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Dynamical quantum systems both driven by unitary evolutions and monitored through measurements have proved to be fertile ground for exploring new dynamical quantum matters. While the entanglement structure and symmetry properties of monitored systems have been intensively studied, the role of topology in monitored dynamics is much less explored. In this work, we investigate novel topological phenomena in the monitored dynamics through the lens of free-fermion systems. Free-fermion monitored dynamics were previously shown to be unified with the Anderson localization problem under the Altland-Zirnbauer symmetry classification. Guided by this unification, we identify the topological area-law-entangled phases in the former setting through the topological classification of disordered insulators and superconductors in the latter. As examples, we focus on 1+1D free-fermion monitored dynamics in two symmetry classes, DIII and A. We construct quantum circuit models to study different topological area-law phases and their domain walls in the respective symmetry classes. We find that the domain wall between topologically distinct area-law phases hosts dynamical topological modes whose entanglement is protected from being quenched by the measurements in the monitored dynamics. We demonstrate how to manipulate these topological modes by programming the domain-wall dynamics. In particular, for topological modes in class DIII, which behave as unmeasured Majorana modes, we devise a protocol to braid them and study the entanglement generated in the braiding process., Comment: 7 pages, 4 figures in the main text

This study is to evaluate the impact of different normal lung volumes on radiation pneumonitis (RP) prediction in patients with locally advanced non-small-cell-lung-cancer (LA-NSCLC) receiving radiotherapy. Three dosimetric variables (V20, V5, and mean lung dose (MLD)) were calculated using treatment plans from 442 patients with LA-NSCLC enrolled in NRG Oncology RTOG 0617. Three lung volumes were defined based on the treatment plan: total lung excluding gross-tumor-target (TL-GTV), total lung excluding clinical-target-volume (TL-CTV), and total lung excluding planning-target-volume (TL-PTV). Binary classification was used for clinical endpoints: no-RP2 (N = 377) for patients with acute RP grades 0 or 1, and RP2 (N = 65) for patients with acute grades 2 or higher. The impact of lung volume definition on RP prediction was investigated with statistical analyses and two supervised machine learning (ML) models: logistic regression (LR) and random forest (RF). Balanced data was generated for comparison to prediction obtained with the imbalanced data. Areas under curve (AUCs) and the Shapley Additive eXplanations (SHAP) were used to examine ML performance and explain the contribution of each feature to the prediction, respectively. Statistical analyses revealed that V20 and MLD were associated with RP but no difference among different lung volume definitions. Mean AUC values from 10-fold cross validation using imbalanced and balanced datasets were < 0.6 except that RF from the latter dataset yielded AUC values > 0.7. SHAP values indicated that MLD and V20 were the most prominent features in RP prediction. In all assessments, no difference among various volume definitions was found. Different lung volumes showed insignificant impact on RP prediction. Low AUC values suggest limited effectiveness of these dosimetric variables in predicting RP risk and more powerful predictors are needed., Comment: 13 page, 6 figures

Charge-conserving dynamics of non-interacting fermions monitored by local charge measurements have been shown to possess in 1D space only an area-law-entangled phase, with no measurement-induced phase transition (MIPT). This phenomenon was elegantly explained by an effective replica field theory given by a non-linear sigma model featuring large replica symmetries. In this work, we focus on the charge-conserving monitored dynamics of interacting fermions in 1D. Using a unifying replica Keldysh field theory, we show that more dynamical phases and transitions emerge owing to the reduction of replica symmetry when interactions are introduced. The reduced symmetry combines a discrete replica permutation symmetry and the charge-conservation within each replica. The former and its spontaneous breaking govern the MIPT between area-law and volume-law entanglement scalings, which can be described by a separatrix in the weak-coupling renormalization group flow. The replica-resolved charge conservation dictates the Kosterlitz-Thouless type ``charge-sharpening" transition between the two kinds of dynamics where the global charge information is either hidden or reconstructible from the local measurements. All the relevant phases and transitions can be understood within the same unifying field theory. Additionally, this field theory provides insight into why the charge-sharpening transition should only happen in the presence of volume-law entanglement scaling. Moreover, we show that our field theory, despite being constructed using the Keldysh formalism, is equivalent to a statistical mechanics model that describes the (replicated) time-evolution of the system's density matrix mapped to a doubled Hilbert space under the Choi-Jamiolkowski isomorphism. This equivalence is the result of the trivialization of the fermion distribution function by measurement-induced heating effects., Comment: 30 pages, 4 figures

