MIT Center for Theoretical Physics — a Leinweber Institute Publications

Entanglement is the hallmark of quantum physics, yet its characterization in interacting many-body systems at thermal equilibrium remains one of the most important challenges in quantum statistical physics. We prove that the Gibbs state of any quantum spin chain can be exactly decomposed into a mixture of matrix product states with a bond dimension that is independent of the system size, at any finite temperature. As a consequence, the Schmidt number, arguably the most stringent measure of bipartite entanglement, is strictly finite for thermal states, even in the thermodynamic limit. Our decomposition is explicit and is accompanied by an efficient classical algorithm to sample the resulting matrix product states.

Dark sectors consisting of atomic constituents (electrons, protons, and photons) offer a well-motivated extension to the Standard Model while providing multiple avenues for phenomenological study. In this work, we explore the impact of conversions between the dark and Standard Model photons in the primordial CMB spectral distortion epoch ($10^3 \lesssim z \lesssim 10^6$). These conversions are resonantly enhanced when the induced thermal masses of both photonic species are equal, thus leading to the possibility that sizeable distortions can be produced. To this end, we solve the Boltzmann equation at early times to determine the (irreducible) freeze-in or freeze-out abundance of dark photons. This procedure also allows us to update the limits on generic milli-charged dark sectors using the ACT DR6 bound on the number of effective radiative degrees of freedom ($N_{\rm eff}$). By then modeling the evolution of the thermal masses in both sectors, we compute the primordial CMB distortion using the Landau-Zener formalism. We find that when the dark electron and proton are roughly similar in mass (the positronium limit), current spectral distortion data from the COBE/FIRAS instrument is able to rule out novel regions of parameter space. We also forecast bounds from the proposed FOSSIL satellite, finding that spectral distortions can also be used to probe the ultra-low dark electric charge regions of parameter space, which are difficult to investigate by other means.

Recently, Jones et al. [arXiv:2310.12859] claimed strong evidence for the statistical anisotropy of the universe. The claim is based on a joint analysis of four different anomaly tests of the cosmic microwave background data, each of which is known to be anomalous, with a lower level of significance. They reported a combined $p$-value of about $3\times 10^{-8}$, which is more than a $5σ$ level of significance. We observe that statistical anisotropy is not even relevant for two of the four considered tests, which seems sufficient to invalidate the authors’ claim. Furthermore, even if one reinterprets the claim as evidence against $Λ$CDM rather than statistical anisotropy, we argue that this result significantly suffers from the look-elsewhere effect. Assuming a set of independent (i.e., uncorrelated) tests, we show that if the four tests with the smallest $p$-values are cherry-picked from 10 independent tests, the $p$-value reported by Jones et al. corresponds to only $3σ$ significance. If there are 27 independent tests, the significance falls to $2σ$. These numbers, however, overstate our argument, since the four tests used by Jones et al. are slightly correlated. Determining the correlation of Jones et al.’s tests by comparing their joint $p$-value with the product of the four separate $p$-values, we find that about 16 or 50 tests are sufficient to reduce the significance of Jones et al.’s results to 3$σ$ or 2$σ$ significance, respectively. We also provide a list of anomaly tests discussed in the literature (and propose a few generalizations), suggesting that very plausibly 16 (or even 50) independent tests have been published, and possibly many more have been considered but not published. We conclude that the current data is consistent with the $Λ$CDM model and, in particular, with statistical isotropy.

