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Physical theories have a limited regime of validity and hence must be accompanied by a breakdown diagnostic to establish when they cease to be valid as parameters are varied. For perturbative theories, estimates of the first neglected order offer valuable guidance, but one is often interested in sharp bounds beyond which perturbation theory necessarily fails. In particle physics, it is common to employ the bounds on partial waves imposed by unitarity as such a diagnostic. Unfortunately, these bounds don't extend to curved spacetime, where scattering experiments are challenging to define. Here, we propose to use the growth of entanglement in momentum space as a breakdown diagnostic for perturbation theory in general field theories. This diagnostic can be readily used in cosmological spacetimes and does not require any flat spacetime limit. More in detail, we consider the so-called purity of the reduced density operator constructed by tracing out all but one of the Fourier modes in an effective theory and we present a diagrammatic technique to compute it perturbatively. Constraints on the theory's regime of validity are then derived when the perturbative purity violates its unitarity bounds. In flat spacetime, we compare these purity bounds to those from partial waves. We find general qualitative agreement but with remarkable differences: purity bounds can be sometimes weaker, but other times they exist when no partial wave bounds exist. We then derive purity bounds for scalar field theories in de Sitter spacetime for a variety of interactions that appear in inflationary models. Importantly, our bounds make no reference to time evolution and in de Sitter they depend exclusively on scale-invariant ratios of the physical kinematics., Comment: 51 pages, 7 figures

Numerical methods based on matrix product states (MPSs) are currently the de facto standard for calculating the ground state properties of (quasi-)one-dimensional quantum many-body systems. While the properties of the low-lying excitations in such systems are often studied in this MPS framework through _dynamics_ by means of time-evolution simulations, we can also look at their _statics_ by directly calculating eigenstates corresponding to these excitations. The so-called MPS excitation ansatz is a powerful method for finding such eigenstates with a single-particle character in the thermodynamic limit. Although this excitation ansatz has been used quite extensively, a general method for calculating expectation values for these states is lacking in the literature: we aim to fill this gap by presenting a recursive algorithm to calculate arbitrary observables expressed as matrix product operators. This method concisely encapsulates existing methods for -- as well as extensions to -- the excitation ansatz, such as excitations with a larger spatial support and multi-particle excitations, and is robust to handle further innovations. We demonstrate the versatility of our method by studying the low-lying excitations in the spin-1 Heisenberg chain and the one-dimensional Hubbard model, looking at how the excitations converge in the former, while in the latter, we present a novel method of targeting single-particle excitations inside of a continuum by minimizing the energy _variance_ rather than the energy itself. We hope that this technique will foster further advancements with the excitation ansatz.

In this note we establish a 1-to-1 correspondence between the class of generalized quadrangles with ovoids and the class of balanced incomplete block designs that posses a non-triangular local resolution system and have the appropriate parameters. We present a non-triangular local resolution system for a difference family BIBD construction of Sprott.

The one-dimensional spin-$s$ ${\rm SU}(2)$ ferromagnetic Heisenberg model, as a paradigmatic example for spontaneous symmetry breaking (SSB) with type-B Goldstone modes (GMs), is expected to exhibit an abstract fractal underlying the ground state subspace. This intrinsic abstract fractal is here revealed from a systematic investigation into the entanglement entropy for a linear combination of factorized (unentangled) ground states on a fractal decomposable into a set of the Cantor sets. The entanglement entropy scales logarithmically with the block size, with the prefactor being half the fractal dimension of a fractal, as long as the norm for the linear combination scales as the square root of the number of the self-similar building blocks kept at each step $k$ for a fractal, under an assumption that the maximum absolute value of the coefficients in the linear combination is chosen to be around one, and the coefficients in the linear combination are almost constants within the building blocks. Actually, the set of the fractal dimensions for all the Cantor sets forms a {\it dense} subset in the interval $[0,1]$. As a consequence, the ground state subspace is separated into a disjoint union of countably infinitely many regions, each of which is labeled by a decomposable fractal. Hence, the interpretation of the prefactor as half the fractal dimension is valid for any support beyond a fractal, which in turn leads to the identification of the fractal dimension with the number of type-B GMs for the orthonormal basis states. Our argument may be extended to any quantum many-body systems undergoing SSB with type-B GMs., Comment: 23 pages, 8 figures