A quantum-inspired optimization approach is proposed to study the portfolio optimization aimed at selecting an optimal mix of assets based on the risk-return trade-off to achieve the desired goal in investment. By integrating conventional approaches with quantum-inspired methods for penalty coefficient estimation, this approach enables faster and accurate solutions to portfolio optimization which is validated through experiments using a real-world dataset of quarterly financial data spanning over ten-year period. In addition, the proposed preprocessing method of two-stage search further enhances the effectiveness of our approach, showing the ability to improve computational efficiency while maintaining solution accuracy through appropriate setting of parameters. This research contributes to the growing body of literature on quantum-inspired techniques in finance, demonstrating its potential as a useful tool for asset allocation and portfolio management.

Fibonacci string-net condensate, a complex topological state that supports non-Abelian anyon excitations, holds promise for fault-tolerant universal quantum computation. However, its realization by a static-lattice Hamiltonian has remained elusive due to the inherent high-order interactions demanded. Here, we introduce a scalable dynamical string-net preparation (DSNP) approach, suitable even for near-term quantum processors, that can dynamically prepare the state through reconfigurable graphs. DSNP enables the creation and manipulation of the Fibonacci string-net condensate (Fib-SNC). Using a superconducting quantum processor, we couple the DSNP approach with a composite error-mitigation strategy on deep circuits to successfully create, measure, and braid Fibonacci anyons in two spatial dimensions (2D) demonstrating their potential for universal quantum computation. To this end, we measure anyon charges for two species of anyons associated with the doubled topological quantum field theory underlying Fid-SNC, with an average experimental accuracy of 94%. We validate that a scalable 2D braiding operation on a logical qubit encoded on three anyons yields the golden ratio $\phi$ with 98% average accuracy and 8% measurement uncertainty. We further sample the Fib-SNC wavefunction to estimate the chromatic polynomial at $\phi+2$ for various graphs. Given the established computational hardness of the chromatic polynomial, the wavefunction amplitude is classically hard to evaluate. Our results establish the first proof of principle that scalable DSNP can open doors to fault-tolerant universal quantum computation and to classically-hard problems., Comment: 4 pages and 4 figures with Supplemental Materials (47 pages, 18 Figures)

The quantum anomaly of a global symmetry is known to strongly constrain the allowed low-energy physics in a clean and isolated quantum system. However, the effect of quantum anomalies in disordered systems is much less understood, especially when the global symmetry is only preserved on average by the disorder. In this work, we focus on disordered systems with both average and exact symmetries $A\times K$, where the exact symmetry $K$ is respected in every disorder configuration, and the average $A$ is only preserved on average by the disorder ensemble. When there is a mixed quantum anomaly between the average and exact symmetries, we argue that the mixed state representing the ensemble of disordered ground states cannot be featureless. While disordered mixed states smoothly connected to the anomaly-compatible phases in clean limit are certainly allowed, we also found disordered phases that have no clean-limit counterparts, including the glassy states with strong-to-weak symmetry breaking, and average topological orders for certain anomalies. We construct solvable lattice models to demonstrate each of these possibilities. We also provide a field-theoretic argument to provide a criterion for whether a given average-exact mixed anomaly admits a compatible average topological order., Comment: 22 pages, 5 figures

In this paper, we propose a fully nonlinear mechanism for obtaining scalarized black holes in Einstein-scalar-Gauss-Bonnet (EsGB) gravity which is beyond the spontaneous scalarization. Introducing three coupling functions $f(\varphi)$ satisfying $f''(0) = 0$, we find that Schwarzschild black hole is linearly stable against scalar perturbation, whereas it is unstable against nonlinear scalar perturbation if the coupling function includes term higher than $\varphi^6$. For a specific choice of coupling function $f(\varphi)=\alpha(\varphi^4-\beta\varphi^6)$, we obtain new black holes with scalar hair in the EsGB gravity. In this case, the coupling parameter $\alpha$ plays a major role in making different nonlinear scalarized black holes, while the other parameter $\beta$ plays a supplementary role. Furthermore, we study thermodynamic aspects of these scalarized black holes and prove the first-law of thermodynamics., Comment: 14 pages, 6 figures

