MIT Center for Theoretical Physics — a Leinweber Institute Publications

Superconducting detectors are a promising technology for probing dark matter at extremely low masses, where dark matter interactions are currently unconstrained. Realizing the potential of such detectors requires new readout technologies to achieve the lowest possible thresholds for deposited energy. Here we perform a prototype search for dark matter--electron interactions with kinetic inductance detectors (KIDs), a class of superconducting detector originally designed for infrared astronomy applications. We demonstrate that existing KIDs can achieve effective thresholds as low as 0.2 eV, and we use existing data to set new dark matter constraints. The relative maturity of the technology underlying KIDs means that this platform can be scaled significantly with existing tools, enabling powerful new searches in the coming years.

The Unruh effect can be formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. In recent years, other examples of states with geometrically local modular flow have played important roles in understanding energy and entropy in quantum field theory and quantum gravity. Here I initiate a general study of the settings in which geometric modular flow can arise, showing (i) that any geometric modular flow must be a conformal symmetry of the background spacetime, and (ii) that in a well behaved class of "weakly analytic" states, geometric modular flow must be future-directed. I further argue that if a geometric transformation is conformal but not isometric, then it can only be realized as modular flow in a conformal field theory. Finally, I discuss a few settings in which converse results can be shown -- i.e., settings in which a state can be constructed whose modular flow reproduces a given vector field.

This work summarizes recent results, both theoretical and experimental, in \(B\)-meson leptonic and semileptonic decays and metrology of \(V_{ub}\) and \(V_{cb}\), which were presented at the CKM 2023 workshop. We place these results in context and discuss future prospects in the field.

We expand the concept of two-dimensional topological insulators to encompass a novel category known as topological dipole insulators (TDIs), characterized by conserved dipole moments along the \(x\)-direction in addition to charge conservation. By generalizing Laughlin's flux insertion argument, we prove a no-go theorem and predict possible edge patterns and anomalies in a TDI with both charge \(U^e(1)\) and dipole \(U^d(1)\) symmetries. The edge of a TDI is characterized as a quadrupolar channel that displays a dipole \(U^d(1)\) anomaly. A quantized amount of dipole gets transferred between the edges under the dipolar flux insertion, manifesting as `quantized quadrupolar Hall effect' in TDIs. A microscopic coupled-wire Hamiltonian realizing the TDI is constructed by introducing a mutually commuting pair-hopping terms between wires to gap out all the bulk modes while preserving the dipole moment. The effective action at the quadrupolar edge can be derived from the wire model, with the corresponding bulk dipolar Chern-Simons response theory delineating the topological electromagnetic response in TDIs. Finally, we enrich our exploration of topological dipole insulators to the spinful case and construct a dipolar version of the quantum spin Hall effect, whose boundary evidences a mixed anomaly between spin and dipole symmetry. Effective bulk and the edge action for the dipolar quantum spin Hall insulator are constructed as well.

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by i) the temporal trajectory of a quantum state under unitary evolution or ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases respectively exemplify the phenomena of "Hilbert-space ergodicity" and "deep thermalization." In both cases, the resultant ensembles are defined by a simple principle: the distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulae for all statistical moments of the ensembles; proving the necessary and sufficient conditions for such universality under widely-accepted assumptions; and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information theoretic tools.

Systems reaching thermal equilibrium are ubiquitous. For classical systems, this phenomenon is typically understood statistically through ergodicity in phase space, but translating this to quantum systems is a long-standing problem of interest. Recently a quantum notion of ergodicity has been proposed, namely that isolated, global quantum states uniformly explore their available state space, dubbed Hilbert-space ergodicity. Here we observe signatures of this process with an experimental Rydberg quantum simulator and various numerical models, before generalizing to the case of a local quantum system interacting with its environment. For a closed system, where the environment is a complementary subsystem, we predict and observe a smooth quantum-to-classical transition in that observables progress from large, quantum fluctuations to small, Gaussian fluctuations as the bath size grows. This transition is universal on a quantitative level amongst a wide range of systems, including those at finite temperature, those with itinerant particles, and random circuits. Then, we consider the case of an open system interacting noisily with an external environment. We predict the statistics of observables under largely arbitrary noise channels including those with correlated errors, allowing us to discriminate candidate error models both for continuous Hamiltonian time evolution and for digital random circuits. Ultimately our results clarify the role of ergodicity in quantum dynamics, with fundamental and practical consequences.