We present a framework for systematic computations of scattering amplitudes for gravitational Raman scattering, — the inelastic scattering of massless fields off compact relativistic objects. We focus on the small-frequency (post-Minkowskian, PM) regime relevant for the study of tidal effects, which can be mapped onto gravitational wave observables during the inspiraling phase of a merger. We demonstrate that this setup is ideal for systematic studies of tidal effects, in a way that is free from coordinate, gauge, and field redefinition ambiguities. We use a combination of worldline effective field theory, the background field method, and advanced scattering amplitude techniques to derive phase shifts for scattering of spin-$0,1,2$ fields off generic compact objects at third PM order. We demonstrate that the inclusion of the recoil of the object is crucial for consistency of this calculation. Focusing on a particular case of black holes, we extract the leading static and dynamical Love numbers of the spin-0 field and the static Love number of the spin-1 field in four dimensions by matching our EFT amplitudes and calculations in General Relativity. We show, fully on-shell, that the leading static Love numbers vanish identically, while the dynamical Love numbers are not zero and run logarithmically. The latter resolves the ambiguities of previous off-shell matching calculations. We also extend our results to seven dimensions, where spin-2 Love numbers undergo a renormalization group running at 2PM, which we compute explicitly. In addition, we extract the leading static Love numbers of spin-0 and spin-1 fields in five dimensions, which also run.

The one-state statement for closed universes has sparked considerable discussion. In this paper we examine its physical meaning in the context of the Hartle-Hawking state and de Sitter space. We argue that the one-state property of closed universes is fully compatible with the finite-dimensional quantum mechanics experienced by observers inside de Sitter space, and that this compatibility requires neither mixing of alpha sectors nor any modification of the rules of the gravitational path integral. The apparent tension is resolved by sharply distinguishing the baby-universe Hilbert space, namely the space of closed universes viewed from the outside, from the bulk Hilbert space that governs quantum mechanics for an observer inside a single de Sitter universe. The baby-universe Hilbert space, together with its commutative operator algebra, is not a quantum-mechanical Hilbert space: it is merely a mathematical repackaging of classical probability theory and does not carry any quantum-mechanical structure at all, a direct consequence of the one-state property of closed universes. Accordingly, attempting to formulate quantum mechanics directly on the baby-universe Hilbert space conflates classical ensemble data with the quantum mechanics experienced by bulk observers and leads to physically incorrect conclusions. By contrast, the quantum mechanics experienced by an observer inside de Sitter space emerges from the classical statistics encoded in the baby-universe Hilbert space, providing a concrete realization of Wheeler’s idea of “It from Bit”. We demonstrate these features by completely solving a topological toy model of one-dimensional de Sitter spacetime. Along the way we clarify the physical meaning of de Sitter entropy, showing that it corresponds to the coarse-grained entropy of the underlying state.

In this paper we extend recent ideas about observers and closed universes to theories where observers can be fluctuated into existence in the Hartle-Hawking state. This introduces a phenomenon that was not considered in these earlier discussions: the dominant transition from one cosmological state to another can go through a fluctuation that annihilates the universe and creates a new one. We nonetheless argue that the observer decoherence rule allows for the third-quantized description of such a theory to emerge from a factorizing holographic theory with a one-dimensional Hilbert space, without any need for $α$-parameters. We also point out a close analogy between the observer rule in this context and the coarse-graining of the spectral form factor at late times for AdS black holes. Along the way we clarify several aspects of the relationship between holography, the gravitational path integral, and $α$-parameters. We also explain why string theory scattering amplitudes do not lead to a one-dimensional Hilbert space on the worldsheet, despite being computed by a gravitational path integral with a sum over topology. Finally we point out that using the path integral to compute integrated local operators conditioned on an observer in the context of a theory with a landscape can lead to rather surprising conclusions. For example we argue that in a landscape with one AdS minimum and one dS minimum, both of which can support observers, an observer almost surely finds themself in dS and not AdS even if the boundary conditions are dual to a state with an observer in AdS.

