The string hypothesis of Bethe roots is a cornerstone in the thermodynamic analysis of quantum integrable systems, since it connects root configurations with physical quantities such as the ground-state energy, surface energy and excitation spectra. For integrable models with $U(1)$ symmetry, this connection is well established. When the $U(1)$ symmetry is broken by generic non-diagonal boundary fields, however, the off-diagonal Bethe Ansatz leads to an inhomogeneous $T\text{--}Q$ relation whose Bethe roots have highly nontrivial distributions. This raises two fundamental questions: whether the zero roots and the ODBA Bethe roots still possess regular and classifiable structures in the large-size limit, and whether such structures can be used to extract physical quantities. In this work, we address these two questions for the isotropic Heisenberg spin chain with non-diagonal open boundaries. By combining tensor-network algorithms with Bethe-Ansatz techniques, we determine the zero-root and Bethe-root configurations associated with the $\Lambda\text{--}\theta$ relation and the inhomogeneous Bethe Ansatz equations for large system sizes, up to $N\simeq 60$ and $100$. We find that, despite the absence of $U(1)$ symmetry, the roots exhibit well-organized patterns. The zero roots form bulk strings, boundary strings, additional roots, and a helical half-spinon, while the ODBA Bethe roots split into four geometric classes: regular roots, line roots, arc roots and paired-line roots. We further show that these root structures are not merely numerical patterns, but contain direct thermodynamic information. In particular, the geometric structure of the ODBA Bethe roots allows us to derive analytic expressions for the surface energy and elementary excitation energies. This demonstrates that the full ODBA Bethe-root configuration can serve as a thermodynamically meaningful object in a $U(1)$-symmetry-broken open spin chain. A comparison with the $t\text{--}W$ scheme shows that the zero-root description has a simpler topology, while the ODBA Bethe roots provide a direct route to physical quantities. Our results therefore provide a framework for studying root structures and thermodynamic properties in quantum integrable models without $U(1)$ symmetry.
Topological edge states (TESs) in valley photonic crystals (VPCs) hold immense potential for robust, backscattering-immune wave routing. Conventionally, the realization of these states relies strictly on opening a real bandgap, within which intrinsic material dissipation is universally viewed as detrimental to topological protection. Here, we demonstrate a loss-driven approach to topological transport by engineering a non-Hermitian VPC with spatially selective dissipation. We reveal that, rather than degrading transport, the introduction of targeted macroscopic loss drives a pronounced splitting of the imaginary eigenvalues, thereby opening a broad imaginary bandgap. This spectral transition explicitly detaches the TESs from the hybridized bulk continuum in the complex-frequency plane. To elucidate this loss-induced bulk-boundary decoupling, we introduce a subspace decomposition framework that projects the system into an asymptotically Hermitian boundary subspace. Within this framework, we analytically confirm the effective restoration of spatial orthogonality and tight mode confinement. Consequently, these decoupled TESs sustain highly efficient transmission and exhibit extraordinary robustness against structural imperfections and inhomogeneous dissipation. Ultimately, our findings recast non-Hermitian dissipation from a fundamental limitation into a powerful, actively engineered degree of freedom for advanced topological photonics.
