Center for Theoretical Physics Publications

Simulations of lattice gauge theories with tensor networks and quantum computing have so far mainly focused on staggered fermions. In this paper, we use matrix product states to study Wilson fermions in the Hamiltonian formulation and present a novel method to determine the additive mass renormalization. Focusing on the single-flavor Schwinger model as a benchmark model, we investigate the regime of a nonvanishing topological \(\theta\)-term, which is inaccessible to conventional Monte Carlo methods. We systematically explore the dependence of the mass shift on the volume, the lattice spacing, the \(\theta\)-parameter, and the Wilson parameter. This allows us to follow lines of constant renormalized mass, and therefore to substantially improve the continuum extrapolation of the mass gap and the electric field density. For small values of the mass, our continuum results agree with the theoretical prediction from mass perturbation theory. Going beyond Wilson fermions, our technique can also be applied to staggered fermions, and we demonstrate that the results of our approach agree with a recent theoretical prediction for the mass shift at sufficiently large volumes.

We generalize the relativistic field-theoretic (RFT) three-particle finite-volume formalism to systems of three identical, massive, spin-\(1/2\) fermions, such as three neutrons. This allows, in principle, for the determination of the three-neutron interaction from the finite-volume spectrum of three-neutron states, which can be obtained from lattice QCD calculations.

Moiré engineering in atomically thin van der Waals heterostructures creates artificial quantum materials with designer properties. We solve the many-body problem of interacting electrons confined to a moiré superlattice potential minimum (the moiré atom) using a 2D fermionic neural network. We show that strong Coulomb interactions in combination with the anisotropic moiré potential lead to striking ``Wigner molecule" charge density distributions observable with scanning tunneling microscopy.

The future electron-ion collider (EIC) will produce the first-ever high energy collisions between electrons and a wide range of nuclei, opening a new era in the study of cold nuclear matter. Quarks and gluons produced in these collisions will propagate through the dense nuclear matter of nuclei, imprinting its structure into subtle correlations in the energy flux of final state hadrons. In this Letter, we apply recent developments from the field of jet substructure, namely the energy correlator observables, to decode these correlations and provide a new window into nuclear structure. The energy correlators provide a calibrated probe of the scale dependence of vacuum QCD dynamics, enabling medium modifications to be cleanly imaged and interpreted as a function of scale. Using the eHIJING parton shower to simulate electron-nucleus collisions, we demonstrate that the size of the nucleus is cleanly imprinted as an angular scale in the correlators, with a magnitude that is visible for realistic EIC kinematics. Remarkably, we can even observe the size difference between the proposed EIC nuclear targets \({}^3\)He, \({}^4\)He, \({}^{12}\)C, \({}^{40}\)Ca, \({}^{64}\)Cu, \({}^{197}\)Au, and \({}^{238}\)U, showing that the energy correlators can image femtometer length scales using asymptotic energy flux. Our approach offers a unified view of jet substructure across collider experiments, and provides numerous new theoretical tools to unravel the complex dynamics of QCD in extreme environments, both hot and cold.

Decaying or annihilating dark matter and other exotic energy injections can modify the spectrum of the universe's photon bath, resulting in e.g. new contributions to spectral distortions of the cosmic microwave background blackbody spectrum and modifications to the temperature and ionization history of the universe. Here, we present an improved version of the \(\texttt{DarkHistory}\) code, which is now capable of consistently calculating the spectrum of low-energy photons by properly treating the interactions of these photons with the levels of hydrogen atoms. Other changes to the code include a more detailed treatment of energy deposition by low-energy electrons, and spectral distortions from heating of the intergalactic medium. All of the improvements we have made to \(\texttt{DarkHistory}\) are publicly available.

