensitivity of bulk properties to the twisted boundary condition

The symmetry and the locality are the two major sources of various nontrivial statements in quantum many-body systems. We demonstrate that, in gapped phases of a U(1) symmetric Hamiltonian with finite-range interactions, the bulk properties such as the expectation value of local operators, the ground state energy and the excitation gap, and the static and low-frequency dynamical responses in general, do not depend on the U(1) phase of the twisted boundary condition in the limit of the large system size. Specifically, their dependence on the twisted angle is exponentially suppressed with the linear dimension of the system. The argument is based on the exponential decay of various types of equal-time correlation functions.

Precise Estimation of the S = 2 Haldane Gap by Numerical Diagonalization

The Haldane gap of the S=2 Heisenberg antiferromagnet in a one-dimensional linear chain is examined by a numerical-diagonalization method. A precise estimate for the magnitude of the gap is successfully obtained by a multistep convergence-acceleration procedure applied to finite-size diagonalization data under the twisted boundary condition.

Grain Boundary Softening: A Potential Mechanism for Lithium Metal Penetration through Stiff Solid Electrolytes.

Models based on linear elasticity suggest that a solid electrolyte with a high shear modulus will suppress "dendrite" formation in batteries that use metallic lithium as the negative electrode. Nevertheless, recent experiments find that lithium can penetrate stiff solid electrolytes through microstructural features, such as grain boundaries. This failure mode emerges even in cases where the electrolyte has an average shear modulus that is an order of magnitude larger than that of Li. Adopting the solid-electrolyte Li7La3Zr2O12(LLZO)as a prototype, here we demonstrate that significant softening in elastic properties occurs in nanoscale regions near grain boundaries. Molecular dynamics simulations performed on tilt and twist boundaries reveal that the grain boundary shear modulus is up to 50% smaller than in bulk regions. We propose that inhomogeneities in elastic properties arising from microstructural features provide a mechanism by which soft lithium can penetrate ostensibly stiff solid electrolytes.

Thermodynamic limit and twisted boundary energy of the XXZ spin chain with antiperiodic boundary condition

We investigate the thermodynamic limit of the inhomogeneous T−Q relation of the antiferromagnetic XXZ spin chain with antiperiodic boundary condition. It is shown that the contribution of the inhomogeneous term for the ground state can be neglected when the system-size N tends to infinity, which enables us to reduce the inhomogeneous Bethe ansatz equations (BAEs) to the homogeneous ones. Then the quantum numbers at the ground states are obtained, by which the system with arbitrary size can be studied. We also calculate the twisted boundary energy of the system.

Effect of Central Longitudinal Dipole Interactions on Chiral Liquid-Crystal Phases

Monte Carlo simulations of chiral liquid-crystals, represented by a simple coarse-grained chiral Gay–Berne model, were performed to investigate the effect of central longitudinal dipole interactions on phase behavior. A systematic analysis of the structural properties and phase behavior of both achiral and chiral systems, with dipole interactions, reveals differing effects; strong dipole interactions enhance the formation of layered structures; however, chiral interactions may prevent the formation of such phases under certain conditions. We also observed a short-ranged smectic structure within the cholesteric phases with strong dipole interactions. This constitutes possible evidence of presmectic ordering and/or the existence of chiral line liquid phases, which have previously been observed in X-ray experiments to occur between the smectic twisted grain boundary and cholesteric phases. These results provide a systematic understanding of how the phase behavior of chiral liquid-crystals changes when alterations are made to the strength of dipole interactions.

Thermal boundary resistance correlated with strain energy in individual Si film-wafer twist boundaries

Nanoscale interfaces, such as grain boundaries (GBs) within a polycrystalline material, play an important role in suppressing the phonon heat transport. The interfacial thermal resistance RK of a GB has a strong dependence on the detailed interfacial atomic structure, including the misorientation between two grains and GB dislocations. Along this line, numerous molecular dynamics simulations on RK have been carried out on a twist Si GB. Owing to the challenge of measuring such a GB within a bulk material, these simulations are rarely compared with experimental data. In this work, a super-flexible 70-nm-thick Si thin film was hot pressed onto a Si wafer to represent a twist GB. The RK of the film-wafer interface was measured as a function of the rotation angle between the film and the wafer. The experimental data were further compared with an analytical model to interpret the twist angle dependence of the measured RK. It was found that the strain part of the grain-boundary energy is correlated with the measured twist-angle-dependent RK.