A Dirac electron passing through a heterojunction with spatially variable tilt experiences an effective curved spacetime. In this work, we show how this experience is manifested in its conductance. We investigate the propagation of electron waves in a two-dimensional tilted Dirac cone heterostructure where tilt depends on the coordinate $z$ along the junction. The resulting Dirac equation in an emergent curved spacetime for the spinor $\psi \left(z\right)$ can be efficiently solved using a fourth-order Runge-Kutta numerical method by a transformation to a suitable spinor $\phi$ where the resulting Dirac cone looks locally upright. The spatial texture of the tilt induces oscillatory behaviors in key physical quantities such as the norm ${\left|\phi \left(z\right)\right|}^2$ of the wave function, polar and azimuthal angles $\mathrm{\Theta }\left(z\right)$ and $\mathrm{\Phi }\left(z\right)$ of the pseudospin, and the integrated transmission $\tau$ where oscillation wavelengths get shorter (longer) in stronger (weaker) tilt regions. Such an oscillatory behavior that is reminiscent of gigantic gravitational redshift is an indicator of an underlying spacetime metric that can be probed in tunneling experiments. We derive analytical approximations for the position-depdendent wave numbers $\mathrm{\Delta }{k}_z\left(z\right)$ that explain the redshift patterns and corroborate it with numerical simulations. For a tilt bump spread over length scale $\ell$, upon increasing $\ell$, the amplitude of redshifted oscillations reduces whereas the number of peaks increases. The scale invariance of the Dirac equation allows us to probe these aspects of $\ell$ dependence by a voltage sweep in transmission experiments. Smooth variations of the tilt reduces impedance mismatch of the electron waves, thereby giving rise to very high transmission rates. This concept can be used in combination with a sigmoid-shaped tilt texture for a gigantic redshift or blueshift engineering of the transmitted waves, depending on whether the sigmoid is downswing or upswing.

Recently, it has become possible to compute real-frequency four-point correlation functions of quantum impurity models using a multipoint extension of the numerical renormalization group (mpNRG). In this work, we perform several numerical consistency checks of the output of mpNRG by investigating exact relations between two- and four-point functions. This includes the Bethe-Salpeter equations and the Schwinger-Dyson equation from the parquet formalism, which we evaluate in two formally identical but numerically nonequivalent ways. We also study the first-order U(1) Ward identity between the vertex and the self-energy for the first time in full generality in the real-frequency Keldysh formalism. We generally find good agreement of all relations, often up to a few percent, both at weak and at strong interaction.

Spectra of non-Hermitian systems with skin effects are sensitive to the boundary conditions. In this work, we introduce a system composed of an impurity and a nonreciprocal Su-Schrieffer-Heeger (SSH) chain with odd number of lattice sites. The shift in the energy of the zero mode can be dramatically changed by adding two vanishingly small couplings between the impurity and two ends of the chain. Here, we propose a multiple physical quantities sensor with exponential-power-law amplification mechanism. Sensitivity of the proposed sensor exhibits an exponential scaling with SSH chain size and a power-law scaling with frequency of the impurity. This system is designed for detecting two small physical quantities, i.e., the impurity-chain coupling strengths. If and only if these two physical quantities exist simultaneously, the energy of zero mode will obviously change. Moreover, sensitivity is also robust against on-site disorder or dissipation of the impurity. Sufficiently strong disorder will change the localization of the eigenstate, and this leads to device failure. We also show the parameter range of the proposed sensor, and this range accurately corresponds to a nontrivial spectral winding number. The single physical quantity sensors suffered from repeated construction and low utilization rate. Thus, our findings pave a basic way toward sensors that couple multiple physical quantities to the boundary of the non-Hermitian topological chain.

Random matrix theory yields valuable insights into the universal features of quantum many-body chaotic systems. Although all-to-all interactions are traditionally studied, many interesting dynamical questions, such as transport of a conserved density, require a notion of spatially local interactions. We study the transport of the energy, the most basic conserved density, in few-body and 1D chains of nearest-neighbor random matrix terms that square to one, which we dub the “Haar-Ising” local random matrix model. In the few-body but large local Hilbert space dimension case, we develop a mapping for the energy dynamics to a single-particle hopping picture. This allows for the computation of the energy density autocorrelators and an out-of-time-ordered correlator of the energy density. In the 1D chain, we numerically study the energy transport for a small local Hilbert space dimension. Throughout, we discuss the density of states and touch upon the relation to free probability theory.

