Papers

The noncentrosymmetric superconductor NbReSi (Tc=6.5 K) is being actively explored for unconventional pairing that is allowed by its broken inversion symmetry. Despite broad experimental interest, what drives its superconductivity remains an open question. We show that the electronic states at the Fermi level are dominated by Nb and Re $d$-states. Vibrations of the same heavy-metal framework contribute more than 95% of the electron-phonon coupling, with the strongest coupling arising from the sublattice-selective breathing mode involving strongly bonded Re atoms. Harmonic Migdal-Eliashberg theory overestimates Tc by more than 60%. The zero-point anharmonic hardening of these modes reduces the coupling by 20%. The leading vertex correction becomes important as well despite low phonon energies due to the contribution of spatially localized Re-d orbitals to the electronic band structure near the Fermi level. Together, anharmonicity and vertex corrections bring the calculated Tc and superconducting gap into close agreement with experiment, establishing NbReSi as a moderately coupled, phonon-mediated superconductor whose quantitative description requires going beyond harmonic Migdal–Eliashberg theory.

We study the structural, thermophysical and dynamical properties of molten MgCl2 over a wide temperature range using Ab Initio Molecular Dynamics (AIMD) and molecular dynamics simulations based on machine-learning interaction potentials (MLIPs). MLIPs can achieve near-AIMD accuracy at a fraction of the computational cost, enabling simulations of larger systems and longer timescales. This opens up the possibility of studying the system under out-of-equilibrium conditions, which in turn allows for the calculation of physical properties, such as the thermal conductivity or viscosity, that cannot be obtained reliably for the typical time and length scales accessible to AIMD. We follow two complementary approaches to develop and evaluate the MLIPs. Firstly, we develop a Deep Potential (DP) from scratch using AIMD trajectories at different temperatures. Secondly, we also evaluate two out-of-the-box foundation models and a fine-tuned version of one of them. The fine-tuning is performed using configurations from the AIMD trajectories originally used to train the Deep Potential. We compare the predictions of the trained DP, the foundation models and AIMD simulations with the available experimental data and provide a comprehensive calculation of the most important physical quantities of molten MgCl2. We compute densities, radial and angular distribution functions, thermal conductivity, heat capacity, viscosity and diffusion coefficients over the 1000-1600 K temperature range. This range is relevant to important technological applications such as thermal energy storage, generation IV nuclear reactors and concentrated solar power systems. Finally, we briefly review the accuracy and performance of the different MLIPs versions used throughout the work.

The mechanical properties of network-based materials have been extensively studied under qui- escent conditions, yet their self-assembly in nature occurs mainly in a mechanically stressed envi- ronment. Here, we show that the stiffness of collagen networks, one of the main building blocks of the mammalian extracellular matrix, can be tuned by applying shear stress during gelation, which first strains and aligns the material, then triggers a dramatic irreversible increase in the elastic modulus. This stiffening is anchored by maintaining the stress until the gel is fully matured. Using particle-based simulations, we show that the underlying microscopic mechanism is likely generic to a broad class of network-based systems and arises from two synergetic effects: changes in the network orientation and topology through the formation of permanent contacts that stabilize the system. Our findings are rationalized using a rigidity percolation framework and offer a general principle for encoding elasticity in biological and synthetic networks.

We study the effects of zero-point spin fluctuations on the nuclear spin-lattice relaxation rate 1/$T_1$ around a two-dimensional antiferromagnetic quantum critical point in the self-consistent renormalization theory. For a weak mode-mode coupling constant $y_1 < $ 0.1, the finite temperature behavior of 1/$T_1$ across the quantum critical point resembles that for only the thermal spin fluctuations. For a strong mode-mode coupling constant $y_1 > $ 0.1, 1/$T_1$ takes its local maximum as a function of temperature in the nearly antiferromagnetic state. Experimental observation of the local maximum in the $^{63}$Cu nuclear spin-lattice relaxation rate 1/$T_1$ of lightly-doped superconductors La$_{2-x}$Sr$_x$CuO$_4$ with $x$ = 0.06-0.10 is associated with the effects of the zero-point spin fluctuations. The two-dimensional magnetic quantum critical point and the role of the zero-point spin fluctuations are discussed in the electron spin dynamics of underdoped superconductors La$_{2-x}$Sr$_x$CuO$_4$.