[Abridged] Some cosmological theories propose that the observable universe is a small part of a much larger universe in which parameters describing the low-energy laws of physics vary from region to region. How can we reasonably assess a theory that describes such a mostly unobservable universe? We propose a Bayesian method based on theory-generated probability distributions for our observations. We focus on basic principles, leaving aside concerns about practicality. (We also leave aside the measure problem, to discuss other issues.) We argue that cosmological theories can be tested by standard Bayesian updating, but we need to use theoretical predictions for “first-person” probabilities — i.e., probabilities for our observations, accounting for all relevant selection effects. These selection effects can depend on the observer, and on time, so in principle first-person probabilities are defined for each observer-instant — an observer at an instant of time. First-person probabilities should take into account everything the observer believes about herself and her surroundings — i.e., her “subjective state”. We advocate a “Principle of Self-Locating Indifference” (PSLI), asserting that any real observer should make predictions as if she were chosen randomly from the theoretically predicted observer-instants that share her subjective state. We believe the PSLI is intuitively very reasonable, but also argue that it maximizes the expected fraction of observers who will make correct predictions. Cosmological theories will in general predict a set of possible universes, each with a probability. To calculate first-person probabilities, we argue that each possible universe should be weighted by the number of observer-instants in the specified subjective state that it contains. We also discuss Boltzmann brains, the humans/Jovians parable of Hartle and Srednicki, and the use of “old evidence”.

Wilson loops are essential objects in QCD and have been pivotal in scale setting and demonstrating confinement. Various generalizations are crucial for computations needed in effective field theories. In lattice gauge theory, Wilson loop calculations face challenges, including excited-state contamination at short times and the signal-to-noise ratio issue at longer times. To address these problems, we develop a new method by using neural networks to parametrize interpolators for the static quark-antiquark pair. We construct gauge-equivariant layers for the network and train it to find the ground state of the system. The trained network itself is then treated as our new observable for the inference. Our results demonstrate a significant improvement in the signal compared to traditional Wilson loops, performing as well as Coulomb-gauge Wilson-line correlators while maintaining gauge invariance. Additionally, we present an example where the optimized ground state is used to measure the static force directly, as well as another example combining this method with the multilevel algorithm. Finally, we extend the formalism to find excited-state interpolators for static quark-antiquark systems. To our knowledge, this work is the first study of neural networks with a physically motivated loss function for Wilson loops.

We propose and analyze a versatile and efficient multiparameter quantum sensing protocol, which simultaneously estimates many non-commuting and time-dependent signals that are coherently or incoherently coupled to sensing particles. Even in the presence of control imperfections and readout errors, our approach can detect exponentially many parameters in the system size while maintaining the optimal scaling of sensitivity. To accomplish this, scrambling dynamics are leveraged to map distinct signals to unique patterns of bitstring measurements, which distinguishes a large number of signals without significant sensitivity loss. Based on this principle, we develop a computationally efficient protocol utilizing random global Clifford unitaries and evaluate its performance both analytically and numerically. Our protocol naturally extends to scrambling dynamics generated by random local Clifford circuits, local random unitary circuits (RUCs), and ergodic Hamiltonian evolution–commonly realized in near-term quantum hardware–and opens the door to applications ranging from precise noise benchmarking of quantum dynamics to learning time-dependent Hamiltonians.

Excited-state effects lead to hard-to-quantify systematic uncertainties in lattice quantum chromodynamics (LQCD) spectroscopy calculations when computationally accessible imaginary times are smaller than inverse excitation gaps, as often arises for multi-hadron systems with signal-to-noise problems. Lanczos residual bounds address this by providing two-sided constraints on energies that do not require assumptions beyond Hermiticity, but often give very conservative systematic uncertainty estimates. Here, a more-constraining set of gap bounds is introduced for hadron spectroscopy. These bounds provide tighter constraints whose validity requires an explicit assumption about an energy gap. Exactly solvable lattice field theory correlators are used to test the utility of residual and gap bounds at finite and infinite statistics. Two-sided bounds and other analysis methods are then applied to a high-statistics LQCD calculation of nucleon-nucleon scattering at $m_π\sim 800$ MeV. Generalized eigenvalue problem (GEVP) and Lanczos energy estimators are compatible when applied to the same correlator data, but analyses including different interpolating operators show statistically significant inconsistencies. However, two-sided bounds from all operators are consistent. Under the assumption that the number of energy levels below $NΔ$ and $ΔΔ$ thresholds is the same as for non-interacting nucleons, gap bounds are sufficient to constrain nucleon-nucleon scattering amplitudes at phenomenologically relevant precision. Lanczos methods further reveal that energy-eigenstate estimates from previously studied asymmetric correlators have not converged over accessible imaginary times. Nevertheless, data-driven examples demonstrate why assumptions are required to draw conclusions about the natures of two-nucleon ground states at these masses.