Dynamical quantum phase transitions (DQPTs) have been established as a rigorous framework for investigating far-from-equilibrium quantum many-body criticality. Although initially thought to be trivially connected to an order parameter flipping sign, a certain kind of \textit{anomalous} DQPTs have been discovered that exhibit no direct connection to the order parameter and have been shown to arise in the presence of confinement. Here, we show in two paradigmatic models how the onset time of anomalous DQPTs is directly connected, through a power law, to the meson mass in the confined regime of a global symmetry-broken phase. This relation becomes more prominent the closer the initial parameters are to the equilibrium quantum critical point, where a relativistic quantum field theory emerges. Our findings draw a direct connection between mesons and anomalous DQPTs, highlighting the power of the latter to classify exotic far-from-equilibrium criticality., Comment: $7+2$ pages, $4+4$ figures

Steady-state currents generically occur both in systems with continuous translation invariance and in nonequilibrium settings with particle drift. In either case, thermal fluctuations advected by the current act as a source of noise for slower hydrodynamic modes. This noise is unconventional, since it is highly correlated along spacetime rays. We argue that, in quasi-one-dimensional geometries, the correlated noise from ballistic modes generically gives rise to anomalous full counting statistics (FCS) for diffusively spreading charges. We present numerical evidence for anomalous FCS in two settings: (1) a two-component continuum fluid, and (2) the totally asymmetric exclusion process (TASEP) initialized in a nonequilibrium state., Comment: 5 pages, 4 figures

We construct an ensemble of two-dimensional nonintegrable quantum circuits that are chaotic but have a conserved particle current, and thus a finite Drude weight. The long-wavelength hydrodynamics of such systems is given by the incompressible Navier-Stokes equations. By analyzing circuit-to-circuit fluctuations in the ensemble we argue that these are negligible, so the circuit-averaged value of transport coefficients like the viscosity is also (in the long-time limit) the value in a typical circuit. The circuit-averaged transport coefficients can be mapped onto a classical irreversible Markov process. Therefore, remarkably, our construction allows us to efficiently compute the viscosity of a family of strongly interacting chaotic two-dimensional quantum systems., Comment: 4+epsilon pages, 3 figures; 8 pages supplemental material

Decarbonizing the building stock in cold countries by replacing fossil fuel boilers with heat pumps is expected to drastically increase electricity demand. While heating flexibility could reduce the impact of additional demand from heat pumps on the power system, characterizing the national spatial distribution of heating flexibility capacity to incorporate into sophisticated power system models is challenging. This paper introduces a novel method for quantifying at large scale and high spatial resolution the energy capacity and duration of heating flexibility in existing building stock based on historical heating consumption and temperature data. This method can reflect the geographic diversity of the national building stock in sophisticated power system models. The proposed heating consumption-based method was tested in Britain using national residential gas data. The results demonstrate the potential of this approach to characterize the heterogeneous distribution of heating flexibility capacity at the national scale. Assuming a 3$^\circ$C temperature flexibility window, a total thermal energy storage capacity of 500 GWh$_{th}$ is identified in the British housing stock. For an illustrative cold weather COP value of 2.5, this thermal energy storage capacity is equivalent to 200 GWh of electricity storage. Regarding heating flexibility duration, gas-heated homes have a median of 5.9 heat-free hours for 20th percentile regional daily winter temperatures from 2010 to 2022. However, extreme cold days nearly halve flexibility duration to a median of 3.6 heat-free hours. These high spatial resolution energy capacity and self-discharge parameters can account for geographic diversity at the national scale and provide a new data-based layer of information for sophisticated power system models to support energy transition.

We study $\mathbb{R}_{\textrm{an},\exp}$-definable functions $f:\mathbb{R}\to \mathbb{R}$ that take integer values at all sufficiently large positive integers. If $|f(x)|= O\big(2^{(1+10^{-5})x}\big)$, then we find polynomials $P_1, P_2$ such that $f(x)=P_1(x)+P_2(x)2^x$ for all sufficiently large $x$. Our result parallels classical theorems of P\'olya and Selberg for entire functions and generalizes Wilkie's classification for the case of $|f(x)|= O(C^x)$, for some $C<2$. Let $k\in \mathbb{N}$ and $\gamma_k=\sum_{j=1}^{k} 1/j$. Extending Wilkie's theorem in a separate direction, we show that if $f$ is $k$-$\textit{concordant}$ and $|f(x)|= O(C^{x})$, for some $C