Hydrostatic pressure commonly suppresses polarization in conventional displacive ferroelectrics by weakening the off-center ionic distortion. Sliding ferroelectrics may provide a contrasting case because their polarization arises from stacking-dependent interlayer charge transfer rather than intra-unit-cell ionic displacement. Here, hydrostatic pressure is shown to enhance, rather than suppress, the polarization of parallel-stacked bilayer boron nitride, a prototypical sliding ferroelectric. A graphene layer placed on top of a ferroelectric boron nitride bilayer is used for sensing the evolution of polarization under pressure. The pressure enhances both the interlayer potential and the ferroelectric polarization, with the latter increasing approximately linearly by 80% up to 1.66GPa. These results establish hydrostatic compression as a tuning parameter for sliding-ferroelectric polarization, with potential implications for ultrathin slidetronic memory devices.

Domain walls in ferroic materials can host nanoscale functionalities absent from the periodic crystal, offering new opportunities to control electronic transport and polarization in semiconductor devices. Metal halide perovskites demonstrate important photophysical properties; however, their ferroic properties remain unclear. Here we discover a hierarchical herringbone network of polar walls within the non-polar halide perovskite CsPbBr3 comprising ferroelastic twin walls and antiphase walls. Atomic-scale imaging reveals that both wall types comprise nanoscale regions whose inversion-symmetry is broken compared to the surrounding bulk lattice. In-situ heating experiments show that these interfaces form sequentially during symmetry-lowering phase transitions, revealing a different formation pathway compared with 'conventional' oxide perovskites. These polar nano-walls, together with their enclosed topology, may impact carrier transport. This reveals a previously unrecognized structural motif in CsPbBr3, providing new insights into their photophysical and optoelectronic behavior.

Hydrogen significantly affects plasticity in bcc iron, but its role is commonly attributed to dislocation-mediated mechanisms, leaving the influence of hydrogen on phase transformation and deformation twinning poorly understood. We use a density-functional-theory-trained deep-neural-network interatomic potential and large-scale molecular dynamics to study pure bcc Fe and Fe containing 10% hydrogen. It is found that hydrogen lowers the yield stress but, more importantly, increases the persistence of {112} twin variants and suppresses detwinning. This effect stabilizes an interconnected {332}-{10 9 3} multimodal twin network and produces pronounced post-yield hardening. Higher temperature promotes the initial transformation but weakens the persistence of the high-index multimodal twin network. Moreover, twinning follows distinct loading-dependent pathways: compression generates {332} and {10 9 3} boundaries through co-zone and non-co-zone twin-twin interactions, whereas tension produces {7 4 1} boundaries through non-co-zone interactions. These results establish a pathway-based picture in which the intermediate phase determines the accessible twin modes and variant crystallography, while hydrogen and temperature control their kinetic survival and the emergence of high-index twin networks.

On the macroscopic scale, active (self-propelled) objects moving through complex environments are often subject to effects arising from both the curvature of the surrounding surface and external influences such as gravity. We study the Kramers escape problem for active Brownian particles in two settings: motion in an external potential driven solely by gradient forces, and motion on a curved manifold subject to an additional constant gravitational force. In the absence of translational noise, a sharp dynamical transition occurs when the self-propulsion velocity $v_0$ reaches a critical velocity $v_c$ required for an escape. Above this threshold, the escape rate $k$ follows a universal scaling form, $k \propto \exp\left[-\mathrm{const}(v_0-v_c)^{-\gamma}\right]$, with an exponent $\gamma=3/2$ for the escape in a potential and $\gamma=1/2$ for the escape on a curved manifold in the presence of gravity. These distinct exponents reveal how the interplay of activity, surface curvature, and gravity determines the critical escape dynamics. Our theoretical predictions are verified by numerical simulations.

Transition metal dichalcogenides (TMDCs) have emerged as highly tunable platforms for electrocatalysis, particularly for the CO2 reduction reaction (CO2RR). While TMDC edge sites exhibit catalytic activity, the basal plane is typically inert, severely limiting the overall active site density. In this work, we show that sulfur vacancies activate the basal plane of 1H-TMDCs, while concurrent solid-solution alloying provides a mechanism to broadly tune intermediate adsorption energies. We evaluate a library of quasi-binary TMDC sulfide alloys comprising V, Nb, Ta, Mo, and W, screening them by stability, defect energetics, and competitive selectivity to identify the most effective catalysts for CO2RR. Electronic-structure analysis reveals that a d-band center closer to the Fermi energy weakens intermediate binding by leaving key bonding states unoccupied above the Fermi energy. Our calculations identify (Nb,Ta)S2 as a promising catalyst with low sulfur vacancy formation energies, near-optimal CO2RR intermediate binding, and selectivity against the hydrogen evolution reaction. Overall, this work establishes a rational design framework for TMDC alloy catalysts through the simultaneous use of defect engineering and alloying.

