Non-interacting Theory Research Articles

Evolution of strictly localized states in noninteracting quantum field theories with background fields

Evolution of strictly localized states in noninteracting quantum field theories with background fields

New Aspect of Chiral SU(2) and U(1) Axial Breaking in QCD

The violation of the U(1) axial symmetry in QCD is stricter than the chiral SU(2) breaking simply because of the presence of the quantum axial anomaly. If the QCD gauge coupling is sent to zero (the asymptotic free limit, where the U(1) axial anomaly does not exist), the strength of the U(1) axial breaking coincides with that of the chiral SU(2) breaking, which we, in short, call an axial–chiral coincidence. This coincidence is trivial since QCD then becomes a non-interacting theory. Actually, there exists another limit in the QCD parameter space, where an axial–chiral coincidence occurs even with nonzero QCD gauge coupling, which can be dubbed a nontrivial coincidence: it is the case with the massive light quarks (ml≠0) and the massless strange quark (ms=0) due to the flavor-singlet nature of the topological susceptibility. This coincidence is robust and tied to the anomalous chiral Ward–Takahashi identity, which is operative even at hot QCD. This implies that the chiral SU(2) symmetry is restored simultaneously with the U(1) axial symmetry at high temperatures. This simultaneous restoration is independent of ml(≠0) and, hence, is irrespective of the order of the chiral phase transition. In this paper, we discuss how the real-life QCD can be evolved from the nontrivial chiral–axial coincidence limit by working on a Nambu–Jona–Lasinio model with the U(1) axial anomaly contribution properly incorporated. It is shown that, at high temperatures, the large differences between the restorations of the chiral SU(2) symmetry and the U(1) axial symmetry for two light quarks and a sufficiently large current mass for the strange quark are induced by a significant interference of the topological susceptibility. Thus, the deviation from the nontrivial coincidence, which is monitored by the strange quark mass controlling the topological susceptibility, provides a new way of understanding the chiral SU(2) and U(1) axial breaking in QCD.

Towards learning optimized kernels for complex Langevin

We present a novel strategy aimed at restoring correct convergence in complex Langevin simulations. The central idea is to incorporate system-specific prior knowledge into the simulations, in order to circumvent the NP-hard sign problem. In order to do so, we modify complex Langevin using kernels and propose the use of modern auto-differentiation methods to learn optimal kernel values. The optimization process is guided by functionals encoding relevant prior information, such as symmetries or Euclidean correlator data. Our approach recovers correct convergence in the non-interacting theory on the Schwinger-Keldysh contour for any real-time extent. For the strongly coupled quantum anharmonic oscillator we achieve correct convergence up to three-times the real-time extent of the previous benchmark study. An appendix sheds light on the fact that for correct convergence not only the absence of boundary terms, but in addition the correct Fokker-Plank spectrum is crucial.

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.

Fabry-Pérot and Aharonov-Bohm interference in ideal graphene nanoribbons

Quantum-mechanical calculations of electron magneto-transport in ideal graphene nanoribbons are presented. In noninteracting theory, it is predicted that an ideal ribbon that is attached to wide leads should reveal Fabry-Perot conductance oscillations in magnetic field. In the theory with Coulomb interaction taken into account, the oscillation pattern should rather be determined by the Aharonov-Bohm interference effect. Both of these theories predict the formation of quasi-bound states, albeit of different structures, inside the ribbon because of strong electron scattering on the interfaces between the connecting ribbon and the leads. Conductance oscillations are a result of resonant backscattering via these quasi-bound states.

Theory of mind in naturalistic conversations between autistic and typically developing children and adolescents.

Conversation is a key part of everyday social interactions. Previous studies have suggested that conversational skills are related to theory of mind, the ability to think about other people's mental states, such as beliefs, knowledge, and emotions. Both theory of mind and conversation are common areas of difficulty for autistic people, yet few studies have investigated how people, including autistic people, use theory of mind during conversation. We developed a new way of measuring cToM using two rating scales: cToM Positive captures behaviors that show consideration of a conversation partner's mental states, such as referring to their thoughts or feelings, whereas cToM Negative captures behaviors that show a lack of theory of mind through violations of neurotypical conversational norms, such as providing too much, too little, or irrelevant information. We measured cToM in 50 pairs of autistic and typically developing children (ages 8-16 years) during 5-min "getting to know you" conversations. Compared to typically developing children, autistic children displayed more frequent cToM Negative behaviors but very similar rates of cToM Positive behaviors. Across both groups, cToM Negative (but not Positive) ratings were related to difficulties in recognizing emotions from facial expressions and a lower tendency to talk about others' mental states spontaneously (i.e., without being instructed to do so), which suggests that both abilities are important for theory of mind in conversation. Altogether, this study highlights both strengths and difficulties among autistic individuals, and it suggests possible avenues for further research and for improving conversational skills.

