Center for Theoretical Physics Publications

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In non-relativistic quantum field theories, the challenge is to parameterize and optimize over the infinitely many \(n\)-particle wave functions comprising the state's Fock space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to non-relativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parameterize all of the \(n\)-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.

The presence of symmetries can convert an otherwise computationally hard task into an efficient one. In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts. As an example, we show that simulating and finding the ground state of permutation invariant Hamiltonians can be efficiently performed in polynomial classical time, further restricting the possible set of symmetries that provide quantum advantage.

The pion light-cone distribution amplitude (LCDA) is a central non-perturbative object of interest for the calculation of high-energy exclusive processes in quantum chromodynamics. This article describes the progress in the lattice QCD calculation of the fourth Mellin moment of the pion LCDA using a heavy-quark operator product expansion (HOPE).

We propose a variational quantum eigensolver suitable for exploring the phase structure of the multi-flavor Schwinger model in the presence of a chemical potential. The parametric ansatz circuit we design is capable of incorporating the symmetries of the model, present in certain parameter regimes, which allows for reducing the number of variational parameters substantially. Moreover, the ansatz circuit can be implementated on both measurement-based and circuit-based quantum hardware. We numerically demonstrate that our ansatz circuit is able to capture the phase structure of the model and allows for faithfully approximating the ground state. Our results show that our approach is suitable for current intermediate-scale quantum hardware and can be readily implemented on existing quantum devices.

Lattice computations in the Hamiltonian formulation have so far mainly focused on staggered fermions. In these proceedings, we study Wilson fermions in the Hamiltonian formulation and propose a new method to determine the resulting mass shift. As a benchmark study, we examine the one-flavour Schwinger model with Wilson fermions and a topological \(\theta\)-term using matrix product states. Wilson fermions explicitly break chiral symmetry; thus, the bare mass of the lattice model receives an additive renormalization. In order to measure this mass shift directly, we develop a method that is suitable for the Hamiltonian formulation, which relies on the fact that the vacuum expectation value of the electric field density vanishes when the renormalized mass is zero. We examine the dependence of the mass shift on the lattice spacing, the lattice volume, the \(\theta\)-parameter, and the Wilson parameter. Using the mass shift, we then perform the continuum extrapolation of the electric field density and compare the resulting mass dependence to the analytical predictions of mass perturbation theory. We demonstrate that incorporating the mass shift significantly improves the continuum extrapolation. Finally, we apply our method to the same model using staggered fermions instead of Wilson fermions and compare the resulting mass shift to recent theoretical predictions.

We study the massless charged spectrum of U(1) gauge fields in F-theory that arise from flux breaking of a nonabelian group. The U(1) charges that arise in this way can be very large. In particular, using vertical flux breaking, we construct an explicit 4D F-theory model with a U(1) decoupled from other gauge sectors, in which the massless/light fields have charges as large as 657. This result greatly exceeds prior results in the literature. We argue heuristically that this result may provide an upper bound on charges for light fields under decoupled U(1) factors in the F-theory landscape. We also show that the charges can be even larger when the U(1) is coupled to other gauge groups.

The infinite-component Chern-Simons-Maxwell (iCSM) theory is a 3+1D generalization of the 2+1D Chern-Simons-Maxwell theory by including an infinite number of coupled gauge fields. It can be used to describe interesting 3+1D systems. In Phys. Rev. B 105, 195124 (2022), it was used to construct gapped fracton models both within and beyond the foliation framework. In this paper, we study the nontrivial features of gapless iCSM theories. In particular, we find that while gapless 2+1D Maxwell theories are confined and not robust due to monopole effect, gapless iCSM theories are deconfined and robust against all local perturbation and hence represent a robust 3+1D deconfined gapless order. The gaplessness of the gapless iCSM theory can be understood as a consequence of the spontaneous breaking of an exotic one-form symmetry. Moreover, for a subclass of the gapless iCSM theories, we find interesting topological features in the correlation and response of the system. Finally, for this subclass of theories, we propose a fully continuous field theory description of the model that captures all these features.

We explore the relationship between renormalization group (RG) flow and error correction by constructing quantum algorithms that exactly recognize 1D symmetry-protected topological (SPT) phases protected by finite internal Abelian symmetries. For each SPT phase, our algorithm runs a quantum circuit which emulates RG flow: an arbitrary input ground state wavefunction in the phase is mapped to a unique minimally-entangled reference state, thereby allowing for efficient phase identification. This construction is enabled by viewing a generic input state in the phase as a collection of coherent `errors' applied to the reference state, and engineering a quantum circuit to efficiently detect and correct such errors. Importantly, the error correction threshold is proven to coincide exactly with the phase boundary. We discuss the implications of our results in the context of condensed matter physics, machine learning, and near-term quantum algorithms.