We propose a "minimal" fractional topological insulator (mFTI), motivated by the recent experimental report on the signatures of FTI at total filling factor $\nu_{\rm tot} = 3$ in a transition metal dichalcogenide moir\'{e} system. The observed FTI at $\nu_{\rm tot} = 3$ is likely given by a topological state living in a pair of half-filled conjugate Chern bands with Chern numbers $C=\pm 1$ on top of another pair of fully-filled conjugate Chern bands. We propose the mFTI as a strong candidate topological state in the half-filled conjugate Chern bands. The mFTI is characterized by the following features: (1) It is a fully gapped topological order (TO) with 16 Abelian anyons if the electron is considered trivial (32 including electrons); (2) the minimally-charged anyon carries electric charge $e^\ast = e/2$, together with the fractional quantum spin-Hall conductivity, implying the robustness of the mFTI's gapless edge state whenever time-reversal symmetry and charge conversation are present; (3) the mFTI is "minimal" in the sense that it has the smallest total quantum dimension (a metric for the TO's complexity) within all the TOs that can potentially be realized at the same electron filling and with the same Hall transports; the mFTI is also the unique one that respects time-reversal symmetry. (4) the mFTI is the common descendant of multiple valley-decoupled "product TOs" with larger quantum dimensions. It can also be viewed as the result of gauging multiple symmetry-protected topological states. Similar mFTIs can be constructed for a pair of $1/q$-filled conjugate Chern bands. We classify the mFTIs via the stability of the gapless interfaces between them., Comment: 10 + 2 pages, 2 figures; An additional appendix provides proof of the uniqueness of the mFTI and the classification of the minimal TOs in the half-filled conjugate Chern bands. The generalization of the mFTI to $1/q$-filled conjugate Chern band is added to the main text

Pulsar halos (also termed 'TeV halo') are a new class of $\gamma$-ray sources in Galaxy, which manifest as extended $\gamma$-ray emission around middle-age pulsars, as discovered around the Geminga pulsar, the Monogem pulsar and PSR~J0622+3749 by HAWC and LHAASO. A consensus has been reached that the TeV emission comes from the inverse Compton scattering of escaping electrons/positrons from the PWN off soft background radiation field, while the particle transport mechanism in the halo is still in dispute. Currently, there are mainly three interpretations, namely, the isotropic, suppressed diffusion model; the isotropic, unsuppressed diffusion model with considering ballistic propagation of newly injected particles; the anisotropic diffusion model. While the predicted gamma-ray surface brightness profiles by all three models can be more or less consistent with the observation, the implication of the three models for cosmic-ray transport mechanisms and the properties of interstellar magnetic field are quite different. In this study, we calculate the anticipated X-ray emission of pulsar halos under the three models. We show that the synchrotron radiation of these escaping electrons can produce a corresponding X-ray halo around the pulsar, and the expected surface brightness profiles are distinct in three models. We suggest that sensitive X-ray detectors of a large field of view (such as eROSITA and Einstein Probe) with a reasonably long exposure time are crucial to understand the formation mechanism of pulsar halos and serve as a probe to the properties of the interstellar turbulence., Comment: 7 figures

Quantum error correction (QEC) codes protect quantum information from errors due to decoherence. Many of them also serve as prototypical models for exotic topological quantum matters. Investigating the behavior of the QEC codes under decoherence sheds light on not only the codes' robustness against errors but also new out-of-equilibrium quantum phases driven by decoherence. The phase transitions, including the error threshold, of the decohered QEC codes can be probed by the systems' R\'enyi entropies $S_R$ with different R\'enyi indices $R$. In this paper, we study the general construction of the statistical models that characterize the R\'enyi entropies of QEC codes decohered by Pauli noise. We show that these statistical models can be organized into a "tapestry" woven by rich duality relations among them. For Calderbank-Shor-Steane (CSS) codes with bit-flip and phase-flip errors, we show that each R\'enyi entropy is captured by a pair of dual statistical models with randomness. For $R=2,3,\infty$, there are additional dualities that map between the two error types, relating the critical bit-flip and phase-flip error rates of the decoherence-induced phase transitions in the CSS codes. For CSS codes with an "$em$ symmetry" between the $X$-type and the $Z$-type stabilizers, the dualities with $R=2,3,\infty$ become self-dualities with super-universal self-dual error rates. These self-dualities strongly constrain the phase transitions of the code signaled by $S_{R=2,3,\infty}$. For general stabilizer codes decohered by generic Pauli noise, we also construct the statistical models that characterize the systems' entropies and obtain general duality relations between Pauli noise with different error rates., Comment: 22+16 pages, 11 figures