Many machine learning applications involve learning a latent representation of data, which is often high-dimensional and difficult to directly interpret. In this work, we propose "Moment Pooling", a natural extension of Deep Sets networks which drastically decrease latent space dimensionality of these networks while maintaining or even improving performance. Moment Pooling generalizes the summation in Deep Sets to arbitrary multivariate moments, which enables the model to achieve a much higher effective latent dimensionality for a fixed latent dimension. We demonstrate Moment Pooling on the collider physics task of quark/gluon jet classification by extending Energy Flow Networks (EFNs) to Moment EFNs. We find that Moment EFNs with latent dimensions as small as 1 perform similarly to ordinary EFNs with higher latent dimension. This small latent dimension allows for the internal representation to be directly visualized and interpreted, which in turn enables the learned internal jet representation to be extracted in closed form.

We investigate the hypothesis that sexaquarks, hypothetical stable six-quark states, could be a significant component of the dark matter. We expand on previous studies of sexaquark cosmology, accounting for the possibility that some relevant interaction cross sections might be strongly suppressed below expectations based on dimensional analysis. We update direct-detection constraints on stable sexaquarks comprising a subdominant fraction of the dark matter, as well as limits on the annihilation of an antisexaquark component from Super-Kamiokande. We argue that the scenario where sexaquarks comprise a \(O(1)\) fraction of the dark matter would require either a suppression of \(O(10^{-19})\) in sexaquark interactions with baryons, combined with a very high yield of net sexaquark number from the quark-hadron transition, or else a very strong suppression of the cross section for antisexaquark annihilation on nucleons (24+ orders of magnitude below the QCD scale). Independently, we find that a sexaquark component comprising more than \(O(10^{-3})\) of the dark matter can be excluded from direct-detection bounds, unless its scattering cross section is severely suppressed compared to the expected scale of strong and even electromagnetic interactions.

In this paper, we present a general framework for quantum many-body simulations called the operator learning renormalization group (OLRG). Inspired by machine learning perspectives, OLRG is a generalization of Wilson's numerical renormalization group and White's density matrix renormalization group, which recursively builds a simulatable system to approximate a target system of the same number of sites via operator maps. OLRG uses a loss function to minimize the error of a target property directly by learning the operator map in lieu of a state ansatz. This loss function is designed by a scaling consistency condition that also provides a provable bound for real-time evolution. We implement two versions of the operator maps for classical and quantum simulations. The former, which we call the Operator Matrix Map, can be implemented via neural networks on classical computers. The latter, which we call the Hamiltonian Expression Map, generates device pulse sequences to leverage the capabilities of quantum computing hardware. We illustrate the performance of both maps for calculating time-dependent quantities in the quantum Ising model Hamiltonian.

The entanglement wedge reconstruction paradigm in AdS/CFT states that for a bulk qudit within the entanglement wedge of a boundary subregion \(\bar{A}\), operators acting on the bulk qudit can be reconstructed as CFT operators on \(\bar{A}\). This naturally fits within the framework of quantum error correction, with the CFT states containing the bulk qudit forming a code protected against the erasure of the boundary subregion \(A\). In this paper, we set up and study a framework for relational bulk reconstruction in holography: given two code subspaces both protected against erasure of the boundary region \(A\), the goal is to relate the operator reconstructions between the two spaces. To accomplish this, we assume that the two code subspaces are smoothly connected by a one-parameter family of codes all protected against the erasure of \(A\), and that the maximally-entangled states on these codes are all full-rank. We argue that such code subspaces can naturally be constructed in holography in a "measurement-based" setting. In this setting, we derive a flow equation for the operator reconstruction of a fixed code subspace operator using modular theory which can, in principle, be integrated to relate the reconstructed operators all along the flow. We observe a striking resemblance between our formulas for relational bulk reconstruction and the infinite-time limit of Connes cocycle flow, and take some steps towards making this connection more rigorous. We also provide alternative derivations of our reconstruction formulas in terms of a canonical reconstruction map we call the modular reflection operator.

