Dimensional Quantum Electrodynamics Research Articles

A relativistic discrete spacetime formulation of 3+1 QED

This work provides a relativistic, digital quantum simulation scheme for both 2+1 and 3+1 dimensional quantum electrodynamics (QED), based on a discrete spacetime formulation of theory. It takes the form of a quantum circuit, infinitely repeating across space and time, parametrised by the discretization step Δt=Δx. Strict causality at each step is ensured as circuit wires coincide with the lightlike worldlines of QED; simulation time under decoherence is optimized. The construction replays the logic that leads to the QED Lagrangian. Namely, it starts from the Dirac quantum walk, well-known to converge towards free relativistic fermions. It then extends the quantum walk into a multi-particle sector quantum cellular automata in a way which respects the fermionic anti-commutation relations and the discrete gauge invariance symmetry. Both requirements can only be achieved at cost of introducing the gauge field. Lastly the gauge field is given its own electromagnetic dynamics, which can be formulated as a quantum walk at each plaquette.

Monopole Josephson effects in a Dirac spin liquid

Dirac Spin liquids (DSLs) are gapless featureless states, yet interesting by virtue of the effective field theory describing them -- (2+1)-dimensional quantum electrodynamics (QED$_3$). Further, a DSL is known to be a "parent state" of various seemingly unrelated ordered states, such as antiferromagnets and valence bond solids in the sense that one can obtain ordered states by condensing magnetic monopoles of the emergent gauge field. Can operators in the effective field theory, such as the emergent electric field, be externally induced and measured? In this work, we exploit the parent state picture to argue that the answer is yes. We propose a range of "monopole Josephson effects" that arise when two ordered states are separated by a region of the parent DSL. In particular, we show that one can induce an AC monopole Josephson effect, which manifests itself as an AC emergent electric field in the spin liquid, accompanied by a measurable spin current. Further, we show that this AC emergent electric field can be measured as a sharp tunable peak in Raman scattering. This work provides a theoretical proof of principle that emergent gauge fields in spin liquids can be externally induced, manipulated, and probed using more conventional states, which offers a generic platform for studying the exotic spin phases.

DMRG study of the higher-charge Schwinger model and its ’t Hooft anomaly

The charge-q Schwinger model is the (1 + 1)-dimensional quantum electrodynamics (QED) with a charge-q Dirac fermion. It has the ℤq 1-form symmetry and also enjoys the ℤq chiral symmetry in the chiral limit, and there is a mixed ’t Hooft anomaly between those symmetries. We numerically study the charge-q Schwinger model in the lattice Hamiltonian formulation using the density-matrix renormalization group (DMRG). When applying DMRG, we map the Schwinger model to a spin chain with nonlocal interaction via Jordan-Wigner transformation, and we take the open boundary condition instead of the periodic one to make the Hilbert space finite-dimensional. When computing the energy density or chiral condensate, we find that using local operators significantly reduces the boundary effect compared with the computation of corresponding extensive quantities divided by the volume. To discuss the consequence of the ’t Hooft anomaly, we carefully treat the renormalization of the chiral condensates, and then we confirm that Wilson loops generate the discrete chiral transformations in the continuum limit.

Conformality and self-duality of Nf = 2 QED3

We study the IR phase of three dimensional quantum electrodynamics (QED3) coupled to Nf=2 flavors of two-component Dirac fermions, which has been controversial for decades. This theory has been proposed to be self-dual with symmetry enhancement (SU(2)f×U(1)t)/Z2→O(4) at the IR fixed point. We focus on the four-point correlator of monopole operators with unit topological charge of U(1)t. We illustrate the O(4)→SU(2)f×U(1)t branching rules based on an O(4) symmetric positive structure in the monopole four-point crossing equations. We use conformal bootstrap method to derive nonperturbative constraints on the CFT data and test the conformality and self-duality of Nf=2 QED3. In particular we find the CFT data obtained from previous lattice simulations can be ruled out by introducing irrelevant assumptions in the spectrum, indicating the IR phase of Nf=2 QED3 is not conformal.

Classically emulated digital quantum simulation of the Schwinger model with a topological term via adiabatic state preparation

We designed a protocol for digital quantum computation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus on $1+1$ dimensional quantum electrodynamics with the $\ensuremath{\theta}$ term known as the Schwinger model and test our protocol for this on an IBM simulator. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a continuum limit we find that our result in the massless case agrees with the known exact result. In the massive case, we find an agreement with mass perturbation theory in the small-mass regime and deviations in the large-mass regime. We estimate computational costs required to take a reasonable continuum limit. Our results imply that digital quantum simulation appears a promising tool to explore nonperturbative aspects of gauge theories with real time and topological terms.