Recent experimental observations of the fractional quantum anomalous Hall effect in spin/valley polarized moir\'{e} systems call for a more expansive theoretical exploration of strongly correlated physics in partially filled topological bands. In this work we study a state that we refer to as the conjugate-composite Fermi liquid (cCFL), which arises when a pair of Chern bands with opposite Chern numbers are both half-filled. We demonstrate that the cCFL is the parent state of various interesting phenomena. As an example, we demonstrate that with the existence of an inplane spin order, the cCFL could be driven into a quantum bad metal phase, in the sense that it is a metallic phase whose zero temperature longitudinal resistivity is finite, but far greater than the Mott-Ioffe-Regal limit, i.e. $\rho^e_{xx} \gg h/e^2$. The bad metal phase is also accompanied with a new Wiedemann-Franz law, meaning the thermal conductivity is proportional to the electrical resistivity rather than conductivity. Other proximate phases of the cCFL such as superconductivity and a chiral spin liquid phase can occur when the composite fermions (CF) form the inter-valley CF-exciton condensate., Comment: 8 pages

Motivated by the recent experimental breakthrough on the observation of the fractional quantum anomalous Hall (FQAH) effects in semiconductor and graphene moir\'{e} materials, we explore the rich physics associated with the coexistence of FQAH effect and the charge density wave (CDW) order that spontaneously breaks the translation symmetry. We refer to a state with both properties as "FQAH-crystal". We show that the interplay between FQAH effect and CDW can lead to a rich phase diagram including multiple topological phases and topological quantum phase transitions at the same moir\'e filling. In particular, we demonstrate the possibility of direct quantum phase transitions from a FQAH-crystal with Hall conductivity $\sigma_H = - 2/3$ to a trivial CDW insulator with $\sigma_H = 0$, and more interestingly, to a QAH-crystal with $\sigma_H= -1$., Comment: 9 pages

We prove that if there exists a $C$-subsolution to a constant coefficients strictly $\Upsilon$-stable general inverse $\sigma_k$ equation, then there exists a unique solution. As a consequence, this result covers all the analytical results of the classical strictly $\Upsilon$-stable general inverse $\sigma_k$ equations, for example, the complex Monge--Amp\`ere equation, the complex Hessian equation, the J-equation, the deformed Hermitian--Yang--Mills equation, etc. Hence, we confirm an analytical conjecture by Collins--Jacob--Yau [arXiv:1508.01934] of the solvability of the deformed Hermitian--Yang--Mills equation. Their conjecture states that the existence of a $C$-subsolution to a supercritical phase deformed Hermitian--Yang--Mills equation gives the solvability., Comment: 45 pages, 3 figures

In recent years a consensus has gradually been reached that the previously proposed deconfined quantum critical point (DQCP) for spin-1/2 systems, an archetypal example of quantum phase transition beyond the classic Landau's paradigm, actually does not correspond to a true unitary conformal field theory (CFT). In this work we carefully investigate another type of quantum phase transition supposedly beyond the similar classic paradigm, the so called ``symmetric mass generation" (SMG) transition proposed in recent years. We employ the sharp diagnosis including the scaling of disorder operator and R\'enyi entanglement entropy in large-scale lattice model quantum Monte Carlo simulations. Our results strongly suggest that the SMG transition is indeed an unconventional quantum phase transition and it should correspond to a true $(2+1)d$ unitary CFT., Comment: 16 pages, 12 figures

We consider Einstein-Weyl gravity with a minimally coupled scalar field in four dimensional spacetime. By using the Minimal Geometric Deformation (MGD) approach, we split the highly nonlinear coupled field equations into two subsystems that describing the background geometry and scalar field source, respectively. Regarding the Schwarzschild-AdS metric as a background geometry, we derive analytical approximate solutions of scalar field and deformation metric functions with Homotopy Analysis Method (HAM), providing their analytical approximations to fourth order. Moreover, we discuss the accuracy of the analytical approximations, showing they are sufficiently accurate throughout the exterior spacetime.