Numerical studies of lattice quantum field theories are conducted in finite spatial volumes, typically with cubic symmetry in the spatial coordinates. Motivated by these studies, this work presents a general algorithm to construct multi-particle interpolating operators for quantum field theories with cubic symmetry. The algorithm automates the block diagonalization required to combine multiple operators of definite linear momentum into irreducible representations of the appropriate little group. Examples are given for distinguishable and indistinguishable particles including cases with both zero and non-zero spin. An implementation of the algorithm is publicly available at https://github.com/latticeqcdtools/mhi.

Jet energy calibration is an important aspect of many measurements and searches at the LHC. Currently, these calibrations are performed on a per-jet basis, i.e. agnostic to the properties of other jets in the same event. In this work, we propose taking advantage of the correlations induced by momentum conservation between jets in order to improve their jet energy calibration. By fitting the \(p_T\) asymmetry of dijet events in simulation, while remaining agnostic to the \(p_T\) spectra themselves, we are able to obtain correlation-improved maximum likelihood estimates. This approach is demonstrated with simulated jets from the CMS Detector, yielding a \(3\)-\(5\%\) relative improvement in the jet energy resolution, corresponding to a quadrature improvement of approximately 35%.

We present an efficient approach to set informative physically motivated priors for EFT-based full-shape analyses of galaxy survey data. We extract these priors from simulated galaxy catalogs based on halo occupation distribution (HOD) models. As a first step, we build a joint distribution between EFT galaxy bias and HOD parameters from a set of 10,500 HOD mock catalogs. We make use of the field level EFT technique that allows for cosmic variance cancellation, enabling a precision calibration of EFT parameters from computationally inexpensive small-volume simulations. As a second step, we use neural density estimators -- normalizing flows -- to model the marginal probability density of the EFT parameters, which can be used as a prior distribution in full shape analyses. As a first application, we use our HOD-based prior distribution in a new analysis of galaxy power spectra and bispectra from the BOSS survey in the context of single field primordial non-Gaussianity. We find that our approach leads to a reduction of the posterior volume of bias parameters by an order of magnitude. We also find \(f_{\rm NL}^{\rm equil} = 650\pm 310\) and \(f_{\rm NL}^{\rm ortho} = 42\pm 130\) (at 68% CL) in a combined two-template analysis, representing a \(\approx 40\%\) improvement in constraints on single field primordial non-Gaussianity, equivalent to doubling the survey volume.

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

We present an update for results on \(B\)-meson semileptonic decays using the highly improved staggered quark (HISQ) action for both valence and 2+1+1 sea quarks. The use of the highly improved action, combined with the MILC collaboration's gauge ensembles with lattice spacings down to \(\sim\)0.03 fm, allows the \(b\) quark to be treated with the same discretization as the lighter quarks. The talk will focus on updated results for \(B_{(s)} \to D_{(s)}\), \(B_{(s)} \to K\) scalar and vector form factors.