The role of nonlinear carrier dynamics in current-driven spin phenomena remains poorly understood in van der Waals magnetic heterostructures. Here, we investigate the spin polarization and the resulting spin-orbit torque (SOT) in transition-metal dichalcogenide/chromium iodide (TMDC/CrI$_3$) heterostructures, focusing on WSe$_2$/CrI$_3$ and MoSe$_2$/CrI$_3$, in the zero-Rashba spin-orbit coupling (SOC) limit and beyond the linear-response regime. We find that linear spin polarization is forbidden by symmetry, making nonlinear intraband transitions the dominant mechanism in this regime. Consequently, the current-driven spin response differs fundamentally from conventional linear-response predictions. The resulting nonlinear spin polarization generates a purely field-like torque whose magnitude and sign depend sensitively on the chemical potential and doping type, with pronounced asymmetries between n- and p-doped systems. A strong material dependence is also observed: n-doped MoSe$_2$/CrI$_3$ exhibits a torque nearly an order of magnitude larger than that of WSe$_2$/CrI$_3$, together with two sign reversals, reflecting differences in their SOC and proximity-exchange parameters. Structural and electrostatic control through the twist angle and gate electric field provides additional means of tuning the nonlinear torque, including substantial modulation and controllable sign reversals. These findings establish TMDC/CrI$_3$ bilayers as a versatile platform for engineering nonlinear spin-orbit phenomena in ultrathin, low-power spintronic devices.

This review surveys diverse types of random motion within a unified framework, introducing essential mathematical tools, including special functions and fractional calculus, in a pedagogical manner. We focus on generalized random motions in one-dimensional space described by Fokker-Planck like equations, whose fundamental solutions take a universal and simple form in the Laplace-Fourier domain in terms of a generic function $\varphi(s)$. By exploring the functional forms of $\varphi(s)$ consistent with physical constraints, we derive a broad class of stochastic dynamics. This includes Brownian and active motion, simple and anomalous diffusion, and processes featuring stochastic resetting or trapping mechanisms. For each case, we provide the corresponding kinetic equation, explicit solutions (where available), and mean-square displacements alongside their asymptotic behaviors. Finally, we discuss the physical interpretation of these motions through the lens of time-changed processes and subordinators.

I review the evolution of electronic non-relativistic current density functional theory (CDFT) from its original formulation in the late 1980's to present day's formulations, which rely on the generalized Kohn-Sham theory. Axel Becke's outstanding contributions are highlighted throughout. I propose a form of the generalized Kohn-Sham equation that combines the exchange-correlation vector potential of the original formulation with an “effective mass term" – the latter following from the inclusion of Becke's kinetic energy density as a basic input of the exchange-correlation energy functional.

Extracting operationally meaningful quantities such as von Neumann entropy and mutual information is central to characterizing many-body quantum systems, yet experiments and numerics often provide direct access only to integer Rényi entropies. Whereas conventional extrapolation relies on a prescribed fitting ansatz, in PRL 137, 100202 we introduced an alternative approach based on stabilized analytic continuation (SAC), which avoids such an ansatz and is inherently robust to noise. Here, we further develop this framework in the noiseless setting and benchmark its performance across several nontrivial many-body problems. We first show that, besides the intrinsic ambiguity of reconstructing the von Neumann entropy from finitely many Rényi samples, analytic continuation can also fail because of genuine nonanalyticities in the Rényi function arising from zeros of $\text{Tr}\rho^z$. We derive universal zero-free domains for $\text{Tr}\rho^z$ and systematically sharpen these bounds using additional spectral information about $\rho$. We then benchmark the performance of SAC in three settings: ($i$) extracting topological entanglement entropy from DMRG Rényi data for the toric code and Kagome Heisenberg models; ($ii$) reconstructing the mutual information between disjoint intervals in a $(1+1)d$ compact-boson CFT; and ($iii$) recovering finite-time ballistic growth of the von Neumann entropy from integer Rényi entropies that cross over toward subballistic growth in diffusive quantum dynamics. In the latter setting, analytic continuation is expected to fail in the long time limit. We illustrate this mechanism with a physically motivated two-sector model, where the asymptotic separation between von Neumann and higher-Rényi growth is accompanied by a zero of $\text{Tr}\rho^z$ pinching the real axis at $z=1$, thereby producing a first-order Rényi phase transition.