The high-energy diffuse gamma-ray emission and neutrino emission are expected from the Galactic plane, generated by hadronuclear interactions between cosmic rays (CR) and interstellar medium (ISM). Therefore, measurements of these diffuse emissions will provide important clues on the origin and nature of Galactic CRs. Comparing the latest observations of LHAASO and IceCube on the diffuse Galactic gamma-ray and neutrino emissions respectively, we suggest that the diffuse gamma-ray emission at multi-TeV energies contains a considerable contribution of a leptonic component. By modelling the gamma-ray halos powered by middle-aged pulsars in our Galaxy with taking into account the magnetic field configuration and the interstellar radiation field in the Galaxy, we demonstrate that the collective contribution of pulsar halos can account for the excess in the measured diffuse gamma-ray emission with respect to the predicted flux from CR-ISM interactions. The resulting one-dimensional profile along the Galactic longitude is also consistent with the observation., Comment: 28 pages, 13 figures; published in Nature Astronomy

The ideal honeycomb lattice, featuring sublattice and SU(2) spin rotation symmetries, is a fundamental model for investigating quantum matters with topology and correlations. With the rise of the moir\'e-based design of model systems, realizing a tunable and symmetric honeycomb lattice system with a narrow bandwidth can open access to new phases and insights. We propose the ABBA-stacked twisted double bilayer WSe$_2$ as a realistic and tunable platform for reaching this goal. Adjusting the twist angle allows the bandwidth and the ratio between hopping parameters of different ranges to be tuned. Moreover, the system's small bandwidth and spin rotation symmetry enable effective control of the electronic structure through an in-plane magnetic field. We construct an extended Hubbard model for the system to demonstrate this tunability and explore possible ordered phases using the Hartree-Fock approximation. We find that at a hole filling of $\nu = 2$ (two holes per moir\'e unit cell), an in-plane magnetic field of a few Tesla can ``dope" the system from a semimetal to a metal. Interactions then drive an instability towards a canted antiferromagnetic insulator ground state. Additionally, we observe a competing insulating phase with sublattice charge polarization. Finally, we discuss the experimental signatures of these novel insulating phases., Comment: 10 pages, 4 figures

We aim to address the following question: if we start with a quantum state with a spontaneously broken higher-form symmetry, what is the fate of the system under weak local quantum measurements? We demonstrate that under certain conditions, a phase transition can be driven by weak measurements, which suppresses the spontaneous breaking of the 1-form symmetry and weakens the 1-form symmetry charge fluctuation. We analyze the nature of the transitions employing the tool of duality, and we demonstrate that some of the transitions driven by weak measurement enjoy a line of fixed points with self-duality., Comment: 14 pages, 2 figure

Defect engineering is promising to tailor the physical properties of two-dimensional (2D) semiconductors for function-oriented electronics and optoelectronics. Compared with the extensively studied 2D binary materials, the origin of defects and their influence on physical properties of 2D ternary semiconductors have not been clarified. In this work, we thoroughly studied the effect of defects on the electronic structure and optical properties of few-layer hexagonal Znln2S4 via versatile spectroscopic tools in combination with theoretical calculations. It has been demonstrated that the Zn-In anti-structural defects induce the formation of a series of donor and acceptor levels inside the bandgap, leading to rich recombination paths for defect emission and extrinsic absorption. Impressively, the emission of donor-acceptor pair (DAP) in Znln2S4 can be significantly tailored by electrostatic gating due to efficient tunability of Fermi level (Ef). Furthermore, the layer-dependent dipole orientation of defect emission in Znln2S4 was directly revealed by back focal plane (BFP) imagining, where it presents obviously in-plane dipole orientation within a dozen layers thickness of Znln2S4. These unique features of defects in Znln2S4 including extrinsic absorption, rich recombination paths, gate tunability and in-plane dipole orientation will definitely benefit to the advanced orientation-functional optoelectronic applications.

HESS J1809-193 is an extended TeV $\gamma$-ray source and the origin of its $\gamma$-ray emission remains ambiguous. Pulsar wind nebula (PWN) of PSR J1809-1917 laying inside the extended $\gamma$-ray emission is a possible candidate. Powered by the central pulsar, ultrarelativistic electrons in PWN can produce radio to X-ray emission through synchrotron and $\gamma$-ray emission by inverse Compton (IC) scattering. To check whether this PWN is the counterpart of HESS J1809-193, we analyzed Chandra X-ray radial intensity profile and the spectral index profile of this PWN. We then adopt a one-zone isotropic diffusion model to fit the keV and the TeV data. We find diffuse nonthermal X-ray emission extending beyond PWN, which is likely an X-ray halo radiated by escaping electron/positron pairs from the PWN. A relatively strong magnetic field of $\sim 20\,\mu$G is required to explain the spatial evolution of the X-ray spectrum (i.e., the significant softening of the spectrum with increasing distance from the pulsar), which, however, would suppress the IC radiation of pairs. Our result implies that a hadronic component may be needed to explain HESS J1809-193., Comment: 20 pages, 8 figures, accepted by APJ. Comments are welcome

