A hyperbolic singularity in the wave function of $s$-wave interacting atoms is the root problem for any accurate numerical simulation. Here, we apply the transcorrelated method, whereby the wave-function singularity is explicitly described by a two-body Jastrow factor, and then folded into the Hamiltonian via a similarity transformation. The resulting nonsingular eigenfunctions are approximated by stochastic Fock-space diagonalization with energy errors scaling with $1/M$ in the number $M$ of single-particle basis functions. The performance of the transcorrelated method is demonstrated on the example of strongly correlated fermions with unitary interactions. The current method provides the most accurate ground-state energies so far for three and four fermions in a rectangular box with periodic boundary conditions.

We present a mathematical framework adapted to the comparison of atomic clocks remotely connected by a complex network of optical or microwave links. This framework facilitates the computation of frequency ratios using a generic set of equations that are valid for a wide variety of clock architectures, making the comparison of a large number of clocks practical. This formalism suggests a generic data exchange protocol that can be used in clock comparison collaborations, for which data logging and decision taking are completely local procedures, independently implemented by the participants.

Weyl points are the simplest topologically protected degeneracy in a three-dimensional dispersion relation. The realization of Weyl semimetals in photonic crystals has allowed these singularities and their consequences to be explored with electromagnetic waves. However, it is difficult to achieve nonlinearities in such systems. One promising approach is to use the strong coupling of photons and excitons, because the resulting polaritons interact through their exciton component. Yet topological polaritons have only been realized in two dimensions. Here, we predict that the dispersion relation for polaritons in three dimensions, in a bulk semiconductor with an applied magnetic field, contains Weyl points and Weyl line nodes. We show that absorption converts these Weyl points to Weyl exceptional rings. We conclude that bulk semiconductors are a promising system in which to investigate topological photonics in three dimensions, and the effects of dissipation, gain, and nonlinearity.

In this work we investigate the effects of configurational disorder on the eigenstates and dynamical properties of a tight-binding model on a quasi-one-dimensional comb lattice, consisting of a backbone decorated with linear offshoots of randomly distributed lengths. We show that all eigenstates are exponentially localized along the backbone of the comb. Moreover, we demonstrate the presence of an extensive number of compact localized states with precisely zero localization length. We provide an analytical understanding of these states and show that they survive in the presence of density-density interactions along the backbone of the system where, for sufficiently low but finite particle densities, they form many-body scar states. Finally, we discuss the implications of these compact localized states on the dynamical properties of systems with configurational disorder, and the corresponding appearance of long-lived transient behavior in the time evolution of physically relevant product states.

Type II superconductors exhibit a fascinating phenomenology that is determined by the dynamical properties of the vortex matter hosted by the material. A crucial element in this phenomenology is vortex pinning by material defects, e.g., immobilizing vortices at small drives and thereby guaranteeing dissipation-free current flow. Pinning models for vortices and other topological defects, such as domain walls in magnets or dislocations in crystals, come in two standard variants: (1) weak-collective pinning, where individual weak defects are unable to pin, while the random accumulation of many force centers within a collective pinning volume combines into an effective pin, and (2) strong pinning, where strong defects produce large vortex displacements and bistabilities that lead to pinning on the level of individual defects. The transition between strong and weak pinning is quantified by the Labusch criterion $\kappa \approx f_p/\overline{C}\xi =1$, where $f_p$ and $\overline{C}$ are the force of one defect and the effective elasticity of the vortex lattice, respectively ($\xi$ is the coherence length). Here, we show that a third generic type of pinning becomes dominant when the pinning force $f_p$ enters the weak regime, the pinning by rare events. We find that within an intermediate regime $1/2<\kappa <1$, compact pairs of weak defects define strong pinning clusters that extend the mechanism of strong pinning into the weak regime. We present a detailed analysis of this cluster-pinning mechanism and show that its pinning force density parametrically dominates over the weak pinning result. The present work is a first attempt to include correlations between defects into the discussion of strong pinning.