Haar randomness is the standard null model for quantum typicality, scrambling, and random-matrix formulations of thermalization. In many physical settings, however, randomness is naturally constrained to subspaces of Hilbert space. This structure arises, in particular, both in systems with symmetry-resolved sectors and in the Eigenstate Thermalization Hypothesis (ETH), where mesoscopic energy windows define subspaces in which nearby energy eigenstates are mixed. Motivated by these settings, we consider a Block-Unitary Ensemble consisting of independently Haar-random unitaries acting on each subspace. We develop a constructive Weingarten Calculus for this ensemble, providing a unified framework across quantum information and many-body physics. This construction reveals a symmetry-resolved Schur-Weyl duality, where the relevant commutant is not the ordinary permutation algebra, but the one of color-preserving permutations. We apply this framework to quantum states under symmetry constraints and to energy-resolved ensembles for ETH.

We consider a tunable hybrid device composed of four quantum dots and a floating superconducting island – the so-called poor man's tetron – close to its effective particle-hole symmetric point and coupled to four external leads. We predict the onset of a charge Kondo effect mediated by Cooper pairs, resulting from the strong crossed Andreev reflections that dominate its low-energy behavior. This two-channel Kondo effect makes the poor man's tetron behave as a double Cooper pair splitter, turning uncorrelated incoming electrons into spatially separated Cooper pairs. Based on renormalization group techniques, we analyze both its weak and strong coupling regimes and we determine its non-Fermi liquid signatures. Our estimates indicate that the fractional conductance and transport features associated to this two-channel charge Kondo effect can be observed over a broad range of temperatures and anisotropies in realistic experimental conditions.

Motivated by recent optical measurements in twisted MoTe$_2$ homobilayers, we numerically study the binding of itinerant anyons to ordinary electronic bound states. Using a minimal few-body model of an anyon alongside holes and electrons in a Gaussian trapping potential, we show that a fractionally charged bound state comprised of an anyon and an ordinary electronic trion can become favorable nearby local electrostatic defects. The resulting object is an anyonic molecule wherein the anyon is bound to the trion “nucleus,” which in turn is localized to the defect and can be excited optically. We find that the resulting anyon-trion can exhibit a photoluminescence red-shift relative to the ordinary trapped trion, with binding on the meV scale for parameters relevant to twisted MoTe$_2$. We find that the value of this red-shift depends on $\textit{both}$ the anyon's fractional charge and its kinetic energy, thereby encoding both universal and non-universal anyon properties. Our results are qualitatively consistent with observations in twisted MoTe$_2$.

Decoherence-induced phase transitions (DIPTs) are associated with singular changes in a quantum system's entanglement structure as the decoherence strength varies. In many cases, their critical strengths depend monotonically on the Rényi index of the entanglement diagnostic, forming a Rényi hierarchy. We identify a general mechanism for this hierarchy based on correlation inequalities in replicated statistical models that describe these DIPTs. We demonstrate it in $\mathbb{Z}_2$ topological stabilizer codes subject to independent phase-flip decoherence on each qubit and in a decohered rotor model with strong $\text{U}(1)$ symmetry. When the relevant correlations diagnose the DIPTs, these inequalities imply that the critical decoherence strength is nondecreasing with integer Rényi index $R\geq2$. We show that this mechanism also applies to a class of models with correlated decoherence.