C3 symmetry breaking metal-insulator transitions in a flat band in the half-filled Hubbard model on the decorated honeycomb lattice

We study the single-orbital Hubbard model on the half-filled decorated honeycomb lattice. In the noninteracting theory at half filling the Fermi energy lies within a flat band where strong correlations are enhanced. The lattice is highly frustrated. We find a correlation driven first-order metal-insulator transition to two different insulating ground states---a dimer valence bond solid Mott insulator when intertriangle correlations dominate, and a broken ${C}_{3}$-symmetry antiferromagnet that arises from frustration when intratriangle correlations dominate. The metal-insulator transitions into these two phases have very different characters. The metal-broken ${C}_{3}$ antiferromagnetic transition is driven by spontaneous ${C}_{3}$ symmetry breaking that lifts the topologically required degeneracy at the Fermi energy and opens an energy gap in the quasiparticle spectrum. The metal-dimer valence bond solid transition breaks no symmetries of the Hamiltonian. It is caused by strong correlations renormalizing the electronic structure into a phase that is adiabatically connected to both the trivial band insulator and the ground state of the spin-1/2 Heisenberg model in the relevant parameter regime. Therefore, neither of these metal-insulator transitions can be understood in either the Brinkmann-Rice or Slater paradigms.

Magnons and magnetic fluctuations in atomically thin MnBi2Te4

Electron band topology is combined with intrinsic magnetic orders in MnBi2Te4, leading to novel quantum phases. Here we investigate collective spin excitations (i.e. magnons) and spin fluctuations in atomically thin MnBi2Te4 flakes using Raman spectroscopy. In a two-septuple layer with non-trivial topology, magnon characteristics evolve as an external magnetic field tunes the ground state through three ordered phases: antiferromagnet, canted antiferromagnet, and ferromagnet. The Raman selection rules are determined by both the crystal symmetry and magnetic order while the magnon energy is determined by different interaction terms. Using non-interacting spin-wave theory, we extract the spin-wave gap at zero magnetic field, an anisotropy energy, and interlayer exchange in bilayers. We also find magnetic fluctuations increase with reduced thickness, which may contribute to a less robust magnetic order in single layers.

Universal dephasing mechanism of many-body quantum chaos

Ergodicity is a fundamental principle of statistical mechanics underlying the behavior of generic quantum many-body systems. However, how this universal many-body quantum chaotic regime emerges due to interactions remains largely a puzzle. This paper demonstrates using both heuristic arguments and a microscopic calculation that a dephasing mechanism, similar to Altshuler-Aronov-Khmelnitskii dephasing in the theory of localization, underlies this transition to chaos. We focus on the behavior of the spectral form factor (SFF) as a function of “time” t, which characterizes level correlations in the many-body spectrum. The SFF can be expressed as a sum over periodic classical orbits and its behavior hinges on the interference of trajectories related to each other by a time translation. In the absence of interactions, time-translation symmetry is present for each individual particle, which leads to a fast exponential growth of the SFF and correspondingly loss of correlations between many-body levels. Interactions lead to dephasing, which disrupts interference, and breaks the massive time-translation symmetry down to a global time-translation/energy conservation. This in turn gives rise to the hallmark linear-in-t ramp in the SFF reflecting Wigner-Dyson level repulsion. This general picture is supported by a microscopic analysis of an interacting many-body model. Specifically, we study the complex SYK2+SYK22 model, which allows to tune between an integrable and chaotic regime. It is shown that the dephasing mass vanishes in the former case, which maps to the noninteracting complex SYK2 model via a time reparameterization. In contrast, the chaotic regime gives rise to dephasing, which suppresses the exponential ramp of the noninteracting theory and induces correlations between many-body levels.Received 14 November 2021Accepted 3 March 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L012037Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum chaosQuantum statistical mechanicsTechniquesSigma modelsCondensed Matter, Materials & Applied PhysicsStatistical Physics

Effect of Coulomb interaction on transport gap in ideal graphene nanoribbons

Quantum-mechanical calculations of electron transport in ideal graphene nanoribbons show that the transport gap that is predicted by noninteracting theories vanishes if the long-range Coulomb interaction between electrons is taken into account. This is a result of charge screening with the lowest subband edge being pinned to the chemical potential. However, the transport gap reappears if a ribbon is connected to wider leads, which is typically realized in an experimental setup that is based on lithographically patterned graphene ribbons. The gap is determined by scattering at the lead-to-ribbon interface, which can already be captured by the noninteracting theory.