We study a 2D measurement-only random circuit motivated by the Bacon-Shor error correcting code. We find a rich phase diagram as one varies the relative probabilities of measuring nearest neighbor Pauli XX and ZZ check operators. In the Bacon-Shor code, these checks commute with a group of stabilizer and logical operators, which therefore represent conserved quantities. Described as a subsystem symmetry, these conservation laws lead to a continuous phase transition between an X-basis and Z-basis spin glass order. The two phases are separated by a critical point where the entanglement entropy between two halves of an L X L system scales as L ln L, a logarithmic violation of the area law. We generalize to a model where the check operators break the subsystem symmetries (and the Bacon-Shor code structure). In tension with established heuristics, we find that the phase transition is replaced by a smooth crossover, and the X- and Z-basis spin glass orders spatially coexist. Additionally, if we approach the line of subsystem symmetries away from the critical point in the phase diagram, some spin glass order parameters jump discontinuously, Comment: 11 pages, 7 figures ; Minor revisions in response to referee comments and corrected typos

We address entanglement transitions in monitored random quantum circuits of non-interacting fermions, in particular, the question of whether Born-rule and forced measurements yield the same universality class. For a generic circuit with no symmetry other than fermion parity, acting on a one-dimensional Majorana chain, we numerically obtain several critical exponents, providing clear evidence that the two transitions with Born-rule and forced measurements are in different universality classes. We provide a theoretical understanding for our numerical results by identifying the underlying statistical mechanics model which follows from the general correspondence, established in Jian et al., Phys. Rev. B 106, 134206, between non-unitary circuits of non-interacting fermions and the ten-fold Altland-Zirnbauer (AZ) symmetry classes. The AZ class is the same for Born-rule and forced measurements of the circuits. For the circuit under consideration (in AZ class DIII), the statistical mechanics model describing the transition is the principal chiral non-linear sigma model whose field variable is an ${\rm SO}(n)$ matrix in the replica limits $n\to 0$ and $n\to 1$ for forced and Born-rule measurements, respectively. The former is in an Anderson localization universality class while we show that the latter is in a novel universality class beyond Anderson localization. Both entanglement transitions are driven by proliferation of $\mathbb{Z}_2$ topological defects. The different replica limits account for the difference in the universality classes. Furthermore, we provide numerical and symmetry-based arguments that the entanglement transition in the previously-studied monitored circuit of Majorana fermions based on the loop model with crossings, a highly fine-tuned circuit, belongs to a universality class different from both transitions in the generic circuits discussed in this paper., Comment: 16+5 pages, 6 figures

The entanglement entropy (EE) of the ground state of a one-dimensional Hamiltonian at criticality has a universal logarithmic scaling with a prefactor given by the central charge $c$ of the underlying 1+1d conformal field theory. When the system is probed by measurements, the entanglement in the critical ground state is inevitably affected due to wavefunction collapse. In this paper, we study the effect of weak measurements on the entanglement scaling in the ground state of the one-dimensional critical transverse-field Ising model. For the measurements of the spins along their transverse spin axis, we identify interesting post-measurement states associated with spatially uniform measurement outcomes. The EE in these states still satisfies the logarithmic scaling but with an alternative prefactor given by the effective central charge $c_{\text{eff}}$. We derive the analytical expression of $c_{\text{eff}}$ as a function of the measurement strength. Using numerical simulations, we show that for the EE averaged over all post-measurement states based on their Born-rule probabilities, the numerically extracted effective central charge appears to be independent of the measurement strength, contrary to the usual expectation that local and non-overlapping measurements reduce the entanglement in the system. We also examine the behavior of the average EE under (biased) forced measurements where the measurement outcomes are sampled with a pre-determined probability distribution without inter-site correlations. In particular, we find an optimal probability distribution that can serve as a mean-field approximation to the Born-rule probabilities and lead to the same $c_{\text{eff}}$ behavior. The effects of the measurements along the longitudinal spin axis and the post-measurement correlation functions are also discussed., Comment: 13+10 pages, 9+5 figures