There is disagreement in the literature concerning whether the nodal point of a three-dimensional Weyl semimetal survives weak short-range disorder: instanton calculations including fluctuations claim that the zero-energy density of states $\rho(0)$ vanishes, while exact numerics find a systematically finite number. We settle this disagreement with a full saddle-point calculation, including both instanton and fluctuations. Within the supersymmetric formulation for disorder, the instanton obeys a nonlinear Weyl equation whose solution is an exact $j=1/2$ hedgehog whose full functional form we numerically compute. We then compute the fluctuations about this saddle point, carefully identifying all zero modes, and computing the reduced superdeterminant as a convergent Fredholm determinant. No fermionic zero mode beyond a Kramers doublet exists, and at finite disorder $w$, the fluctuations become a finite one-loop prefactor, $\rho(0)=\mathcal{A} w^{-4} \exp(-s^*/w^2)(1+O(w^2))$, in normalized units with $s^* = 6.4163(2)$ and $\mathcal{A} = 27.47(8)$ for Gaussian-correlated disorder. This expression matches exact numerics on a single Weyl cone over four orders of magnitude with no fitted parameters (the amplitude is $\times 0.76$ the one-loop value), establishing that the density of states is finite for any disorder strength.

We study entanglement transitions for pairs of disjoint intervals in two-dimensional holographic interface conformal field theories. We consider several holographic models with equal central charges on the two sides of the interface: thin-wall geometries with one and two branes, the Janus solution, and the super-Janus solution. We first discuss the finite interface contribution to the entanglement entropy of a single interval, distinguishing intervals that cross the interface from those that lie entirely on one side. We then use the mutual information to locate the transition between connected and disconnected Ryu–Takayanagi geodesic configurations for two intervals. When the interface lies between the two intervals, increasing the boundary entropy $\log g$, which provides a measure of interface strength in the models considered here, generally decreases the critical separation at which the connected configuration ceases to dominate. When both intervals lie on the same side of the interface, the behavior is model dependent: the connected phase persists to larger separations in the Janus and super-Janus models, while the critical separation is unchanged in the thin-wall models. Thus, as diagnosed by the two-interval transition, the interface weakens correlations across the interface while preserving or enhancing correlations between regions on the same side. We also identify a universal “Silver Blaze” configuration, in which the interface lies inside one of the intervals and the transition occurs at the same location as in a CFT without an interface, independently of the interface parameters and of the holographic model. This universality follows from a cancellation between crossing and non-crossing interface contributions to the mutual information.

The observation of superconducting behaviour near a fractional Chern insulator in twisted MoTe$_2$ has sparked excitement about a possible direct "anyon superconducting" transition between a topologically ordered and a symmetry-broken phase. We carefully examine the experimentally measured transport data in the relevant region of the low-temperature tMoTe$_2$ phase diagram and propose a scenario where the nearby reentrant integer quantum Hall effect (RIQHE) acts as an intervening phase between the two. While the RIQHE is most prominent at large displacement fields, we propose that it extends to smaller fields at very low temperatures. Based on this picture, we model the sample as a patchwork of the three phases and show that such a model can explain the main qualitative features of the transport phase diagram, including its dependence on temperature and displacement field. The model predicts that at lower electronic temperatures the apparent FCI-SC transition at zero displacement field should split into two transitions separated by a narrow RIQHE region.

We demonstrate repulsion-driven topological superconductivity of a single species of Dirac fermions, motivated by valley-polarized phases observed in two-dimensional materials such as rhombohedral graphene. Using density-matrix renormalization group calculations on the Qi-Wu-Zhang lattice model on cylinders of width up to eight, we find a robust phase of spinless chiral $p$-wave superconductivity. Pairing already starts at low doping and thus occurs on a small, nearly isotropic Fermi pocket, and is therefore not tied to the particular details or anisotropy of the dispersion but instead seems tied to the non-trivial quantum geometry of the bands. In fact, the winding of the superconductor order parameter is opposite ("$p-ip$") to that of the anomalous Hall metal which forms the parent state, in agreement with expectations recently derived from weak coupling calculations. At larger doping, we find that a pair-density-wave component develops alongside zero-momentum pairing. Our work shows that the combination of strong repulsion, absence of time-reversal in the parent state, and non-trivial quantum geometry form a promising platform to realize topological superconductivity.