Classically emulated digital quantum simulation for screening and confinement in the Schwinger model with a topological term

We perform digital quantum simulation, using a classical simulator, to study screening and confinement in a gauge theory with a topological term, focusing on ($1+1$)-dimensional quantum electrodynamics (Schwinger model) with a theta term. We compute the ground state energy in the presence of probe charges to estimate the potential between them, via adiabatic state preparation. We compare our simulation results and analytical predictions for a finite volume, finding good agreements. In particular our result in the massive case shows a linear behavior for noninteger charges and a nonlinear behavior for integer charges, consistently with the expected confinement (screening) behavior for noninteger (integer) charges.

Radiative effects in two-dimensional models of quantum electrodynamics in a constant magnetic field

The radiative energy shift of an electron in a constant magnetic field has been considered in the framework of the ($2+1$)-dimensional quantum electrodynamics with four-component fermions as well as in reduced ${\mathrm{QED}}_{3+1}$ in which photons propagate in a ($3+1$)-dimensional bulk and fermions are localized on a 2-brane. Analytical expressions are obtained for the energy of interaction of the electron spin with an external field and the radiative shift of the electron mass after averaging over the spin states of the electron. For ultrarelativistic energies of an electron and relatively weak magnetic fields, the total probability of a photon emission by a massive electron and the anomalous magnetic moment of an electron in a reduced ${\mathrm{QED}}_{3+1}$ are calculated. The dependence of the obtained values on the invariant dynamic parameter of synchrotron radiation is investigated. The total probabilities of synchrotron radiation of a charged massless fermion and the production of a pair of charged massless fermions by a photon in an external magnetic field are calculated in ($2+1$)-dimensional models of quantum electrodynamics.

A resource efficient approach for quantum and classical simulations of gauge theories in particle physics

Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding of fundamental interactions. The present limitations of MCMC techniques may be overcome by Hamiltonian-based simulations on classical or quantum devices, which further provide the potential to address questions that lay beyond the capabilities of the current approaches. However, for continuous gauge groups, Hamiltonian-based formulations involve infinite-dimensional gauge degrees of freedom that can solely be handled by truncation. Current truncation schemes require dramatically increasing computational resources at small values of the bare couplings, where magnetic field effects become important. Such limitation precludes one from `taking the continuous limit' while working with finite resources. To overcome this limitation, we provide a resource-efficient protocol to simulate LGTs with continuous gauge groups in the Hamiltonian formulation. Our new method allows for calculations at arbitrary values of the bare coupling and lattice spacing. The approach consists of the combination of a Hilbert space truncation with a regularization of the gauge group, which permits an efficient description of the magnetically-dominated regime. We focus here on Abelian gauge theories and use 2+1 dimensional quantum electrodynamics as a benchmark example to demonstrate this efficient framework to achieve the continuum limit in LGTs. This possibility is a key requirement to make quantitative predictions at the field theory level and offers the long-term perspective to utilise quantum simulations to compute physically meaningful quantities in regimes that are precluded to quantum Monte Carlo.

Revisiting relativistic magnetohydrodynamics from quantum electrodynamics

We provide a statistical mechanical derivation of relativistic magnetohydrodynamics on the basis of (3 + 1)-dimensional quantum electrodynamics; the system endowed with a magnetic one-form symmetry. The conservation laws and constitutive relations are presented in a manifestly covariant way with respect to the general coordinate transformation. The method of the local Gibbs ensemble (or nonequilibrium statistical operator) combined with the path-integral formula for a thermodynamic functional enables us to obtain exact forms of constitutive relations. Applying the derivative expansion to exact formulas, we derive the first-order constitutive relations for nonlinear relativistic magnetohydrodynamics. Our results for the QED plasma preserving parity and charge-conjugation symmetries are equipped with two electrical resistivities and five (three bulk and two shear) viscosities. We also show that those transport coefficients satisfy the Onsager’s reciprocal relation and a set of inequalities, indicating semi-positivity of the entropy production rate consistent with the local second law of thermodynamics.