Electron-boson-interaction induced particle-hole symmetry breaking of conductance into subgap states in superconductors

Particle-hole symmetry (PHS) of conductance into subgap states in superconductors is a fundamental consequence of a noninteracting mean-field theory of superconductivity. The breaking of this PHS has been attributed to a noninteracting mechanism, i.e., quasiparticle poisoning (QP), a process detrimental to the coherence of superconductor-based qubits.Here, we show that the ubiquitous electron-boson interactions in superconductors can also break the PHS of subgap conductances. We study the effect of such couplings on the PHS of subgap conductances in superconductors using both the rate equation and Keldysh formalism, which have different regimes of validity. In both regimes, we found that such couplings give rise to a particle-hole $asymmetry$ in subgap conductances which increases with increasing coupling strength, increasing subgap-state particle-hole content imbalance and decreasing temperature. Our proposed mechanism is general and applies even for experiments where the subgap-conductance PHS breaking cannot be attributed to QP.

비간섭화 제어이론기반 정밀작업용 테이블의 진동억제시스템 구축에 관한 연구

This paper presents a novel method for designing a active vibration isolation system (AVIS) by noninteracting control theory. In the result, the designed system can effectively reject the impact of disturbances on high precision fabrication table. In particular, the authors provide a noninteracting control scheme to decrease and delete the interactions appeared in the controlled system dynamics such that the control performance can be improved. For designing an optimal servo system, the LMI (linear matrix inequality) approach is introduced. To verify the effectiveness of the proposed method, a simulation is performed. In the result, the vibration suppression performance is significantly improved, thereby enabling higher precision works.

Zilch vortical effect for fermions

We consider the notion of zilch current that was recently discussed in the literature as an alternative helicity measure for photons. Developing this idea, we suggest the generalization of the zilch for the systems of fermions. We start with the definition of the photonic zilch current in chiral kinetic theory framework and work out field-theoretical definition of the fermionic zilch using the Wigner function formalism. This object has similar properties to the photonic zilch and is conserved in the non-interacting theory. We also show that, in full analogy with a case of photons, the fermionic zilch acquires a non-trivial contribution due to the medium rotation - zilch vortical effect (ZVE) for fermions. Combined with a previously studied ZVE for photons, these results form a wider set of chiral effects parameterized by the spin of the particles and the spin of the current. We briefly discuss the origin of the ZVE, its possible relation to the anomalies in the underlying microscopic theory and possible application for studying the spin polarization in chiral media.

Neural networks and quantum field theory

We propose a theoretical understanding of neural networks in terms of Wilsonian effective field theory. The correspondence relies on the fact that many asymptotic neural networks are drawn from Gaussian processes (GPs), the analog of non-interacting field theories. Moving away from the asymptotic limit yields a non-Gaussian process (NGP) and corresponds to turning on particle interactions, allowing for the computation of correlation functions of neural network outputs with Feynman diagrams. Minimal NGP likelihoods are determined by the most relevant non-Gaussian terms, according to the flow in their coefficients induced by the Wilsonian renormalization group. This yields a direct connection between overparameterization and simplicity of neural network likelihoods. Whether the coefficients are constants or functions may be understood in terms of GP limit symmetries, as expected from ’t Hooft’s technical naturalness. General theoretical calculations are matched to neural network experiments in the simplest class of models allowing the correspondence. Our formalism is valid for any of the many architectures that becomes a GP in an asymptotic limit, a property preserved under certain types of training.

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.

Application of the differential effective medium theory to determine fluid saturation and crack density from measured P- and S-wave velocities

SUMMARY The differential effective medium (DEM) theory studied in this paper describes elastic moduli of a fractured medium with help of differential equations, where crack density is the independent variable and fluid saturation is a parameter. The effective medium is isotropic for randomly oriented flat ellipsoidal cracks and thus fully characterized by two elastic constants. In this article we derive an analytical solution of the equation for Poisson’s ratio and we transform the differential equation for Young’s modulus into a non-linear algebraic equation. Fluid saturation and crack density can then be determined from measured wave propagation velocities by a simple algorithm. We also derive approximate solutions for elastic moduli as a function of crack density and saturation, which allows to quantify the uncertainty of the result due to measurement errors. The DEM theory leads to higher crack densities than the self-consistent method and to lower crack densities than the non-interacting theory for measured elastic moduli, while all three methods give similar fluid saturation fractions. As an example of application of our theoretical results, we study weathered granite in the Strengbach water catchment in the Vosges mountains in France. We have performed full waveform sonic logging measurements in an 86-m-deep borehole located at an altitude of 1130 m above sea level, which is used for hydrogeophysical and geochemical studies of a granitic aquifer. The logging data allows us to investigate P and S waves in the depth range between 40 and 80 m. The P- and S-wave propagation velocities take average values of 5.0 and 2.7 km s–1, respectively, with the highest values of 5.8 and 3.2 km s–1 at 75–80 m depth. From these velocities we obtain a water saturation of 75 ± 25 per cent. The crack density describes the degree of weathering of the granite, which generally decreases with depth, but takes high values near layers of strongly weathered granite. Crack density is on average 0.5, with the highest value of 1.0 at 65 m and the lowest value of 0.2 at 75 m depth. The analysis of the full waveform logging data by the DEM method supports results from previous geochemical and hydrological studies in the Strengbach catchment which concluded that water is stored in deeper layers of the granitic aquifer.