Exact matrix product state representations for a type of scale-invariant states are presented, which describe highly degenerate ground states arising from spontaneous symmetry breaking with type-B Goldstone modes in one-dimensional quantum many-body systems. As a possible application, such a representation offers a convenient but powerful means for evaluating the norms of highly degenerate ground states. This in turn allows us to perform a universal finite system-size scaling analysis of the entanglement entropy. Moreover, this approach vividly explains why the entanglement entropy does not depend on what types of the boundary conditions are adopted, either periodic boundary conditions or open boundary conditions. Illustrative examples include the ${\rm SU}(2)$ spin-$s$ Heisenberg ferromagnetic model, the ${\rm SU}(2s+1)$ ferromagnetic model, and the staggered ${\rm SU}(3)$ spin-1 ferromagnetic biquadratic model., Comment: 12 pages, 5 figures, 3 tables

Quantum many-body scarring (QMBS) has emerged as an intriguing paradigm of weak ergodicity breaking in nonintegrable quantum many-body models, particularly lattice gauge theories (LGTs) in $1+1$ spacetime dimensions. However, an open question is whether QMBS exists in higher-dimensional LGTs with dynamical matter. Given that nonergodic dynamics in $d{=}1$ spatial dimension tend to vanish in $d{>}1$, it is important to probe this question. Using matrix product state techniques for both finite and infinite systems, we show that QMBS occurs in the $2{+}1$D $\mathrm{U}(1)$ quantum link model (QLM), as evidenced in persistent coherent oscillations in local observables, a marked slowdown in the growth of the bipartite entanglement entropy, and revivals in the fidelity. Interestingly, we see that QMBS is more robust when the matter degrees of freedom are bosonic rather than fermionic. Our results further shed light on the intimate connection between gauge invariance and QMBS, and highlight the persistence of scarring in higher spatial dimensions. Our findings can be tested in near-term analog and digital quantum simulators, and we demonstrate their accessibility on a recently proposed cold-atom analog quantum simulator., Comment: $7+2$ pages, $4+4$ figures. v2 includes longer evolution times and updated references

Spontaneous symmetry breaking (SSB) with type-B Goldstone modes is investigated in the macroscopically degenerate phase for a quantum spin-1 many-body system with competing dimer and trimer interactions. The SSB involves three distinct patterns. The first occurs at the dimer point, with the pattern from staggered ${\rm SU}(3)$ to ${\rm U}(1)\times{\rm U}(1)$. The second occurs at the trimer point, with the pattern from uniform ${\rm SU}(3)$ to ${\rm U}(1)\times{\rm U}(1)$. The third occurs in the dimer-trimer regime, with the pattern from uniform ${\rm SU}(2)$ to ${\rm U}(1)$. The number of type-B Goldstone modes is thus two, two and one for the three patterns, respectively. The ground state degeneracies arising from the three patterns are exponential with the system size, which may be recognized as sequences of integers relevant to self-similar logarithmic spirals. This in turn is attributed to the presence of an emergent symmetry operation tailored to a specific degenerate ground state. As a consequence, the residual entropy is non-zero, which measures the disorder present in a unit cell of highly degenerate ground state generated from a generalized highest weight state. An exact Schmidt decomposition exists for the highly degenerate ground states, thus exposing the self-similarities underlying an abstract fractal, described by the fractal dimension. The latter is extracted from performing a universal finite system-size scaling analysis of the entanglement entropy, which is identical to the number of type-B Goldstone modes. The model under investigation thus accommodates an exotic scale invariant quantum state of matter., Comment: 14 pages, 3 figures, 2 tables