We calculate the post-recombination contribution to the Cosmic Microwave Background (CMB) spectral distortion due to general exotic energy injections, including dark matter (DM) decaying or annihilating to Standard Model particles. Upon subtracting the background distortion that would be present even without such energy injections, we find residual distortions that are still potentially large enough to be detectable by future experiments such as PIXIE. The distortions also have a high-energy spectral feature that is a unique signature of the injection of high-energy particles. We present a calculation of the global ionization history in the presence of decaying dark matter with sub-keV masses, and also show that previous calculations of the global ionization history in the presence of energy injection are not significantly modified by these additional spectral distortions. Our improved treatment of low-energy electrons allows us to extend calculations of the CMB anisotropy constraints for decaying DM down to arbitrarily low masses. We also recast these bounds as constraints on the coupling of axion-like particles to photons.

We numerically study the phase structure of the two-flavor Schwinger model with matrix product states, focusing on the (1+1)-dimensional analog of the CP-violating Dashen phase in QCD. Simulating the model around the point where the positive mass of one fermion flavor corresponds to the negative mass of the other fermion flavor, we explore a regime afflicted by the sign problem for conventional Monte Carlo techniques. Our results indicate that the model undergoes a CP-violating Dashen phase transition at this point, which manifests itself in abrupt changes of the average electric field and the analog of the pion condensate in the model. Studying the scaling of the bipartite entanglement entropy as a function of the volume, we find clear indications that this transition is not of first order.

We perform a Markov Chain Monte Carlo (MCMC) analysis of a simple yet generic multifield inflation model characterized by two scalar fields coupled to each other and nonminimally coupled to gravity, fit to Planck 2018 cosmic microwave background (CMB) data. In particular, model parameters are constrained by data on the amplitude of the primordial power spectrum of scalar curvature perturbations on CMB scales \(A_s\), the spectral index \(n_s\), and the ratio of power in tensor to scalar modes \(r\), with a prior that the primordial power spectrum should also lead to primordial black hole (PBH) production sufficient to account for the observed dark matter (DM) abundance. We find that \(n_s\) in particular controls the constraints on our model. Whereas previous studies of PBH formation from an ultra-slow-roll phase of inflation have highlighted the need for at least one model parameter to be highly fine-tuned, we identify a degeneracy direction in parameter space such that shifts by \(\sim 10\%\) of one parameter can be compensated by comparable shifts in other parameters while preserving a close fit between model predictions and observations. Furthermore, we find this allowed parameter region produces observable gravitational wave (GW) signals in the frequency ranges to which upcoming experiments are projected to be sensitive, including Advanced LIGO and Virgo, the Einstein Telescope (ET), DECIGO, and LISA.

We present an efficient algorithm for computing the prepotential in compactifications of type II string theory on mirror pairs of Calabi-Yau threefolds in toric varieties. Applying this method, we exhibit the first systematic computation of genus-zero Gopakumar-Vafa invariants in compact threefolds with many moduli, including examples with up to 491 vector multiplets.

New physics in the rare top decays \(t \to q \ell^+\ell^-\) is currently very weakly constrained. We show that in a large class of Standard Model extensions, existing experimental constraints on new physics in flavor-conserving processes imply strong indirect bounds on new physics contributions to flavor-violating processes of the form \(t \to q \ell^+\ell^-\). These indirect bounds arise from basic principles of quantum field theory together with a few generic conditions on the UV structure of the theory, and are roughly an order of magnitude stronger than the present experimental bounds on the same processes. These constraints provide a theoretically-motivated target for experimental searches for \(t \to q \ell^+\ell^-\): violation of these bounds would exclude a large class of new physics models, and would provide nontrivial insight into the UV behavior of the new physics.

The combination of precise determinations of \(V_{us}\) and \(V_{ud}\) hints towards a violation of the CKM first row unitarity at about \(3\sigma\) level. Conversely, the recent measurement of the \(W\)-boson mass by the CDF Collaboration exhibits significant tension with the SM prediction, intensifying the conflict that may arise in models addressing the unitarity violation. We demonstrate that one vector-like \(SU(2)_L\) doublet with mass of a few TeV mixing with light quarks and the top quark can simultaneously account for the two anomalies, without conflicting with flavour-changing phenomena and electroweak observables. Moreover, another tension in the value of the Cabibbo angle is reported also at \(3\sigma\) level, between two determinations of \(V_{us}\) obtained from semi-leptonic \(K\ell3\) and leptonic \(K\mu 2\) kaon decays. We show that the vector-like doublet can be at the origin of this discrepancy and the substantial positive shift in the \(W\)-boson mass. This unique feature of the vector-like quark doublet may render it a crucial puzzle piece in new physics scenarios addressing the CKM unitarity problem. The model can be potentially probed in future colliders.