The thermal partition function, Z Z , of a CFT_d C F T d on S^{d-1} S d − 1 is parameterized by the inverse temperature \beta β along with \lfloor d/2\rfloor ⌊ d / 2 ⌋ angular velocities \omega_i ω i . In this paper, we investigate the behaviour of this partition function when n n of the \omega_i ω i are scaled to unity (the largest allowed value) at fixed values of the other (\lfloor d/2\rfloor-n) ( ⌊ d / 2 ⌋ − n ) angular velocities. We argue that \ln Z ln Z develops a simple pole in (1-\omega_i) ( 1 − ω i ) for each \omega_i ω i that is scaled to unity. The residue of this product of poles is a theory-dependent (so non-universal) function of \beta β and the fixed angular velocities. The inverse Laplace transformation of this partition function constrains the functional form of the field theory entropy as a function of charges in a limit in which angular momenta and the twist are scaled as follows. While n n special angular momenta J_1\ldots J_n J 1 … J n are scaled to infinity, the twist and the other angular momenta – collectively denoted x_i x i – are also taken to infinity but at the slower rate that ensures that the scaled charges x_i/(J_1 J_2 \ldots J_n)^{\frac{1}{n+1}} x i / ( J 1 J 2 … J n ) 1 n + 1 are held fixed. In this limit, we demonstrate that the scaled entropy S/(J_1 J_2 \ldots J_n)^{\frac{1}{n+1}} S / ( J 1 J 2 … J n ) 1 n + 1 depends only on the \lfloor d/2\rfloor-n+1 ⌊ d / 2 ⌋ − n + 1 scaled charges defined above (the precise form of this dependence is non-universal). We verify our predictions (and compute all non-universal functions) in the case of free scalar theories (which show surprisingly rich behaviour) as well as large N N , strongly coupled {\cal N}=4 Yang-Mills theory. The last theory is analyzed in the bulk via the AdS/CFT correspondence. In the scaling limit described above, its phase diagram displays sharp phase transitions between black hole, grey galaxy, and thermal gas phases.
We discuss Euclidean geometries in AdS$_3$ whose Lorentzian slicing gives rise to closed baby Universes with a spatial geometry given by genus $g≥ 2$ surfaces. Our setup only involves a two-dimensional holographic CFT defined on a higher genus Riemann surface and thus provides a well-posed alternative to shell states whose microscopic duals are less well understood. We find that geometries giving rise to baby Universes are always subdominant. It follows that the baby Universe does not provide a semi-classical description of the state since it is encoded in an exponentially suppressed part of the wave function. We then apply a prescription developed in [A. Belin, SciPost Phys. 20, 183 (2026)] to make the baby Universe geometry the leading saddle. In the process, the CFT state becomes mixed, in agreement with the qualitative gravitational picture. We show that the fluctuations in the baby Universe are small, even at fixed central charge, making the geometry reliable in the semi-classical limit. Finally, we discuss the interpretation of this mixed state in pure gravity from the perspective of the Virasoro TQFT.
We derive two-loop scattering amplitudes for bottom-quark pair production in association with a Higgs boson at the LHC, focusing on terms proportional to the top-quark Yukawa coupling. We treat the bottom quark as a massless parton and employ both the leading-colour and heavy-top-quark approximations. The finite remainder of the two-loop amplitude is expressed in terms of one-mass pentagon functions, and the corresponding rational coefficients are reconstructed analytically from evaluations over finite fields. The scattering processes considered in this work also constitute a subset of Higgs+2-jet production at the LHC in the heavy-top-quark approximation.
We explore the sum over topologies in $\mathrm{AdS}_3$ quantum gravity and its relationship with the statistical interpretation of the boundary theory. We formulate a statistical version of the conformal bootstrap that systematizes the universal statistical properties of high-energy CFT$_2$ data. We identify a series of surgery moves on bulk manifolds that precisely reflect the requirements of typicality and crossing symmetry of the boundary ensemble. These surgery moves generate a large number of bulk manifolds that have to be included in any reasonable definition of the gravitational path integral. We show that this procedure generates only on-shell (hyperbolic) manifolds, although it does not produce all of them. These proofs rely on structure theorems of 3-manifolds, which non-trivially interact with the requirements of the statistical boundary ensemble. We illustrate the application of this procedure with many examples, such as Euclidean wormholes, twisted $I$-bundles and handlebody-knots. Our findings reveal a large space of possible choices of which manifolds can be included in the gravitational path integral, reflecting a wide range of possible statistical ensembles consistent with crossing symmetry and typicality.
We study perturbations induced by a light particle scattering off a Schwarzschild black hole. Exploiting recent results for the wave propagation in this geometry, we derive the fields that this process induces on the horizon to leading order in the post-Minkowskian (PM) regime, when the light probe is far from the black hole. We then use these results to calculate the fluxes of energy and angular momentum that enter the black hole. We consider the effects due to gravitational, electromagnetic and scalar radiation, finding agreement with recent computations of the absorbed energy, while the absorbed angular momentum provides a new PM result.