Commuting-projector Hamiltonians with integer spectrum such as the 1+1d Ising ferromagnet and the 2+1d toric code may be regarded as the generators of non-on-site $U(1)$ symmetries. In this paper we study whether these symmetries can be made on-site in the presence of finite and infinite-dimensional ancillae. In the finite-dimensional case, we prove that the fractionalized excitations, such as domain walls and anyons, make it impossible to on-site these Hamiltonians. On the other hand, we show that when infinite dimensional ancillae (e.g., rotors) are allowed, both the 1+1d Ising ferromagnet and the 2+1d toric code can be disentangled, yielding on-site symmetries. This is not in contradiction with the non-trivial ground state order of these Hamiltonians, since the ancilla Hamiltonians are no longer bounded from below. Our results indicate agreement between lattice and quantum field theory anomalies in the presence of infinite-dimensional ancillae, while with finite-dimensional ancillae the obstruction to on-siteability may even be non-invertible.

Renormalization group (RG) is a core concept in physics from statistical mechanics to quantum field theory, yet its schemes differ widely between field theory and many-body physics. We formulate the Wilsonian RG as a quantum channel, whose Kraus representation yields pure conditional trajectories for pure inputs and recovers mixed-state flows upon averaging. We then develop an algebraic extension applicable beyond the usual momentum-space, factorized setting: the low-energy algebra is constructed from the one-particle spectrum, and coarse graining is a conditional expectation onto it. We further construct a resource theory of RG whose free states are fixed points. For thermal states, the resulting relative-entropy monotone is proportional to $c-c_{\rm IR}$ to quadratic order along a single stable RG direction near a two-dimensional IR fixed point. We also introduce a complementary measure of the UV information discarded by coarse graining, establish its monotonicity for successive coarse-graining maps, and discuss its holographic realization.

I show that the initial conditions imposed by Balan [Phys. Fluids 35, 113108 (2023)] are incompatible with a nonzero retardation time, so that the problem solved is not impulsive start-up, but, as I prove exactly, the start-up of a plate ramped as $1 - \mathrm{e}^{-t/\lambda_2}$ on the retardation timescale $\lambda_2$ (a material parameter, not a setting in a rheometer). Values digitized from that paper's viscoelastic figures fall on the ramped-plate solution, not on Tanner's start-up solution. The large negative wall normal stress reported for the corotational model is a grid-dependent artifact due to the same error in the initial data. An open-source code repository provides annotated notebooks reproducing every figure and number in this Comment.

We study the homology of percolation clusters on disk-shaped patches of the regular $\{3,q\}$ triangle tilings for $q\ge7$. Varying $q$ gives a one-parameter family of hyperbolic tilings, from mildly curved ($q=7$) to deeply hyperbolic ($q=20$), and this paper measures and derives loop content as a function of curvature. A single growth-rate parameter $\lambda(q)$, the asymptotic ratio of successive ring sizes, governs every result. Total persistent $H_1$ of the bond-percolation complex, per vertex, is measured across $q=7,\dots,20$ and found to be a nearly linear function of $1/\lambda(q)$. An exact identity reduces total loop persistence to the weight of the lattice's minimum spanning tree minus a boundary correction. The boundary correction follows from the ring recursion, and the spanning-tree weight is derived to first order in $1/\lambda(q)$ by attaching rings one at a time to a contracted interior, with a correction for loops that close through the ring outside. The resulting formula has no free parameters, gives the large-curvature intercept in closed form as $5/4-2\pi/(3\sqrt3)$, and agrees with the measurements to within the size of the next-order term.

Early string descriptions of doped antiferromagnets associate hole motion in a locally Néel ordered background with a path dependent antiferromagnetic string. We ask what becomes of this mechanism when long range Neel order is lost while short range antiferromagnetic correlations persist. The loss of long range order makes the projective RP^2 description admissible and opens a new topologically nontrivial sector. Its elementary defects are half vortices that globally minimize the RP^2 sigma-model energy within the nontrivial Z_2 sector. An a posteriori energetic comparison further shows why, once accessible, the projective director sector is favored over the corresponding vector reference texture. A pair of half vortices with opposite windings is logarithmically confined, V(R) = \kappa \ln\left(R/r_{\text{core}}\right), \kappa = \pi \rho_s /2. The resulting confinement is carried not by a one dimensional string but by an extended two dimensional spin texture. Thus, the loss of long range Néel order does not eliminate antiferromagnetic confinement but opens a distinct projective mechanism in which a local path dependent string is replaced, at long wavelengths, by a global topological texture with logarithmic confinement.