We study the interactions of systems of two and three nondegenerate mesons composed of pions and kaons at maximal isospin using lattice QCD, specifically \(\pi^+K^+\), \(\pi^+\pi^+K^+\) and \(K^+K^+\pi^+\). Utilizing the stochastic LapH method, we determine the spectrum of these systems on two CLS \(N_f=2+1\) ensembles with pion masses of \(200\) MeV and \(340\) MeV, and include many levels in different momentum frames. We constrain the K matrices describing two- and three-particle interactions by fitting the spectrum to the results predicted by the finite-volume formalism, including up to \(p\) waves. This requires also results for the \(\pi^+\pi^+\) and \(K^+ K^+\) spectrum, which have been obtained previously on the same configurations. We explore different fitting strategies, comparing fits to energy shifts with fits to energies boosted to the rest frame, and also comparing simultaneous global fits to all relevant two- and three-particle channels to those where we first fit two-particle channels and then add in the three-particle information. We provide the first determination of the three-particle K matrix in \(\pi^+\pi^+K^+\) and \(K^+ K^+ \pi^+\) systems, finding statistically significant nonzero results in most cases. We include \(s\) and \(p\) waves in the K matrix for \(\pi^+ K^+\) scattering, finding evidence for an attractive \(p\)-wave scattering length. We compare our results to Chiral Perturbation Theory, including an investigation of the impact of discretization errors, for which we provide the leading order predictions obtained using Wilson Chiral Perturbation Theory.

The determination of the string vertices of closed string field theory is shown to be a conformal field theory problem solvable by combining insights from Liouville theory, hyperbolic geometry, and conformal bootstrap. We first demonstrate how Strebel differentials arise from hyperbolic string vertices by performing a WKB approximation to the associated Fuchsian equation, which we subsequently use it to derive a Polyakov-like conjecture for Strebel differentials. This result implies that the string vertices are generated by the interactions of \(n\) zero momentum tachyons, or equivalently, a certain limit of suitably regularized on-shell Liouville action. We argue that the latter can be related to the interaction of three zero momentum tachyons on a generalized cubic vertex through classical conformal blocks. We test this claim for the quartic vertex and discuss its generalization to higher-string interactions.

The identification of interesting substructures within jets is an important tool for searching for new physics and probing the Standard Model at colliders. Many of these substructure tools have previously been shown to take the form of optimal transport problems, in particular the Energy Mover's Distance (EMD). In this work, we show that the EMD is in fact the natural structure for comparing collider events, which accounts for its recent success in understanding event and jet substructure. We then present a Shape Hunting Algorithm using Parameterized Energy Reconstruction (SHAPER), which is a general framework for defining and computing shape-based observables. SHAPER generalizes N-jettiness from point clusters to any extended, parametrizable shape. This is accomplished by efficiently minimizing the EMD between events and parameterized manifolds of energy flows representing idealized shapes, implemented using the dual-potential Sinkhorn approximation of the Wasserstein metric. We show how the geometric language of observables as manifolds can be used to define novel observables with built-in infrared-and-collinear safety. We demonstrate the efficacy of the SHAPER framework by performing empirical jet substructure studies using several examples of new shape-based observables.

Studying the dynamics of open quantum systems holds the potential to enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Due to the high-dimensional nature of the problem, customized deep generative neural networks have been instrumental in modeling the high-dimensional density matrix \(\rho\), which is the key description for the dynamics of such systems. However, the complex-valued nature and normalization constraints of \(\rho\), as well as its complicated dynamics, prohibit a seamless connection between open quantum systems and the recent advances in deep generative modeling. Here we lift that limitation by utilizing a reformulation of open quantum system dynamics to a partial differential equation (PDE) for a corresponding probability distribution \(Q\), the Husimi Q function. Thus, we model the Q function seamlessly with off-the-shelf deep generative models such as normalizing flows. Additionally, we develop novel methods for learning normalizing flow evolution governed by high-dimensional PDEs, based on the Euler method and the application of the time-dependent variational principle. We name the resulting approach Q-Flow and demonstrate the scalability and efficiency of Q-Flow on open quantum system simulations, including the dissipative harmonic oscillator and the dissipative bosonic model. Q-Flow is superior to conventional PDE solvers and state-of-the-art physics-informed neural network solvers, especially in high-dimensional systems.