On the creation of charged massless fermion pair by a photon in an external constant uniform magnetic field in 2+1 dimensions

Creation of charged massless fermion pair by a photon in a constant uniform magnetic field is considered in the one-loop approximation of the [Formula: see text]-dimensional quantum electrodynamics (QED[Formula: see text]). We calculate the elastic scattering amplitude (EAS) of photon using the polarization operator of photon in the above magnetic field obtained earlier in our work. We analyze the elastic scattering amplitude of photon at various values of the photon energy and magnetic field strength. Very simple analytical formulas for EAS of photon are obtained in the so-called quasi-classical region. In the massive quantum electrodynamics the elastic scattering amplitude of photon defines its “mass” squared in the presence of external electromagnetic field and the imaginary part of EAS describes the total probability of charged massive fermion pair creation in the electromagnetic field; we assume that it is the case and in the massless quantum electrodynamics.

Disorder-free localization in a simple U(1) lattice gauge theory

Localization due to the presence of disorder has proven crucial for our current understanding of relaxation in isolated quantum systems. The many-body localized phase constitutes a robust alternative to the thermalization of complex interacting systems, but recently the importance of disorder has been brought into question. Starting from translationally invariant $(1 + 1)$-dimensional quantum electrodynamics, we modify the dynamics of the gauge field and reveal a mechanism of disorder-free localization. We consider two different discretizations of the continuum model resulting in a free-fermion soluble model in one case and an interacting model in the other. We diagnose the localization in the far-from-equilibrium dynamics following a global quantum quench.

Real Time Dynamics and Confinement in the Zn Schwinger-Weyl lattice model for 1+1 QED

We study the out-of-equilibrium properties of 1+1 dimensional quantum electrodynamics (QED), discretized via the staggered-fermion Schwinger model with an Abelian Zn gauge group. We look at two relevant phenomena: first, we analyze the stability of the Dirac vacuum with respect to particle/antiparticle pair production, both spontaneous and induced by an external electric field; then, we examine the string breaking mechanism. We observe a strong effect of confinement, which acts by suppressing both spontaneous pair production and string breaking into quark/antiquark pairs, indicating that the system dynamics displays a number of out-of-equilibrium features.

On elastic scattering amplitude of planar charged fermions in a constant magnetic field

The elastic scattering amplitude (ESA) is obtained in the one-loop approximation of the (2[Formula: see text]+[Formula: see text]1)-dimensional quantum electrodynamics (QED[Formula: see text]) for planar charged fermions in an external constant magnetic field. We obtain the elastic scattering amplitude in the corresponding massive theory and then discuss and calculate the massless limit of ESA. The imaginary part of ESA are related to the total probability of photons emission by charged fermions in the considered magnetic field. Simple analytical formulas are obtained when planar charged fermions in initial states occupy high excited Landau levels.

Radiative dynamical mass of planar charged fermion in a constant homogeneous magnetic field

The effective Lagrangian and mass operator are calculated for planar charged massive and massless fermions in a constant external homogeneous magnetic field in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED_{2+1}). We obtain the renormalizable effective Lagrangian and the fermion mass operator for a charged fermion of mass m and then calculate these quantities for the massless case. The radiative corrections to the mass of charged massless fermion when it occupies the lowest Landau level are found for the cases of the pure QED_{2+1} as well as the so-called reduced QED_{3+1} on a 2-brane. The fermion masses were found can be generated dynamically in an external magnetic field in the pure QED_{2+1} if the charged fermion has small bare mass m_0 and in the reduced QED_{3+1} on a 2-brane even at m_0=0. The dynamical mass seems to be likely to be revealed in monolayer graphene in the presence of constant homogeneous magnetic field (normal to the graphene sample).

Erratum: Metallic phases from disordered (2+1)-dimensional quantum electrodynamics [Phys. Rev. B 95 , 235145 (2017)

Received 25 January 2019DOI:https://doi.org/10.1103/PhysRevB.99.079903©2019 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDiffusionInsulatorsLocalizationMetalsQuantum phase transitionsQuantum statistical mechanicsStatistical PhysicsCondensed Matter, Materials & Applied Physics

Soft pair excitations and double-log divergences due to carrier interactions in graphene

Interactions between charge carriers in graphene lead to logarithmic renormalization of observables mimicking the behavior known in (3+1)-dimensional quantum electrodynamics (QED). Here we analyze soft electron-hole (e-h) excitations generated as a result of fast charge dynamics, a direct analog of the signature QED effect - multiple soft photons produced by the QED vacuum shakeup. We show that such excitations are generated in photon absorption, when a photogenerated high-energy e-h pair cascades down in energy and gives rise to multiple soft e-h excitations. This fundamental process is manifested in a double-log divergence in the emission rate of soft pairs and a characteristic power-law divergence in their energy spectrum of the form $\frac{1}{\omega}\ln \left(\frac{\omega}{\Delta}\right) $. Strong carrier-carrier interactions make pair production a prominent pathway in the photoexcitation cascade.