We consider the fermionic quantum criticality of anisotropic nodal point semimetals in $d=d_L+d_Q$ spatial dimensions that disperse linearly in $d_L$ dimensions, and quadratically in the remaining $d_Q$ dimensions. When subject to strong interactions, these systems are susceptible to semimetal-insulator transitions concurrent with spontaneous symmetry breaking. Such quantum critical points are described by effective field theories of anisotropic nodal fermions coupled to dynamical order parameter fields. We analyze the universal scaling in the physically relevant spatial dimensions, generalizing to a large number $N_f$ of fermion flavors for analytic control. Landau damping by gapless fermionic excitations gives rise to nonanalytic self-energy corrections to the bosonic order-parameter propagator that dominate the long-wavelength behavior. We show that perturbative momentum shell RG leads to nonuniversal, cutof-dependent results, as it does not correctly account for this nonanalytic structure. In turn, using a completely general soft cutoff formulation, we demonstrate that the correct IR scaling of the dressed bosonic propagator can be deduced by enforcing that results are independent of the cutoff scheme. Using the soft cutoff RG with the dressed dynamical RPA boson propagator, we compute the exact critical exponents for anisotropic semi-Dirac fermions $(d_L=1$, $d_Q=1)$ to leading order in $1/N_f$ and to all loop orders. Applying the same method to relativistic Dirac fermions, we reproduce the critical exponents obtained by other methods, such as conformal bootstrap. Unlike in the relativistic case, where the UV-IR connection is reestablished at the upper critical dimension, nonanalytic IR contributions persist near the upper critical line $2d_L+d_Q=4$ of anisotropic nodal fermions. We present $\epsilon$ expansions in both the number of linear and quadratic dimensions. The corrections to critical exponents are nonanalytic in $\epsilon$, with a functional form that depends on the starting point on the upper critical line.

We show that the topological phase transition for a Kitaev chain embedded in a cavity can be identified by measuring experimentally accessible photon observables such as the Fano factor and the cavity quadrature amplitudes. Moreover, based on density matrix renormalization group numerical calculations, endorsed by an analytical Gaussian approximation for the cavity state, we propose a direct link between those observables and quantum entropy singularities. We study two bipartite entanglement measures, the von Neumann and Rényi entanglement entropies, between light and matter subsystems. Even though both display singularities at the topological phase transition points, remarkably only the Rényi entropy can be analytically connected to the measurable Fano factor. Consequently, we show a method to recover the bipartite entanglement of the system from a cavity observable. Thus, we put forward a path to experimentally access the control and detection of a topological quantum phase transition via the Rényi entropy, which can be measured by standard low noise linear amplification techniques in superconducting circuits. In this way, the main quantum information features of Majorana polaritons in photon-fermion systems can be addressed in feasible experimental setups.

Inspired by a recently proposed superconducting mechanism for a new cuprate superconductor ${\mathrm{Ba}}_2{\mathrm{CuO}}_{3+\delta }$, we theoretically design an unconventional nickelate superconductor with a $d^8$ electron configuration. Our strategy is to enlarge the on-site energy difference between $3d_{x^2-y^2}$ and other $3d$ orbitals by adopting halogens or hydrogen as out-of-plane anions, so that the $3d$ bands other than $d_{x^{-}{y}^2}$ lie just below the Fermi level for the $d^8$ configuration, acting as incipient bands that enhance superconductivity. We also discuss a possible relevance of the present proposal to the recently discovered superconductor $(\mathrm{Nd},\mathrm{Sr}){\mathrm{NiO}}_2$.

We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results show that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the existence of a nonergodic metallic phase with multifractal eigenstates. The scaling analysis gives critical exponent $\nu =0.94\pm 0.08$ and critical disorder $W_{\mathrm{c}}=18.17\pm 0.02.$ Our data support that ergodicity is only recovered at zero disorder.

In this work, we investigate models for bulk, bi-, and multilayers containing half-metallic ferromagnets (HMFs), at zero and at finite temperature, in order to elucidate the effects of strong electronic correlations on the spectral properties (density of states). Our focus is on the evolution of the finite-temperature many-body induced tails in the half-metallic gap. To this end, the dynamical mean-field theory (DMFT) is employed. For the bulk, a Bethe lattice model is solved using a matrix product states based impurity solver at zero temperature and a continuous-time quantum Monte Carlo (CT-QMC) solver at finite temperature. We demonstrate numerically, in agreement with the analytical result, that the tails vanish at the Fermi level at zero temperature. In order to study multilayers, taken to be square lattices within the layers, we use the real-space DMFT extension with the CT-QMC impurity solver. For bilayers formed by the HMF with a band or correlated insulator, we find that charge fluctuations between the layers enhance the finite-temperature tails. In addition, in the presence of interlayer hopping, a coherent quasiparticle peak forms in the otherwise correlated insulator. In the multilayer heterostructure setup, we find that by suitably choosing the model parameters, the tails at the HMF-Mott insulator interface can be reduced significantly and that a high spin polarization is conceivable, even in the presence of long-ranged electrostatic interactions.