In a recent Letter [Phys. Rev. Lett. 130, 246402 (2023)], Gleis, Li, and von Delft present an algorithm for expanding the bond dimension of a Matrix Product State wave function, giving accuracy similar to 2-site DMRG, but computationally more efficient, closer to the performance of 1-site DMRG. The Controlled Bond Expansion (CBE) algorithm uses the Hamiltonian projected onto two sites, and then further projected onto the two-site tangent space, to extract a set of $k$ vectors that are used to expand the basis between the two sites. CBE achieves this with a complicated sequence of five singular value decompositions (SVDs), in order to project onto the 2-site tangent space and reduce the bond dimension of the tensor network such that the contraction can be done in time $O(dwD^3)$. In this Comment, we show that (1) the projection onto the 2-site tangent space is unnecessary, and is generally not helpful; (2) the sequence of 5 SVDs can be replaced by a single $QR$ decomposition (optionally with one SVD as well), making use of the randomized SVD (RSVD) with high accuracy and significantly improved efficiency, scaling as $O(dwkD^2)$ i.e., the most expensive operations are only quadratic in the bond dimension $D$ and linear in the number of expansion vectors $k$; (3) several statements about the variational properties of the CBE algorithm are incorrect, and the variational properties are essentially identical to existing algorithms including 2-site DMRG and single-site subspace expansion (3S); (4) a similar RSVD approach can be applied to the 3S algorithm, which leads to many advantages over CBE, especially in systems with long range interactions. We also make some comments on the benchmarking MPS algorithms, and the overall computational efficiency with respect to the accuracy of the calculation., Comment: Added some references; added appendix C

The squeezed limit of the primordial curvature bispectrum is an extremely sensitive probe of new physics and encodes information about additional fields active during inflation such as their masses and spins. In the conventional setup, additional fields are stable with a positive mass squared, and hence induce a decreasing signal in the squeezed limit, making a detection challenging. Here we consider a scalar field that is temporarily unstable by virtue of a transient tachyonic mass, and we construct models in which it is embedded consistently within inflation. Assuming IR-finite couplings between the tachyon and the inflaton, we find an exchange bispectrum with an enhanced long-short scale coupling that grows in the squeezed limit parametrically faster than local non-Gaussianity. Our approximately scale-invariant signal can be thought of as a cosmological tachyon collider. In a sizeable region of parameter space, the leading constraint on our signal comes from the cross correlation of $\mu$-type spectral distortions and temperature anisotropies of the microwave background, whereas temperature and polarization bispectra are less sensitive probes. By including anisotropic spectral distortions in the analysis, future experiments such as CMB-S4 will further reduce the allowed parameter space., Comment: 31 pages, 5 figures

Dirac fluids - interacting systems obeying particle-hole symmetry and Lorentz invariance - are among the simplest hydrodynamic systems; they have also been studied as effective descriptions of transport in strongly interacting Dirac semimetals. Direct experimental signatures of the Dirac fluid are elusive, as its charge transport is diffusive as in conventional metals. In this paper we point out a striking consequence of fluctuating relativistic hydrodynamics: the full counting statistics (FCS) of charge transport is highly non-gaussian. We predict the exact asymptotic form of the FCS, which generalizes a result previously derived for certain interacting integrable systems. A consequence is that, starting from quasi-one dimensional nonequilibrium initial conditions, charge noise in the hydrodynamic regime is parametrically enhanced relative to that in conventional diffusive metals., Comment: 5 pages, 2 figures

Heterogeneous mechanical dyskinesis during acute myocardial ischaemia is thought to contribute to arrhythmogenic alterations to cardiac electrophysiology. Various forms of mechano-electric coupling (MEC) mechanisms have been suggested to contribute to these changes, with two primary mechanisms being: (1) myofilament-dependent calcium release events, and (2) the activation of stretch-activated currents (SACs). In this computational investigation, we assessed the collective impact of these processes on mechanically-induced alternans that create an arrhythmogenic substrate during acute ischaemia. To appraise the potential involvement of MEC in ischaemia-induced arrhythmias, we developed a coupled model of ventricular myocyte electrophysiology and contraction including SACs and stretch-dependent calcium buffering and release. The model, reflecting observed electrophysiological changes during ischaemia, was exposed to a series of stretch protocols that replicated both physiological and pathological mechanical conditions. Pathologically realistic myofiber stretch variations revealed calcium sensitivity changes dependent on myofilament, leading to alterations in cytosolic calcium concentrations. Under calcium overload conditions, these changes resulted in electrical alternans. The study implies that strain impacts cellular electrophysiology through myofilament calcium release and SAC opening in ventricular mechano-electrical models, parameterised to available data. This supports experimental evidence suggesting that both calcium-driven instability via MEC and SAC-induced effects contribute to electrical alternans in acute ischaemia., Comment: 20 pages; 8 figures; original paper