Entanglement renormalization for gauge invariant quantum fields

The continuous multiscale entaglement renormalization ansatz (cMERA) [Haegeman et al., Phys. Rev. Lett., 110, 100402 (2013)] is a variational wavefunctional for ground states of quantum field theories. So far, only scalar bosons and fermions have been considered. In this paper we explain how to generalize the cMERA framework to gauge invariant quantum fields. The fundamental difficulty to be addressed is how to make the gauge constraints (local linear constraints in the Hilbert space) compatible with the UV structure of the cMERA wavefunctional (which is generated by a quasi-local entangler). For simplicity, we consider $U(1)$ gauge theory in $d+1$ spacetime dimensions, a non-interacting theory with massless Hamiltonian $H_{U(1)}$ and Gaussian scale invariant ground state $|\Psi_{U(1)}\rangle$. We propose a gauge invariant cMERA wavefunctional $|\Psi^{\Lambda}_{U(1)}\rangle$ that, by construction, accurately reproduces the long distance properties of $|\Psi_{U(1)}\rangle$ while remaining somewhat unentangled at short distances. Moreover, $|\Psi^{\Lambda}_{U(1)}\rangle$ is the exact ground state of a gauge invariant, local Hamiltonian $H^{\Lambda}_{U(1)}$ whose low energy properties coincide with those of $H_{U(1)}$. Our construction also extends the cMERA formalism to massive (non-gauge invariant) vector boson quantum fields.

Mathcal{N} = 1 Super-Yang-Mills theory on the lattice with twisted mass fermions

Super-Yang-Mills theory (SYM) is a central building block for supersymmetric extensions of the Standard Model of particle physics. Whereas the weakly coupled subsector of the latter can be treated within a perturbative setting, the strongly coupled subsector must be dealt with a non-perturbative approach. Such an approach is provided by the lattice formulation. Unfortunately a lattice regularization breaks supersymmetry and consequently the mass degeneracy within a supermultiplet. In this article we investigate the properties of mathcal{N} = 1 supersymmetric SU(3) Yang-Mills theory with a lattice Wilson Dirac operator with an additional parity mass, similar as in twisted mass lattice QCD. We show that a special 45° twist effectively removes the mass splitting of the chiral partners. Thus, at finite lattice spacing both chiral and supersymmetry are enhanced resulting in an improved continuum extrapolation. Furthermore, we show that for the non-interacting theory at 45° twist discretization errors of order mathcal{O}(a) are suppressed, suggesting that the same happens for the interacting theory as well. As an aside, we demonstrate that the DDαAMG multigrid algorithm accelerates the inversion of the Wilson Dirac operator considerably. On a 163× 32 lattice, speed-up factors of up to 20 are reached if commonly used algorithms are replaced by the DDαAMG.

Space-time-resolved quantum electrodynamics description of Compton scattering

The standard method for approaching quantum electrodynamic (QED) field theory uses a perturbative $S$-matrix approach. This approach is explicitly nondynamical and provides only a one-time, static map between an initial state to be evolved by the ``full propagator'' of a bona-fide interacting field theory and an asymptotically equivalent effective initial state to be evolved by the ``free propagator'' of the corresponding noninteracting field theory. We provide a detailed derivation of a nonperturbative and dynamical approach to QED that allows one to study the space-time dynamics of electron-photon interactions directly. As an example of this method, we compute the time-resolved dynamics of Compton scattering for a system with a nontrivial spatial structure in only one dimension while restricting to the case of a single electron and at most one photon. This approach retains the massless photon of quantum electrodynamics in contrast to previous approaches that resorted to using massive bosons [T. Cheng, E. R. Gospodarczyk, Q. Su, and R. Grobe, Ann. Phys. 325, 265 (2010)] to represent the photon. The dynamics of Compton scattering are illustrated using joint probability distributions that evolve in time. This information is compared to that provided by the $S$ matrix.

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.