When do nonequilibrium forms of disordered energy qualify as heat? We address this question in the context of cyclically operating heat engines feeding on nonequilibrium energy reservoirs that defy the zeroth law of thermodynamics into work. To consistently address a nonequilibrium bath as a heat bath in the sense of the second law of thermodynamics requires the existence of a precise mapping to an equivalent cycle with an equilibrium bath at a time-dependent effective temperature. We identify the most general setup for which this can generically be ascertained and thoroughly discuss an analytically tractable, experimentally relevant scenario: a Brownian particle confined in a periodically modulated harmonic potential and coupled to some nonequilibrium bath of variable activity. We deduce formal limitations for its thermodynamic performance, including maximum efficiency, efficiency at maximum power, and maximum efficiency at fixed power. The results can guide the design of new micromachines and clarify how much these can outperform passive-bath designs, which has been a debated issue for recent experimental realizations. To illustrate the practical implications of the general principles for quasistatic and finite-rate protocols, we further analyze a specific realization of such an active heat engine based on the paradigmatic active Brownian particle (ABP) model. This reveals some nonintuitive features of the explicitly computed dynamical effective temperature, illustrates various conceptual and practical limitations of the effective-equilibrium mapping, and clarifies the operational relevance of various coarse-grained measures of dissipation.

Networks of limit cycle oscillators can show intricate patterns of synchronization such as splay states and cluster synchronization. Here we analyze dynamical states that display a continuum of seemingly independent splay clusters. Each splay cluster is a block splay state consisting of subclusters of fully synchronized nodes with uniform amplitudes. Phases of nodes within a splay cluster are equally spaced, but nodes in different splay clusters have an arbitrary phase difference that can be fixed or evolve linearly in time. Such coexisting splay clusters form a decoupled state in that the dynamical equations become effectively decoupled between oscillators that can be physically coupled. We provide the conditions that allow the existence of particular decoupled states by using the eigendecomposition of the coupling matrix. We also provide an alternate approach using the external equitable partition and orbital partition considerations combined with symmetry groupoid formalism to develop an algorithm to search for admissible decoupled states. Unlike previous studies, our approach is applicable when existence does not follow from symmetries alone and also illustrates the differences between adjacency and Laplacian coupling. We show that the decoupled state can be linearly stable for a substantial range of parameters using a simple eight-node cube network and its modifications as an example. We also demonstrate how the linear stability analysis of decoupled states can be simplified by taking into account the symmetries of the Jacobian matrix. Some network structures can support multiple decoupled patterns. To illustrate that, we show the variety of qualitatively different decoupled states that can arise on two-dimensional square and hexagonal lattices.

The field of quantum sensing aims at improving the detection and estimation of classical parameters that are encoded in physical systems by resorting to quantum sources of light and quantum detection strategies. The same approach can be used to improve the current classical measurements that are performed on biological systems. Here we consider the scenario of two bacteria (E. coli and Salmonella) growing in a Luria-Bertani broth and monitored by classical spectrophotometers. Their concentration can be related to the optical transmissivity via the Beer-Lambert-Bouguer's law and their growth curves can be described by means of Gompertz functions. Starting from experimental data points, we extrapolate the growth curves of the two bacteria and we study the theoretical performance that would be achieved with a quantum setup. In particular, we discuss how the bacterial growth can in principle be tracked by irradiating the samples with orders of magnitude fewer photons, identifying the clear superiority of quantum light in the early stages of growth. We then show the superiority and the limits of quantum resources in two basic tasks: (i) the early detection of bacterial growth and (ii) the early discrimination between two bacteria species.

We determine the ground-state phase diagram of the three-band Hubbard model across a range of model parameters using density matrix embedding theory. We study the atomic-scale nature of the antiferromagnetic (AFM) and superconducting (SC) orders, explicitly including the oxygen degrees of freedom. All parametrizations of the model display AFM and SC phases, but the decay of AFM order with doping is too slow compared to the experimental phase diagram, and further, coexistence of AFM and SC orders occurs in all parameter sets. The local magnetic moment localizes entirely at the copper sites. The magnetic phase diagram is particularly sensitive to ${\mathrm{\Delta }}_{pd}$ and $t_{pp}$, and existing estimates of the charge transfer gap ${\mathrm{\Delta }}_{pd}$ appear too large in so-called minimal model parametrizations. The electron-doped side of the phase diagram is qualitatively distinct from the hole-doped side and we find an unusual two-peak structure in the SC in the full model parametrization. Examining the SC order at the atomic scale, within the larger scale $d_{x^2-y^2}$-wave SC pairing order between Cu-Cu and O-O, we also observe a local $p_{x\left(y\right)}$ [or $d_{xz\left(yz\right)}$] symmetry modulation of the pair density on the Cu-O bonds. Our work highlights some of the features that arise in a three-band versus one-band picture, the role of the oxygen degrees of freedom in new kinds of atomic-scale SC orders, and the necessity of re-evaluating current parametrizations of the three-band Hubbard model.