Metallic phases from disordered (2+1)-dimensional quantum electrodynamics

Metallic phases have been observed in several disordered two dimensional (2d) systems, including thin films near superconductor-insulator transitions and quantum Hall systems near plateau transitions. The existence of 2d metallic phases at zero temperature generally requires an interplay of disorder and interaction effects. Consequently, experimental observations of 2d metallic behavior have largely defied explanation. We formulate a general stability criterion for strongly interacting, massless Dirac fermions against disorder, which describe metallic ground states with vanishing density of states. We show that (2+1)-dimensional quantum electrodynamics (QED$_3$) with a large, even number of fermion flavors remains metallic in the presence of weak scalar potential disorder due to the dynamic screening of disorder by gauge fluctuations. We also show that QED$_3$ with weak mass disorder exhibits a stable, dirty metallic phase in which both interactions and disorder play important roles.

Dynamical mass generation in QED3 beyond the instantaneous approximation**Supported by National Natural Science Foundation of China (11475085, 11535005, 11690030), Natural Science Foundation of Jiangsu Province (BK20130387) and Jiangsu Planned Projects for Postdoctoral Research Funds (1501035B)

In this paper, we investigate dynamical mass generation in (2+1)-dimensional quantum electrodynamics at finite temperature. Many studies are carried out within the instantaneous-exchange approximation, which ignores all but the zero-frequency component of the boson propagator and fermion self-energy function. We extend these studies by taking the retardation effects into consideration. In this paper, we get the explicit frequency n and momentum p dependence of the fermion self-energy function and identify the critical temperature for different fermion flavors in the chiral limit. Also, the phase diagram for spontaneous symmetry breaking in the theory is presented in Tc-Nf space. The results show that the chiral condensate is just one-tenth of the scale of previous results, and the chiral symmetry is restored at a smaller critical temperature.

Bosonic analog of a topological Dirac semimetal: Effective theory, neighboring phases, and wire construction

We construct a bosonic analog of a two-dimensional topological Dirac Semi-Metal (DSM). The low-energy description of the most basic 2D DSM model consists of two Dirac cones at positions $\pm\mathbf{k}_0$ in momentum space. The local stability of the Dirac cones is guaranteed by a composite symmetry $Z_2^{\mathcal{TI}}$, where $\mathcal{T}$ is time-reversal and $\mathcal{I}$ is inversion. This model also exhibits interesting time-reversal and inversion symmetry breaking electromagnetic responses. In this work we construct a bosonic version by replacing each Dirac cone with a copy of the $O(4)$ Nonlinear Sigma Model (NLSM) with topological theta term and theta angle $\theta=\pm \pi$. One copy of this NLSM also describes the gapless surface termination of the 3D Bosonic Topological Insulator (BTI). We compute the time-reversal and inversion symmetry breaking electromagnetic responses for our model and show that they are twice the value one gets in the DSM case matching what one might expect from, for example, a bosonic Chern insulator. We also investigate the stability of the BSM model and find that the composite $Z_2^{\mathcal{TI}}$ symmetry again plays an important role. Along the way we clarify many aspects of the surface theory of the BTI including the electromagnetic response, the charges and statistics of vortex excitations, and the stability to symmetry-allowed perturbations. We briefly comment on the relation between the various descriptions of the $O(4)$ NLSM with $\theta=\pi$ used in this paper (a dual vortex description and a description in terms of four massless fermions) and the recently proposed dual description of the BTI surface in terms of $2+1$ dimensional Quantum Electrodynamics with two flavors of fermion ($N=2$ QED$_3$). In a set of four Appendixes we review some of the tools used in the paper, and also derive some of the more technical results.

Anomalous dimensions of scalar operators in QED3

The infrared dynamics of $2+1$ dimensional quantum electrodynamics (QED$_3$) with a large number $N$ of fermion flavors is governed by an interacting CFT that can be studied in the $1/N$ expansion. We use the $1/N$ expansion to calculate the scaling dimensions of all the lowest three scalar operators that transform under the $SU(N)$ flavor symmetry as a Young diagram with two columns of not necessarily equal heights and that have vanishing topological charge. In the case of $SU(N)$ singlets, we study the mixing of $(\bar \psi_i \psi^i)(\bar \psi_j \psi^j)$ and $F_{\mu\nu} F^{\mu\nu}$, which are the lowest dimension parity-even singlets. Our results suggest that these operators are irrelevant for all $N>1$.