We study the lattice version of higher-form symmetries on tensor-product Hilbert spaces. Interestingly, at low energies, these symmetries may not flow to the topological higher-form symmetries familiar from relativistic quantum field theories, but instead to non-topological higher-form symmetries. We present concrete lattice models exhibiting this phenomenon. One particular model is an $\mathbb{R}$ generalization of the Kitaev honeycomb model featuring an $\mathbb{R}$ lattice 1-form symmetry. We show that its low-energy effective field theory is a gapless, non-relativistic theory with a non-topological $\mathbb{R}$ 1-form symmetry. In both the lattice model and the effective field theory, we demonstrate that the non-topological $\mathbb{R}$ 1-form symmetry is not robust against local perturbations. In contrast, we also study various modifications of the toric code and their low-energy effective field theories to demonstrate that the compact $\mathbb{Z}_2$ lattice 1-form symmetry does become topological at low energies unless the Hamiltonian is fine-tuned. Along the way, we clarify the rules for constructing low-energy effective field theories in the presence of multiple superselection sectors. Finally, we argue on general grounds that non-compact higher-form symmetries (such as $\mathbb{R}$ and $\mathbb{Z}$ 1-form symmetries) in lattice systems generically remain non-topological at low energies, whereas compact higher-form symmetries (such as $\mathbb{Z}_{n}$ and $U(1)$ 1-form symmetries) generically become topological.

We initiate the precision study of boosted jet substructure using energy correlators, applying this framework to hadronic Higgs decays. We demonstrate that the two-body decay of the Higgs manifests as a distinct angular peak at $θ\sim \arccos(1-2/γ^2)$ for Lorentz boost factor $γ$. We show that infrared scales, such as the dead-cone effect and confinement transition, are also resolved within the boosted distribution. Precision analytic studies of boosted jet substructure may enable precision electroweak studies and open new avenues for new physics searches.

Gapped two-dimensional gauge theories with massless fermions generically have rich vacuum structures consisting of many degenerate vacua related by the action of topological line operators. The algebra of such operators has been used to calculate ratios of vacuum expectation values of local operators and to predict nontrivial particle-soliton degeneracies. In this paper, we use recently-developed tensor network methods to study several examples of such theories via their Hamiltonian lattice descriptions. Our lattice results agree with all previously-made predictions. Furthermore, we identify the lattice strong-coupling states that can be adiabatically continued to the degenerate vacua in the continuum limit. We conjecture a procedure, referred to as a lattice decay rule, for how this identification works in general. This rule allows us to compute the continuum vacuum degeneracy by studying the lattice Hamiltonian in the strong-coupling limit.