Bayesian Additive Regression Trees (BART) has gained widespread popularity, prompting the development of various extensions for different applications. However, limited attention has been given to analyzing dependent data. Based on a general correlated error assumption and an innovative dummy representation, we introduces a novel extension of BART, called Correlated BART (CBART), designed to handle correlated errors. By integrating CBART with a Gaussian process (GP), we propose the CBART-GP model, in which the CBART and GP components are loosely coupled, allowing them to be estimated and applied independently. CBART captures the covariate mean function E[y|x]=f(x), while the Gaussian process models the dependency structure in the response $y$. We also developed a computationally efficient approach, named two-stage analysis of variance with weighted residuals, for the estimation of CBART-GP. Simulation studies demonstrate the superiority of CBART-GP over other models, and a real-world application illustrates its practical applicability.

Solar home systems (SHS) provide low-cost electricity access for rural off-grid communities. Batteries are a crucial part of the system, however they are often the first point of failure due to shorter lifetimes. Using field data, this work models the degradation of lead-acid batteries for different SHS use-cases, finding the dominant ageing mechanisms in each case. Corrosion is the dominant ageing mechanisms in all cases apart from the highest use case. This is caused by extended time at high state of charge (SOC) and hence high voltage. A new voltage control scheme is proposed for one of the use cases dominated by corrosion, whereby the number of days between full recharges varies depending on the degradation mechanisms the battery experiences. Simulating the new voltage control scheme yields a 25% increase in battery lifetime whilst ensuring no loss of load to the user.

Systems in the built environment continuously emit time series data about resource usage (e.g., energy and water), embedded electrical generation/storage, status of equipment, patterns of building occupancy, and readings from IoT sensors. This presents opportunities for new analytics and supervisory control applications that help reduce greenhouse gas emissions due to energy demand, if the barrier of data heterogeneity can be overcome. Semantic models of buildings -- representing structure, integrated equipment, and the many internal connections -- can help achieve interoperable data re-use by describing overall context, in addition to metadata. In this paper, we describe the Data Clearing House (DCH), a semantic building platform that hosts sensor data, building models, and analytics applications. This fulfills the key phases in the lifecycle of semantic building data, which includes: cost-effective ingestion of Building Management System (BMS), IoT, metering and meteorological time series data from a wide range of open and proprietary systems; importing and validating semantic models of sites and buildings using the Brick Schema; interacting with a discovery API via a high-level domain-specific query language; and deploying applications to modelled buildings. Having onboarded multiple buildings belonging to our own organisation and external partners, we are able to comment on the challenges to success of this approach. As an example use-case of the semantic building platform, we describe a measurement and verification (M&V) application implementing the 'whole facility' (Option C) method of the International Performance Measurement and Verification Protocol (IPMVP) for evaluating electrical metering data. This compares energy consumption between nominated baseline and analysis time periods, to quantify the energy savings achieved after implementing an intervention on a site., Comment: 13 pages, 4 figures. Accepted for presentation at Climate Smart Engineering 2023 (CSE23)

In this paper, we describe an experimental investigation into the effect of passivation layer thickness on heat dissipation between a quartz substrate and liquid helium. We have observed that by depositing SiN from 0 to 240 nm, the Kapitza resistance increases by 0.0365 m^2.K/W per nanometer more than for an unpassivated semiconductor. We hypothesize that this increase in Kapitza resistance represents an additional barrier to the cooling of semiconductor devices in liquid helium., Comment: 7 pages

The Q&U Bolometric Interferometer for Cosmology (QUBIC) is the first bolometric interferometer designed to measure the primordial B-mode polarization of the Cosmic Microwave Background (CMB). Bolometric interferometry is a novel technique that combines the sensitivity of bolometric detectors with the control of systematic effects that is typical of interferometry, both key features in the quest for the faint signal of the primordial B-modes. A unique feature is the so-called "spectral imaging", i.e., the ability to recover the sky signal in several sub-bands within the physical band during data analysis. This feature provides an in-band spectral resolution of \Delta{\nu}/{\nu} \sim 0.04 that is unattainable by a traditional imager. This is a key tool for controlling the Galactic foregrounds contamination. In this paper, we describe the principles of bolometric interferometry, the current status of the QUBIC experiment and future prospects., Comment: To appear in Proc. of the mm Universe 2023 conference, Grenoble (France), June 2023, published by F. Mayet et al. (Eds), EPJ Web of conferences, EDP Sciences