Decoherence inevitably happens when a quantum state is exposed to its environment, which can affect quantum critical points (QCP) in a nontrivial way. As was pointed out in recent literature on $(1+1)d$ conformal field theory (CFT), the effect of weak measurement can be mathematically mapped to the problem of boundary CFT. In this work, we focus on the $(2+1)d$ QCPs, whose boundary and defect effects have attracted enormous theoretical and numerical interests very recently. We focus on decoherence caused by weak measurements with and without post-selecting the measurement outcomes. Our main results are: (1) for an O(N) Wilson-Fisher QCP under weak measurement with post-selection, an observer would in general observe two different types of boundary/defect criticality with very different behaviors from the well-known Wilson-Fisher fixed points; in particular, it is possible to observe the recently proposed exotic "extraordinary-log" correlation. (2) An extra quantum phase transition can be driven by decoherence, if we consider quantities nonlinear with the decohered density matrix, such as the Renyi entropy. We demonstrate the connection between this transition to the information-theoretic transition driven by an error in the toric code model. (3) When there is no post-selection, though correlation functions between local operators remain the same as the undecohered pure state, nonlocal operators such as the "disorder operator" would have qualitatively distinct behaviors; and we also show that the decoherence can lead to confinement., Comment: 18 pages, 5 figures (Accepted to PRX Quantum)

We prove that if a level set of a degree $n$ general inverse $\sigma_k$ equation $f(\lambda_1, \cdots, \lambda_n) = \lambda_1 \cdots \lambda_n - \sum_{k = 0}^{n-1} c_k \sigma_k(\lambda) = 0$ is contained in $q + \Gamma_n$ for some $q \in \mathbb{R}^n$, where $c_k$ are real numbers not necessary to be non-negative and $\Gamma_n$ is the positive orthant, then this level set is convex. As an application, this result justifies the convexity of the level set of all general inverse $\sigma_k$ type equations, for example, the Monge--Amp\`ere equation, the Hessian equation, the J-equation, the deformed Hermitian--Yang--Mills equation, the special Lagrangian equation, etc. Moreover, we find a numerical condition to verify whether a level set of a general inverse $\sigma_k$ equation is contained in $q + \Gamma_n$ for some $q \in \mathbb{R}^n$, which is a way to determine the convexity of this level set., Comment: 53 pages, 3 figures; v3 fixes a mistake in the proof of the convexity theorem

The semiclassical description of two-dimensional ($2d$) metals based on the quasiparticle picture suggests that there is a universal threshold of the resistivity: the resistivity of a $2d$ metal is bounded by the so called Mott-Ioffe-Regal (MIR) limit, which is at the order of $h/e^2$. If a system remains metallic while its resistivity is beyond the MIR limit, it is referred to as a "bad metal", which challenges our theoretical understanding as the very notion of quasiparticles is invalidated. The description of the system becomes even more challenging when there is also strong correlation between the electrons. Partly motivated by the recent experiment on transition metal dichalcogenides moir\'{e} heterostructure, we seek for understanding of strongly correlated bad metals whose resistivity far exceeds the MIR limit. For some strongly correlated bad metals, though a microscopic description based on electron quasiparticles fails, a tractable dual description based on the "vortex of charge" is still possible. We construct a concrete example of such strongly correlated bad metals where vortices are fermions with a Fermi surface, and we demonstrate that its resistivity can be exceptionally large at zero temperature. And when extra charge $\delta n_e$ is doped into the system away from half-filling, a small Drude weight proportional to $(\delta n_e)^2$ will emerge in the optical conductivity ., Comment: 9 pages

Pulsar wind nebula (PWN) Boomerang and the associated supernova remnant (SNR) G106.3+2.7 are among candidates for the ultra-high-energy (UHE) gamma-ray counterparts published by LHAASO. Although the centroid of the extended source, LHAASO J2226+6057, deviates from the pulsar's position by about $0.3^\circ$, the source partially covers the PWN. Therefore, we cannot totally exclude the possibility that a part of the UHE emission comes from the PWN. Previous studies mainly focus on whether the SNR is a PeVatron, while neglecting the energetic PWN. Here, we explore the possibility of the Boomerang Nebula being a PeVatron candidate by studying its X-ray radiation. By modelling the diffusion of relativistic electrons injected in the PWN, we fit the radial profiles of the X-ray surface brightness and the photon index. The solution with a magnetic field $B=140\mu$G can well reproduce the observed profiles and implies a severe suppression of IC scattering of electrons. Therefore, a proton component need be introduced to account for the UHE emission, in light of recent LHAASO's measurement on Crab Nebula, if future observations reveal part of the UHE emission originating from the PWN. In this sense, Boomerang Nebula would be a hadronic PeVatron., Comment: 15 pages, 5 figures, 5 tables; Invited contribution to Special Issue of Universe "Advances in Astrophysics and Cosmology in China - in Memory of Prof. Tan Lu"