We present cosmological parameters measurements from the full combination of DESI DR1 galaxy clustering data described with large-scale structure effective field theory. By incorporating additional datasets (photometric galaxies and CMB lensing cross-correlations) and extending the bispectrum likelihood to smaller scales using a consistent one-loop theory computation, we achieve substantial gains in constraining power relative to previous analyses. Combining with the latest DESI baryon acoustic oscillation data and using cosmic microwave background (CMB) priors on the power spectrum tilt and baryon density, we obtain tight constraints on the $Λ$CDM model, finding the Hubble constant $H_0=69.08\pm 0.37~\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$, the matter density fraction $Ω_m=0.2973\pm 0.0050$, and the mass fluctuation amplitude $σ_8 = 0.815\pm 0.016$ (or the lensing parameter $S_8\equivσ_8\sqrt{Ω_m/0.3}=0.811\pm 0.016$), corresponding to $0.6\%$, $1.7\%$, and $2\%$ precision respectively. Adding the Pantheon+ supernova sample (SNe), we find a preference of $2.6σ$ for the $w_0w_a$ dynamical dark energy model from low-redshift data alone, which increases to $2.8σ$ when exchanging the SNe with Planck CMB data. Combining full-shape data with BAO, CMB, and SNe likelihoods, we improve the dark energy figure-of-merit by $18\%$ and bound the sum of the neutrino masses to $M_ν<0.057$ eV in $Λ$CDM and $M_ν<0.095$ eV in the $w_0w_a$ dynamical dark energy model (both at 95% CL). This represents an improvement of $25\%$ over the background expansion constraints and the strongest bound on neutrino masses in $w_0w_a$CDM to date. Our results suggest that the preference for the normal ordering of neutrino mass states holds regardless of the cosmological background model, and is robust in light of tensions between cosmological datasets.

Primordial black holes (PBHs) are theorized to form from the collapse of overdensities in the very early Universe. PBHs in the asteroid-mass range $10^{17} \, {\rm g}\lesssim M \lesssim 10^{23} \, {\rm g}$ could serve as all or most of the dark matter today, but are particularly difficult to detect due to their modest rates of Hawking emission and sub-micron Schwarzschild radii. We consider whether the steep gradients of a PBH’s gravitational field could generate tidal forces strong enough to disrupt atoms and nuclei. Such phenomena may yield new observables that could uniquely distinguish a PBH from a macroscopic object of the same mass. We first consider the gravitational ionization of ambient neutral hydrogen and evaluate prospects for detecting photon radiation from the recombination of ionized atoms. During the present epoch, this effect would be swamped by Hawking radiation — which would itself be difficult to detect for PBHs at the upper end of the asteroid-mass window. We then consider the gravitational ionization and heating of neutral hydrogen immediately following recombination at $z\simeq1090$, and identify a broad class of PBH distributions with typical mass $5\times10^{21}\,{\rm g}\lesssim M \lesssim 10^{23}\, {\rm g}$ within which gravitational interactions would have been the dominant form of energy deposition to the medium. We also identify conditions under which tidal forces from a transiting PBH could overcome the strong nuclear force, either by dissociating deuterons, which would be relevant during big bang nucleosynthesis (BBN), or by inducing fission of heavy nuclei. We find that gravitational dissociation of deuterons dominates photodissociation rates due to Hawking radiation for PBHs with masses $10^{14}\,{\rm g}\lesssim M \lesssim 10^{16}\,{\rm g}$. We additionally identify the phenomenon of gravitationally induced fission of heavy nuclei via tidal deformation.

We investigate the sensitivity of the Electron-Ion Collider (EIC) to invisible final states in coherent exclusive electroproduction. The characteristic signal is a forward proton with reduced energy and little additional detector activity. Using the excellent particle detection capabilities and kinematics reconstruction at the EIC, we argue that backgrounds can be strongly suppressed. While our analysis applies to various states, we specifically focus on pseudoscalar particles: (i) neutral mesons ($π^0,η^{(\prime)}$), whose invisible Standard Model decays are extremely suppressed, and (ii) gluon-coupled axion-like particles (ALPs) decaying invisibly to a dark sector. Depending on the meson species and the achievable background rejection, the EIC could strengthen existing bounds on invisible decays of pseudoscalar mesons by up to four orders of magnitude, probing branching ratios as small as ${\rm BR}(η^{(\prime)}\to{\rm inv})\sim 10^{-8}$. In addition, the EIC would directly probe invisibly decaying ALPs with the couplings up to $f_a\sim 10^5\,\text{GeV}$ and masses in the range $0.1$-$2\,\text{GeV}$.