Neutrinoless double-beta (\(0\nu\beta\beta\)) decay is a heretofore unobserved process which, if observed, would imply that neutrinos are Majorana particles. Interpretations of the stringent experimental constraints on \(0\nu\beta\beta\)-decay half-lives require calculations of nuclear matrix elements. This work presents the first lattice quantum-chromodynamics (LQCD) calculation of the matrix element for \(0\nu\beta\beta\) decay in a multi-nucleon system, specifically the \(nn \rightarrow pp ee\) transition, mediated by a light left-handed Majorana neutrino propagating over nuclear-scale distances. This calculation is performed with quark masses corresponding to a pion mass of \(m_\pi = 806\) MeV at a single lattice spacing and volume. The statistically cleaner \(\Sigma^- \rightarrow \Sigma^+ ee\) transition is also computed in order to investigate various systematic uncertainties. The prospects for matching the results of LQCD calculations onto a nuclear effective field theory to determine a leading-order low-energy constant relevant for \(0\nu\beta\beta\) decay with a light Majorana neutrino are investigated. This work, therefore, sets the stage for future calculations at physical values of the quark masses that, combined with effective field theory and nuclear many-body studies, will provide controlled theoretical inputs to experimental searches of \(0\nu\beta\beta\) decay.

Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum ergodicity for closed systems with time-dependent Hamiltonians, defined as statistical randomness exhibited in their long-time dynamics. Concretely, we consider the temporal ensemble of quantum states (time-evolution operators) generated by the evolution, and investigate the conditions necessary for them to be statistically indistinguishable from uniformly random states (operators) in the Hilbert space (space of unitaries). We find that the number of driving frequencies underlying the Hamiltonian needs to be sufficiently large for this to occur. Conversely, we show that statistical pseudo-randomness -- indistinguishability up to some large but finite moment, can already be achieved by a quantum system driven with a single frequency, i.e., a Floquet system, as long as the driving period is sufficiently long. Our work relates the complexity of a time-dependent Hamiltonian and that of the resulting quantum dynamics, and offers a fresh perspective to the established topics of quantum ergodicity and chaos from the lens of quantum information.

This work presents a determination of the quark Collins-Soper kernel, which relates transverse-momentum-dependent parton distributions (TMDs) at different rapidity scales, using lattice quantum chromodynamics (QCD). This is the first such determination with systematic control of quark mass, operator mixing, and discretization effects. Next-to-next-to-leading logarithmic matching is used to match lattice-calculable distributions to the corresponding TMDs. The continuum-extrapolated lattice QCD results are consistent with several recent phenomenological parameterizations of the Collins-Soper kernel and are precise enough to disfavor other parameterizations.

Ab-initio simulations of multiple heavy quarks propagating in a Quark-Gluon Plasma are computationally difficult to perform due to the large dimension of the space of density matrices. This work develops machine learning algorithms to overcome this difficulty by approximating exact quantum states with neural network parametrisations, specifically Neural Density Operators. As a proof of principle demonstration in a QCD-like theory, the approach is applied to solve the Lindblad master equation in the 1+1d lattice Schwinger Model as an open quantum system. Neural Density Operators enable the study of in-medium dynamics on large lattice volumes, where multiple-string interactions and their effects on string-breaking and recombination phenomena can be studied. Thermal properties of the system at equilibrium can also be probed with these methods by variationally constructing the steady state of the Lindblad master equation. Scaling of this approach with system size is studied, and numerical demonstrations on up to 32 spatial lattice sites and with up to 3 interacting strings are performed.

We revisit the path integral description of quantum tunneling and show how it can be generalized to excited states. For clarity, we focus on the simple toy model of a point particle in a double-well potential, for which we perform all steps explicitly. Instead of performing the familiar Wick rotation from physical to imaginary time - which is inconsistent with the requisite boundary conditions when treating tunneling from excited states - we regularize the path integral by adding an infinitesimal complex contribution to the Hamiltonian, while keeping time strictly real. We find that this gives rise to a complex stationary-phase solution, in agreement with recent insights from Picard-Lefshitz theory. We then show that there exists a class of analytic solutions for the corresponding equations of motion, which can be made to match the appropriate boundary conditions in the physically relevant limits of a vanishing regulator and an infinite physical time. We provide a detailed discussion of this non-trivial limit. We find that, for systems without an explicit time-dependence, our approach reproduces the picture of an instanton-like solution defined on a finite Euclidean-time interval. Lastly, we discuss the generalization of our approach to broader classes of systems, for which it serves as a reliable framework for high-precision calculations.