The Yukawa-Sachdev-Ye-Kitaev (YSYK) model, a solvable model of non-Fermi liquids with a proposed cavity-QED realization, couples $N$ complex fermions to $M$ bosons of frequency $\omega_0$ through random Yukawa couplings of strength $g$, and its dynamics depends only on $R\equiv\omega_0/g^{2/3}$. For $R\ll1$ the bosons are slow and act as a static random background in which the fermions are free, while for $R\gg1$ they are only virtually excited and generate a random four-fermion interaction of rank $M$, which is generically chaotic for $M\geq2$. Using exact diagonalization at infinite temperature, we follow the emergence of random-matrix statistics between these limits with unfolded spectral statistics and the Krylov complexity of the thermofield-double state. For complex couplings the level-spacing distribution evolves from Poisson to Gaussian-unitary-ensemble (GUE) statistics, the spectral form factor develops a correlation hole and a ramp, and the Krylov complexity evaluated on the unfolded spectrum develops a peak above its late-time plateau whose height reaches the GUE value. All diagnostics locate the onset around $R\approx0.3$, and adding boson modes moves it to smaller $R$. This delineates the parameter regime in which a cavity-QED realization would display random-matrix spectral correlations. On the other hand, real couplings give the same crossover towards Gaussian-orthogonal-ensemble (GOE) statistics, and along an interpolation between the two the peak height follows the mean gap ratio, so the peak identifies the symmetry class as well as the onset of chaos. Without unfolding the peak stays about 20$\%$ below its random-matrix value in both classes, which we trace to the non-semicircular density of states, and at larger $R$ the boson-number bands slow down the spreading of the state in Krylov space.

We consider a fixed finite number of independent two-dimensional discrete Gaussian free fields on a box of side $n$, with zero boundary values, conditioned so that the vector-valued field stays outside a fixed ball on a macroscopic interior domain. We prove that the field, divided by $\log n$, converges in distribution in $L^2$ to twice the equilibrium potential of the domain multiplied by a uniform random unit vector. We also identify the exact capacity cost of the conditioning event and obtain alignment on a deterministic density-one set of sites, with no restriction on their mutual distance. The proof combines the norm repulsion theorem of Korzhenkova and Sepúlveda with Gaussian large deviations and the equality case in the capacity variational problem.

Weyl or Dirac fermions with the iconic linear energy-momentum relation and average density of states (ADOS) $\rho(E) \sim |E|^{d-1}$ at energy $E$ in $d$ spatial dimensions, constitute a unique setup to study the disorder-driven semimetal-to-metal quantum phase transition (QPT) between ballistic (realized for weak disorder) and diffusive (stabilized at stronger disorder) quasiparticles. Such a QPT takes place only for $d>2$ and falls beyond the realm of the Anderson metal-to-insulator transition. From numerically computed ADOS (using the kernel polynomial method) in dirty Weyl systems in $d=2$ to $6$, here we show that $d=2$ and $d=4$ are the lower ($d_\ell$) and upper ($d_u$) critical dimensions for such an unconventional QPT, respectively, as suggested from the solution of quasiparticle lifetime within the self-consistent Born approximation. Consequently, for $d \geq 4$ the associated correlation length exponent is found to be $\nu \approx 0.5$ (within numerical accuracy). However, the dynamic scaling exponent at the quantum critical point is pinned close to $z \approx d/2$ (numerically) for any $d \geq 3$, which is shown to be an exact result from a field-theoretic renormalization group calculation. Therefore, Weyl semimetal-to-metal QPTs can be studied field theoretically around both $d_\ell$ and $d_u$.

We introduce projected amorphous topological insulators (PATIs) that despite containing only a fraction ($x$) of otherwise randomly selected disconnected sites of a parent crystal, feature a quantized global topological invariant (strong PATIs) when its effective Hamiltonian is constructed by integrating out the residual sites of the original lattice. Within the topological regime of the parent model, additionally, there exists a critical $x$ below which such systems foster a fragile PATI that only supports quantized local topological marker on a small fraction of sites therein. Both strong and fragile PATIs accommodate in-gap modes near the boundary. The system also hosts a normal insulator in the entire trivial parameter regime of the lattice-based model for any $x$, devoid of gapless boundary modes, for which both global topological invariant and local topological marker vanish. We demonstrate these possibly generic outcomes by starting with a parent square lattice-based model for time-reversal symmetry breaking insulators. Then the strong-to-fragile PATI quantum phase transition, tunable via $x$, is characterized by the mean correlation length exponent $\nu \in (1.00,1.46)$.