The geometry of 4-string contact interaction of closed string field theory is characterized using machine learning. We obtain Strebel quadratic differentials on 4-punctured spheres as a neural network by performing unsupervised learning with a custom-built loss function. This allows us to solve for local coordinates and compute their associated mapping radii numerically. We also train a neural network distinguishing vertex from Feynman region. As a check, 4-tachyon contact term in the tachyon potential is computed and a good agreement with the results in the literature is observed. We argue that our algorithm is manifestly independent of number of punctures and scaling it to characterize the geometry of \(n\)-string contact interaction is feasible.

We prove novel speed limits on the growth of entanglement, equal time correlators, and spacelike Wilson loops in spatially uniform time-evolving states in strongly coupled CFTs with holographic duals. These bounds can also be viewed as quantum weak energy conditions. Several of the speed limits are valid for regions of arbitrary size and with multiple connected components, and our findings imply new bounds on the effective entanglement velocity of small subregions. In 2d CFT, our results prove a conjecture by Liu and Suh for a large class of states. Key to our findings is a momentum-entanglement correspondence, showing that entanglement growth is computed by the momentum crossing the HRT surface. In our setup, we prove a number of general features of boundary-anchored extremal surfaces, such as a sharp bound on the smallest radius that a surface can probe, and that the tips of extremal surfaces cannot lie in trapped regions. Our methods rely on novel global GR techniques, including a delicate interplay between Lorentzian and Riemannian Hawking masses. While our proofs assume the dominant energy condition in the bulk, we provide numerical evidence that our bounds are true under less restrictive assumptions.

Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However, these demonstrations have been at the scale of toy models, and it remains to be determined whether they can be applied to state-of-the-art lattice quantum chromodynamics calculations. Assessing the viability of sampling algorithms for lattice field theory at scale has traditionally been accomplished using simple cost scaling laws, but as we discuss in this work, their utility is limited for flow-based approaches. We conclude that flow-based approaches to sampling are better thought of as a broad family of algorithms with different scaling properties, and that scalability must be assessed experimentally.

We study the properties of three-body resonances using a lattice complex scalar \(\varphi^4\) theory with two scalars, with parameters chosen such that one heavy particle can decay into three light ones. We determine the two- and three-body spectra for several lattice volumes using variational techniques, and then analyze them with two versions of the three-particle finite-volume formalism: the Relativistic Field Theory approach and the Finite-Volume Unitarity approach. We find that both methods provide an equivalent description of the energy levels, and we are able to fit the spectra using simple parametrizations of the scattering quantities. By solving the integral equations of the corresponding three-particle formalisms, we determine the pole position of the resonance in the complex energy-plane and thereby its mass and width. We find very good agreement between the two methods at different values of the coupling of the theory.

Gauge Theory plays a crucial role in many areas in science, including high energy physics, condensed matter physics and quantum information science. In quantum simulations of lattice gauge theory, an important step is to construct a wave function that obeys gauge symmetry. In this paper, we have developed gauge equivariant neural network wave function techniques for simulating continuous-variable quantum lattice gauge theories in the Hamiltonian formulation. We have applied the gauge equivariant neural network approach to find the ground state of 2+1-dimensional lattice gauge theory with U(1) gauge group using variational Monte Carlo. We have benchmarked our approach against the state-of-the-art complex Gaussian wave functions, demonstrating improved performance in the strong coupling regime and comparable results in the weak coupling regime.

Finding efficient optimization methods plays an important role for quantum optimization and quantum machine learning on near-term quantum computers. While backpropagation on classical computers is computationally efficient, obtaining gradients on quantum computers is not, because the computational complexity usually scales with the number of parameters and measurements. In this paper, we connect Koopman operator theory, which has been successful in predicting nonlinear dynamics, with natural gradient methods in quantum optimization. We propose a data-driven approach using Koopman operator learning to accelerate quantum optimization and quantum machine learning. We develop two new families of methods: the sliding window dynamic mode decomposition (DMD) and the neural DMD for efficiently updating parameters on quantum computers. We show that our methods can predict gradient dynamics on quantum computers and accelerate the variational quantum eigensolver used in quantum optimization, as well as quantum machine learning. We further implement our Koopman operator learning algorithm on a real IBM quantum computer and demonstrate their practical effectiveness.