To compute the string one-loop correction to the Kahler potential of moduli fields of string compactifications in Einstein-frame, one must compute: the string one-loop correction to the Einstein-Hilbert action, the string one-loop correction to the moduli kinetic terms, the string one-loop correction to the definition of the holomorphic coordinates. In this note, we compute the string one-loop correction to the Einstein-Hilbert action of type II string theory compactified on orientifolds of Calabi-Yau threefolds. We find that the one-loop correction is determined by the new supersymmetric index studied by Cecotti, Fendley, Intriligator, and Vafa. As a simple application, we apply our results to estimate the size of the one-loop corrections around a conifold point in the Kahler moduli space.

We investigate the performance of the variational quantum eigensolver (VQE) for the optimal flight gate assignment problem. This problem is a combinatorial optimization problem that aims at finding an optimal assignment of flights to the gates of an airport, in order to minimize the passenger travel time. To study the problem, we adopt a qubit-efficient binary encoding with a cyclic mapping, which is suitable for a digital quantum computer. Using this encoding in conjunction with the Conditional Value at Risk (CVaR) as an aggregation function, we systematically explore the performance of the approach by classically simulating the CVaR-VQE. Our results indicate that the method allows for finding a good solution with high probability, and the method significantly outperforms the naive VQE approach. We examine the role of entanglement for the performance, and find that ansätze with entangling gates allow for better results than pure product states. Studying the problem for various sizes, our numerical data show that the scaling of the number of cost function calls for obtaining a good solution is not exponential for the regimes we investigate in this work.

By explicit counterexample, we show that the "reflected entropy" defined by Dutta and Faulkner is not monotonically decreasing under partial trace, and so is not a measure of physical correlations. In fact, our counterexamples show that none of the Rényi reflected entropies \(S_{R}^{(\alpha)}\) for \(0 < \alpha < 2\) is a correlation measure; the usual reflected entropy is realized as the \(\alpha=1\) member of this family. The counterexamples are given by quantum states that correspond to classical probability distributions, so reflected entropy fails to measure correlations even at the classical level.

In an isolated quantum many-body system undergoing unitary evolution, the entropy of a subsystem (smaller than half the system size) thermalizes if at long times, it is to leading order equal to the thermodynamic entropy of the subsystem at the same energy. In this paper, we prove entropy thermalization for a nearly integrable Sachdev-Ye-Kitaev model initialized in a pure product state. The model is obtained by adding random all-to-all \(4\)-body interactions as a perturbation to a random free-fermion model.

The concept of space-evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time and evolving the system using a space transfer matrix. The infinite-volume limit is then described by the fixed points of this operator, also known as influence matrices. To evaluate the potential of this method as a numerical scheme, it is important to understand whether the influence matrices can be efficiently encoded in a classical computer. It is then natural to wonder what is the scaling of their entanglement, dubbed temporal entanglement, as a function of time. In this work we study space evolution in chaotic quantum circuits. First, we extend the concept of space-evolution to include evolution in any generic space-like direction, which enables us to use influence matrices on a generic time-like surface, or path, to describe any two-point function. Then we study their entanglement, finding that it scales linearly with time for all paths but with two interesting marginal cases: (i) vertical paths in generic chaotic systems (ii) any path in dual-unitary circuits. In these cases Rényi entropies with index larger than one are sub-linear in time, while the von Neumann entanglement entropy is linear but grows at a slower rate compared to regular state entanglement. We attribute this behaviour to the existence of a product state with large overlap with the influence matrices, similarly to what has been observed for regular entanglement in systems with conservation laws.