We propose a numerical method which embeds the variational non-Gaussian wave-function approach within exact diagonalization, allowing for efficient treatment of correlated systems with both electron-electron and electron-phonon interactions. Using a generalized polaron transformation, we construct a variational wave function that absorbs entanglement between electrons and phonons into a variational non-Gaussian transformation; exact diagonalization is then used to treat the electronic part of the wave function exactly, thus taking into account high-order correlation effects beyond the Gaussian level. Keeping the full electronic Hilbert space, the complexity is increased only by a polynomial scaling factor relative to the exact diagonalization calculation for pure electrons. As an example, we use this method to study ground-state properties of the two-dimensional Hubbard-Holstein model, providing evidence for the existence of intervening phases between the spin and charge-ordered states. In particular, we find one of the intervening phases has strong charge susceptibility and binding energy, but is distinct from a charge-density-wave ordered state, while the other intervening phase displays superconductivity at weak couplings. This method, as a general framework, can be extended to treat excited states and dynamics, as well as a wide range of systems with both electron-electron and electron-boson interactions.

A general framework to describe a vast majority of biology-inspired systems is to model them as stochastic processes in which multiple couplings are in play at the same time. Molecular motors, chemical reaction networks, catalytic enzymes, and particles exchanging heat with different baths, constitute some interesting examples of such a modelization. Moreover, they usually operate out of equilibrium, being characterized by a net production of entropy, which entails a constrained efficiency. Hitherto, in order to investigate multiple processes simultaneously driving a system, all theoretical approaches deal with them independently, at a coarse-grained level, or employing a separation of time scales. Here, we explicitly take in consideration the interplay among time scales of different processes and whether or not their own evolution eventually relaxes toward an equilibrium state in a given subspace. We propose a general framework for multiple coupling, from which the well-known formulas for the entropy production can be derived, depending on the available information about each single process. Furthermore, when one of the processes does not equilibrate in its subspace, even if much faster than all the others, it introduces a finite correction to the entropy production. We employ our framework in various simple and pedagogical examples, for which such a corrective term can be related to a typical scaling of physical quantities in play.

We describe a protocol to prepare solitons in a quasi-one-dimensional (quasi-1D) box-trapped Bose-Einstein condensate using a quench of the isotropic $s$-wave scattering length. A quench to exactly four times the initial 1D coupling strength creates one soliton at each boundary of the box, which then propagate in a uniform background density and collide with one another. In the ideal case, no nonsolitonic excitations are created during the quench. The procedure is robust against realistic box shapes, imperfections in the scattering length ramp rate, and a mismatch of the final scattering length. We simulate the condensate in full 3D and propose a modification to the protocol that is effective outside of the strict quasi-1D regime.

We theoretically study the thermoelectric response of ionic conductors to an applied temperature gradient. As a main result, we find that open and closed systems with respect to charge exchange result in different expressions for the thermopower, which may even take opposite signs. For the experimentally most relevant zero-current steady state, we show that the thermopower of ionic conductors does not depend on the mobilities, contrary to what is known for metals and semiconductors. The different behaviors of ionic and electronic conductors are traced back to the unlike conservation laws for ionic carriers and electron-hole pairs.

We present two approaches capable of describing the dynamics of an interacting many-body system on a lattice coupled globally to a dissipative bosonic mode. Physical realizations are, for example, ultracold atom gases in optical lattice coupled to a photonic mode of an optical cavity or electronic gases in solids coupled to THz cavity fields. The first approach, applicable for large dissipation strengths and any system size, is a variant of the many-body adiabatic elimination method for investigating the long-time dynamics of the system. The second method extends the time-dependent matrix product techniques to capture the global coupling of the interacting particles to the bosonic mode and its open nature. It gives numerically exact results for small to intermediate system sizes. As a benchmark for our methods we perform the full quantum evolution of a Bose-Hubbard chain coupled to a cavity mode. We show that important deviations from the mean-field behavior occur when considering the full atoms cavity coupling [C.-M. Halati, A. Sheikhan, H. Ritsch, and C. Kollath, Phys. Rev. Lett. 125, 093604 (2020)].

The ability of a body-centered-cubic metal to deform plastically is limited by the thermally activated glide motion of screw dislocations, which are line defects with a mobility exhibiting complex dependence on temperature, stress, and dislocation segment length. We derive an analytical expression for the velocity of dislocation glide, based on a statistical mechanics argument, and identify an apparent phase transition marked by a crossover temperature above which the activation energy for glide effectively halves, changing from the formation energy of a double kink to that of a single kink. The analysis is in quantitative agreement with direct kinetic Monte Carlo simulations.