We study Euclidean M5-branes wrapping vertical divisors in elliptic Calabi-Yau fourfold compactifications of M/F-theory that admit a Sen limit. We construct these Calabi-Yau fourfolds as elliptic fibrations over coordinate flip O3/O7 orientifolds of toric hypersurface Calabi-Yau threefolds. We devise a method to analyze the Hodge structure (and hence the dimension of the intermediate Jacobian) of vertical divisors in these fourfolds, using only the data available from a type IIB compactification on the O3/O7 Calabi-Yau orientifold. Our method utilizes simple combinatorial formulae (that we prove) for the equivariant Hodge numbers of the Calabi-Yau orientifolds and their prime toric divisors, along with a formula for the Euler characteristic of vertical divisors in the corresponding elliptic Calabi-Yau fourfold. Our formula for the Euler characteristic includes a conjectured correction term that accounts for the contributions of pointlike terminal \(\mathbb{Z}_2\) singularities corresponding to perturbative O3-planes. We check our conjecture in a number of explicit examples and find perfect agreement with the results of direct computations.

A number of proposals have been put forward for detecting axion dark matter (DM) with grand unification scale decay constants that rely on the conversion of coherent DM axions to oscillating magnetic fields in the presence of static, laboratory magnetic fields. Crucially, such experiments \(\unicode{x2013}\) including ABRACADABRA \(\unicode{x2013}\) have to-date worked in the limit that the axion Compton wavelength is larger than the size of the experiment, which allows one to take a magnetoquasistatic (MQS) approach to modeling the axion signal. We use finite element methods to solve the coupled axion-electromagnetism equations of motion without assuming the MQS approximation. We show that the MQS approximation becomes a poor approximation at frequencies two orders of magnitude lower than the naive MQS limit. Radiation losses diminish the quality factor of an otherwise high-\(Q\) resonant readout circuit, though this may be mitigated through shielding and minimizing lossy materials. Additionally, self-resonances associated with the detector geometry change the reactive properties of the pickup system, leading to two generic features beyond MQS: there are frequencies that require an inductive rather than capacitive tuning to maintain resonance, and the detector itself becomes a multi-pole resonator at high frequencies. Accounting for these features, competitive sensitivity to the axion-photon coupling may be extended well beyond the naive MQS limit.

Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in either parameters or dataset size until bottlenecked by the other resource. To understand this better, we first identify the necessary properties allowing such scaling laws to arise and then propose a statistical model -- a joint generative data model and random feature model -- that captures this neural scaling phenomenology. By solving this model in the dual limit of large training set size and large number of parameters, we gain insight into (i) the statistical structure of datasets and tasks that lead to scaling laws, (ii) the way nonlinear feature maps, such as those provided by neural networks, enable scaling laws when trained on these datasets, (iii) the optimality of the equiparameterization scaling of training sets and parameters, and (iv) whether such scaling laws can break down and how they behave when they do. Key findings are the manner in which the power laws that occur in the statistics of natural datasets are extended by nonlinear random feature maps and then translated into power-law scalings of the test loss and how the finite extent of the data's spectral power law causes the model's performance to plateau.

Self-interacting dark matter (SIDM) offers the potential to mitigate some of the discrepancies between simulated cold dark matter (CDM) and observed galactic properties. We introduce a physically motivated SIDM model to understand the effects of self interactions on the properties of Milky Way and dwarf galaxy sized haloes. This model consists of dark matter with a nearly degenerate excited state, which allows for both elastic and inelastic scattering. In particular, the model includes a significant probability for particles to up-scatter from the ground state to the excited state. We simulate a suite of zoom-in Milky Way-sized N-body haloes with six models with different scattering cross sections to study the effects of up-scattering in SIDM models. We find that the up-scattering reaction greatly increases the central densities of the main halo through the loss of kinetic energy. However, the physical model still results in significant coring due to the presence of elastic scattering and down-scattering. These effects are not as apparent in the subhalo population compared to the main halo, but the number of subhaloes is reduced compared to CDM.

Large-time correlation functions have a pivotal role in extracting particle masses from Euclidean lattice field theory calculations, but little is known about the statistical properties of these quantities. In this work, the distributions of correlation functions at vanishing momentum are calculated exactly in the case of free real scalar field theory. It is further demonstrated that the results found for this simple case are valid for all local and hermitian operators in bosonic systems with a unique gapped vacuum at large Euclidean-time.

We propose a new mechanism to dynamically select the electroweak scale during inflation. An axion-like field \(\phi\) that couples quadratically to the Higgs with a large initial velocity towards a critical point \(\phi_c\) where the Higgs becomes massless. When \(\phi\) crosses this point, it enters a region where the Higgs mass is tachyonic and this results into an explosive production of Higgs particles. Consequently, a back-reaction potential is generated and the field \(\phi\) is attracted back to \(\phi_c\). After a series of oscillations around this point it is eventually trapped in its vicinity due to the periodic term of the potential. The model avoids transplanckian field excursions, requires very few e-folds of inflation and it is compatible with inflation scales up to \(10^5~\rm GeV\). The mass of \(\phi\) lies in the range of hundreds of GeV to a few TeV and it can be potentially probed in future colliders.