In this study, the gravitational decoupling approach via extended geometric deformation is utilized to generate analytical black hole solutions owing to its simplicity and effectiveness. Considering the external fields surrounding Schwarzschild AdS black holes, we derive hairy black hole solutions in asymptotic AdS spacetime, satisfying the strong and dominant energy conditions. Moreover, we find that if the black hole spacetime is a fluid system, the fluid under each of these conditions is anisotropic., Comment: 22 pages, 1 figures

Supersymmetry has been studied at a linear level between normal modes of metamaterials described by rigidity matrices and non-interacting quantum Hamiltonians. The connection between classical and quantum was made through the matrices involved in each problem. Recently, insight into the behavior of nonlinear mechanical systems was found by defining topological indices via the Poincar\'e-Hopf index. It turns out, because of the mathematical similarity, this topological index shows a way to approach supersymmetric quantum theory from classical mechanics. Using this mathematical similarity, we establish a topological connection between isostatic mechanical metamaterials and supersymmetric quantum systems, such as electrons coupled to phonons in metals and superconductors. Firstly, we define $Q_{net}$ for an isostatic mechanical system that counts the minimum number of zero-energy configurations. Secondly, we write a supersymmetric Hamiltonian that describes a metal or a superconductor interacting with anharmonic phonons. This Hamiltonian has a Witten index, a topological invariant that captures the balance of bosonic and fermionic zero-energy states. We are able to connect these two systems by showing that $Q_{net}=W$ under very general conditions. Our result shows that (1) classical metamaterials can be used to study the topology of interacting quantum systems with aid of supersymmetry, and (2) with fine-tuning between anharmonicity of phonons and couplings among Majorana fermions and phonons, it is possible to realize such a supersymmetric quantum system that shares the same topology as classical mechanical systems.

We present a general algebraic framework for gauging a 0-form compact, connected Lie group symmetry in (2+1)d topological phases. Starting from a symmetry fractionalization pattern of the Lie group $G$, we first extend $G$ to a larger symmetry group $\tilde{G}$, such that there is no fractionalization with respect to $\tilde{G}$ in the topological phase, and the effect of gauging $\tilde{G}$ is to tensor the original theory with a $\tilde{G}$ Chern-Simons theory. To restore the desired gauge symmetry, one then has to gauge an appropriate one-form symmetry (or, condensing certain Abelian anyons) to obtain the final result. Studying the consistency of the gauging procedure leads to compatibility conditions between the symmetry fractionalization pattern and the Hall conductance. When the gauging can not be consistently done (i.e. the compatibility conditions can not be satisfied), the symmetry $G$ with the fractionalization pattern has an 't Hooft anomaly and we present a general method to determine the (3+1)d topological term for the anomaly. We provide many examples, including projective simple Lie groups and unitary groups to illustrate our approach., Comment: 31+5 pages

Two-dimensional semiconductor moir\'e materials have emerged as a highly controllable platform to simulate and explore quantum condensed matter. Compared to real solids, electrons in semiconductor moir\'e materials are less strongly attracted to the moir\'e lattice sites, making the nonlocal contributions to the magnetic interactions as important as the Anderson super-exchange. It provides a unique platform to study the effects of competing magnetic interactions. Here, we report the observation of strongly frustrated magnetic interactions in a Wigner-Mott insulating state at 2/3 filling of the moir\'e lattice in angle-aligned WSe2/WS2 heterobilayers. Magneto-optical measurements show that the net exchange interaction is antiferromagnetic for filling factors below 1 with a strong suppression at 2/3 filling. The suppression is lifted upon screening of the long-range Coulomb interactions and melting of the Wigner-Mott insulator by a nearby metallic gate. The results can be qualitatively captured by a honeycomb-lattice spin model with an antiferromagnetic nearest-neighbor coupling and a ferromagnetic second-neighbor coupling. Our study establishes semiconductor moir\'e materials as a model system for the lattice-spin physics and frustrated magnetism.