In the case of high-fluence implantations, the approximation that every new incoming particle interacts with a pristine substrate material no longer holds. Dynamical changes to the substrate can induce different phenomena, one of which is self-sputtering. Self-sputtering occurs when incoming ions remove previously implanted ions from the implantation substrate. This phenomenon is significant in target production for nuclear structure studies and medical radionuclide separation, where self-sputtering limits can be reached during isotope implantation. Self-sputtering can be modeled using TRIDYN simulations in order to guide implantations. This work explores the ability of TRIDYN to give order-of-magnitude estimates for the onset of self-sputtering for these nuclear physics applications. This is performed through the implantation of Yb in Zn and Al, relevant to both fundamental and medical nuclear physics research. Our findings indicate that TRIDYN predicts general dependencies reasonably well. However, it is important to carefully consider input parameters and validity of the TRIDYN simulations. Copyright M. Heines et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.
It has recently been conjectured [S. Kim et al., J. High Energy Phys. 11, 024 (2023)] that the end point of the rotational superradiant instability of black holes in $AdS_4$ is a Grey Galaxy: an $\omega=1$ black hole sitting at the centre of $AdS_4$, surrounded by a large disk of rapidly rotating gravitons and other bulk fields. In this paper we study Grey Galaxies in $AdS_5$. In this case, the rotational group is of rank 2, and so has two distinct angular velocities $\omega_1$ and $\omega_2$. We demonstrate that $AdS_5$ hosts two qualitatively distinct Grey Galaxy phases: the first with either $\omega_1≈ 1$ or $\omega_2≈ 1$, and the second with both angular velocities $≈ 1$. We use these results to present a conjecture for a part of the phase diagram of ${\cal N}=4$ Yang-Mills (as a function of energy and the two angular momenta) that displays several phase transitions between regular black holes and various Grey Galaxy phases. We present an explicit gravitational construction of the phases in which $\omega_1$ and $\omega_2$ are both parametrically close to unity, and demonstrate that the corresponding boundary stress tensor is the sum of two pieces. The first is the stress tensor of the central black hole. The second - the contribution of the bulk gas - has the spatial distribution of the stress tensor of an equilibrated boundary conformal fluid, rotating at the given angular speeds $\omega_i$. We also briefly comment on the structure of Grey Galaxies in $AdS_D$ for $D > 5$.
Uncertainty relations represent a foundational principle in quantum mechanics, imposing inherent limits on the precision with which mechanically conjugate variables such as position and momentum can be simultaneously determined. This work establishes analogous relations for thermodynamically conjugate variables — specifically, a classical intensive parameter $\theta$ and its corresponding extensive quantum operator $\hat{O}$ — in equilibrium states. We develop a framework to derive a rigorous thermodynamic uncertainty relation for such pairs, where the uncertainty of the classical parameter $\theta$ is quantified by its quantum Fisher information $\mathcal{F}_\theta$. The framework is based on an exact integral representation that relates $\mathcal{F}_{\theta}$ to the power spectral density of $\hat{O}$. Using this representation, we demonstrate how fundamental information-theoretic limits naturally emerge as thermodynamic constraints. This yields a tight thermodynamic uncertainty relation: $\Delta\theta\,\overline{\Delta O} ≥ k_\text{B}T$, where $\overline{\Delta O}\equiv -\text{Tr}[\hat{O}\partial_\theta\hat{\rho}]\,\Delta\theta$, and $T$ is the system temperature. The result establishes a fundamental precision limit for quantum sensing and metrology in thermal systems, directly connecting it to the thermodynamic properties of linear response and fluctuations.