We develop a quadratic-in-Riemann worldline action for a Kerr black hole at infinite spin orders by matching to a proposed tree-level Kerr Compton amplitude, originally obtained from higher-spin QFT considerations. A worldline action is an effective theory, and as such the tree-level matching needs to be corrected by loop effects, including UV counter terms, renormalization, and higher-order matching to general relativity. However, we anticipate that many features of the Wilson coefficients of the proposed tree-level action will remain unchanged even after a loop-level matching. While the worldline action is given in closed form, it contains an infinite number of quadratic-in-Riemann operators $R^2$, even for the same-helicity sector. We argue that in the same-helicity sector the $R^2$ operators have no intrinsic meaning, as they merely remove unwanted terms produced by the linear-in-Riemann operators, which are well-established in the literature. The opposite-helicity sector is somewhat more complicated, it contains both $R^2$ operators that removes unwanted terms, and $R^2$ operators that add new needed terms to the Compton amplitude. We discuss and classify all independent $R^2$ operators that can feature in the worldline action.

Gapless quantum phases can become distinct when internal symmetries are enforced, in analogy with gapped symmetry-protected topological (SPT) phases. However, this distinction does not always lead to protected edge modes, raising the question of how the bulk-boundary correspondence is generalized to gapless cases. We propose that the spatial interface between gapless phases — rather than their boundaries — provides a more robust fingerprint. We show that whenever two 1+1d conformal field theories (CFTs) differ in symmetry charge assignments of local operators or twisted sectors, any symmetry-preserving spatial interface between the theories must flow to a non-invertible defect. We illustrate this general result for different versions of the Ising CFT with $\mathbb{Z}_2 \times \mathbb{Z}_2^T$ symmetry, obtaining a complete classification of allowed conformal interfaces. When the Ising CFTs differ by nonlocal operator charges, the interface hosts 0+1d symmetry-breaking phases with finite-size splittings scaling as $1/L^3$, as well as continuous phase transitions between them. For general gapless phases differing by an SPT entangler, the interfaces between them can be mapped to conformal defects with a certain defect ‘t Hooft anomaly. This classification also gives implications for higher-dimensional examples, including symmetry-enriched variants of the 2+1d Ising CFT. Our results establish a physical indicator for symmetry-enriched criticality through symmetry-protected interfaces, giving a new handle on the interplay between topology and gapless phases.

It was recently shown that black holes decohere any quantum superpositions in their vicinity. This decoherence is mediated by soft radiation through the horizon, and can be understood as the result of the fact that quantum states in the exterior source distinguishable states of long-range fields in the interior. To study this phenomenon and others, we extend Tomita-Takesaki theory to accommodate states of soft radiation such as arise in the electromagnetic and gravitational memory effects, and provide a general framework for computing the distinguishability of general coherent states. Applying these tools, we use the methods of unambiguous state discrimination and approximate quantum error correction to prove some new relations regarding the distinguishability of quantum states, and the quantum information content of soft radiation, and thereby show that a black hole (or any horizon) decoheres its environment as though its interior were full of optimal observers.

In this paper, we study pole-skipping in non-maximally quantum chaotic systems. Using Rindler conformal field theories and the large-$q$ SYK chain as illustrative examples, we argue that the pole-skipping points of few-body operators organize into trajectories in the complex frequency-momentum plane, with the leading trajectory encoding the quantum Lyapunov exponent. We further propose that these trajectories admit a natural interpretation as Regge trajectories of stringy excitations in a dual stringy black hole geometry. From this perspective, pole-skipping for an individual operator can be viewed as tracking the stringy horizon through the response of a single excitation. Our results suggest that pole-skipping reflects intrinsic properties of quantum chaotic systems and may be deeply connected to the structure of horizons in the stringy regime.