Symmetry protected topological phases protected by crystalline symmetries and internal symmetries are shown to enjoy fascinating one-to-one correspondence in classification. Here we investigate the physics content behind the abstract correspondence in three or higher-dimensional systems. We show correspondence between anomalous boundary states, which provides a new way to explore the quantum anomaly of symmetry from its crystalline equivalent counterpart. We show such a correspondence directly in two scenarios, including the anomalous symmetry-enriched topological orders (SET) and critical boundary states. (1) First of all, for the surface SET correspondence, we demonstrate it by considering examples involving time-reversal symmetry and mirror symmetry. We show that one 2D topological order can carry the time reversal anomaly as long as it can carry the mirror anomaly and vice versa, by directly establishing the mapping of the time reversal anomaly indicators and mirror anomaly indicators. Besides, we also consider other cases involving continuous symmetry, which leads us to introduce some new anomaly indicators for symmetry from its counterpart. (2) Furthermore, we also build up direct correspondence for (near) critical boundaries. In this perspective, we first consider the edge-corner correspondence between edge theory as 1+1D conformal field theory of internal fermionic SPT and the 0+1D corner modes of (higher-order) crystalline fermionic SPT. By viewing the corner modes on 1D boundary as perturbed CFT is crucial insight for the correspondence, but also help to discover the boundary theory of some intrinsically interacting fermionic SPT, whcih are challenging. Next, we discuss this correspondence bosonic systems, again taking topological phases protected by time reversal and mirror symmetry as examples, the direct correspondence of their (near) critical boundaries can be built up by coupled chain construction that was first proposed by Senthil and Fisher. The examples of critical boundary correspondence we consider in this paper can be understood in a unified framework that is related to hierarchy structure of topological O(n) nonlinear sigma model (NL sigma M), that generalizes the Haldane's derivation of O(3) sigma model from spin one-half system. To our best of knowledge, this hierarchy structure of the O(n) NL sigma M is first exposed, which inspires us to explore more interesting connection between different theories in the light of the boundary correspondence.
Estimating ground-state energies of quantum many-body systems is challenging due to the exponential growth of Hilbert space. Sample-based diagonalization (SBD) addresses this by projecting the Hamiltonian onto a subspace of selected basis configurations but works only for concentrated ground-state wave functions. We propose two neural network-enhanced SBD methods: sample-based neural diagonalization (SND) and adaptive-basis SND (AB-SND). Both leverage autoregressive neural networks for efficient sampling; AB-SND also optimizes a basis transformation to concentrate the wave function. We explore classically tractable single- and two-spin rotations, and more expressive unitaries implementable on quantum computers. On quantum Ising models, SND performs well for concentrated states, while AB-SND consistently outperforms SND and standard SBD in less concentrated regimes.
We introduce a new perspective on the connection between many-body physics and information theory. We study phase transitions in models with randomness, such as localization in disordered systems, or random quantum circuits with measurements. Utilizing information-based arguments regarding probability distribution differentiation, rigorous results for bounds on critical exponents in such phase transitions are obtained with minimal effort. This allows us to rigorously prove bounds which were previously only conjectured for dynamical critical exponents in localization transitions. In addition, we obtain new bounds on critical exponents in many-body Fock space localization transition and localization in Coulomb-interacting models. Somewhat surprisingly, our bounds are not obeyed by previous studies of these systems, indicating inconsistencies in previous results, which we discuss. Finally, we apply our method to measurement-induced phase transition in random quantum circuits, obtaining bounds transcending recent mapping to percolation problems.
We ask whether a measured Michel distribution, apparently in excellent agreement with the Standard Model interpretation of the ℓ_i →ℓ_j ν decay, could instead arise from a different invisible sector. Within a general low-energy effective field theory, we analyze lepton decays ℓ_i →ℓ_j + XX̅ for electrically neutral, color-singlet, mutually conjugate invisible pairs XX̅ of spin up to 2, allowing (pseudo)scalar, (axial)vector, and antisymmetric tensor interactions in the lepton current, focusing on the massless limit relevant for exact degeneracies. We formulate a criterion for indistinguishability based on the full set of measurable differential distributions. Under these assumptions, besides the obvious spin 1/2 case, there is a unique nontrivial solution: a massless complex scalar pair coupled through a purely left-handed vector current exactly reproduces the standard Michel pattern, including its extensions to daughter-lepton polarization and radiative channels. All other cases studied here are distinguishable, in particular because higher-spin invisible pairs produce additional kinematic prefactors. These results isolate the only nonstandard and nontrivial invisible sector that can remain hidden in Michel-type lepton decay measurements.