Numerical studies of ionic motion through solid electrolytes commonly involve static nudged-elastic band methods or costly ab initio molecular dynamics. Building on a time-local model of current carrier-electrolyte interaction and incorporating thermal motion, we introduce an approach that is intermediate between the two well-established methodologies by treating the electrolyte as an effective medium that interacts with the mobile particle. Through this coupling, the thermally vibrating electrolyte imparts energy to the charge carriers while also absorbing energy from them due to its own finite elasticity. Using a simple model system, we validate our approach through a series of numerical simulations. Our methodology reproduces both dissipative and diffusive behavior and helps link microscopic system parameters to measurable macroscopic properties.

Fractonic superfluids are featured by the interplay of spontaneously broken charge symmetry and mobility constraints on single-particle kinematics due to the conservation of higher moments, such as dipoles, angular charge moments, and quadrupoles. Building on prior studies by Yuan et al. [Phys. Rev. Res. 2, 023267 (2020)] and Chen et al. [Phys. Rev. Res. 3, 013226 (2021)], we study a class of fractonic superfluids, termed hybrid fractonic superfluids (HFS), in which bosons of multiple species interact while moment hybridization is conserved. We explore the consequences of hybridization via two model series: Model Series A, conserving total moments of the same order across species, and Model Series B, conserving total moments of different orders. In Model Series A, we analyze dipole moment hybridization and extend the discussion to higher-order moments, examining the ground state, Goldstone modes, correlation functions, and so on. We compute the minimal spatial dimensions, where the total charge symmetry begins to get partially broken via particle-hole condensation, leading to true off-diagonal long-range order. In Model Series B, we focus on HFS with hybrid dipole-quadrupole conservation. For both series, we introduce Bose-Hubbard–type lattice models that reduce to either of both series in the weak Hubbard interaction regime. We perform a mean-field analysis on the global phase diagram and discuss experimental realizations in strongly tilted optical lattices via a third-order perturbation theory. This work, alongside prior studies, completes a trilogy on fractonic superfluids, uncovering symmetry-breaking physics emerging from higher moment conservation, leaving various promising studies for future investigation.

We present a general recipe to describe topological phase transitions in condensed matter systems with interactions. We show that topological invariants in the presence of interactions can be efficiently calculated by means of a non-Hermitian quasiparticle Hamiltonian introduced on the basis of the Green's function. As an example analytically illustrating the application of the quasiparticle concept, we consider a topological phase transition induced by the short-range electrostatic disorder in a two-dimensional system described by the Bernevig-Hughes-Zhang model. The latter allows us to explicitly demonstrate the change in the ${\mathbb{Z}}_2$ topological invariant and explain the quantized values of the longitudinal conductance in a certain range of the Fermi energy and the disorder strength found previously in numerical calculations.

Motivated by the magnetism of pyrochlore oxides, we consider the effect of quantum fluctuations in the most general symmetry-allowed nearest-neighbor Kramers exchange Hamiltonian on the pyrochlore lattice. At the classical level, this Hamiltonian exhibits a rich landscape of classical spin liquids and a variety of nonconventional magnetic phases. In contrast, much remains unclear for the quantum model, where quantum fluctuations have the potential to alter the classical landscape and stabilize novel magnetic phases. Employing state-of-the-art pseudofermion functional renormalization group calculations for the spin-$1/2$ model, we determine the quantum phase diagram at relevant cross-sections, where the classical model hosts an algebraic nodal rank-2 spin liquid and a spin nematic order. We find large regions in parameter space where dipolar magnetic order is absent, and, based on known fingerprints in the correlation functions, we suggest that this nonconventional region is composed of an ensemble of distinct phases stabilized by quantum fluctuations. Our results hint at the existence of a spin nematic phase, and we identify the quantum analog of the classical rank-2 spin liquid. Furthermore, we highlight the importance of assessing the subtle interplay of quantum and thermal fluctuations in reconciling the experimental findings on the nature of magnetic order in ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$.

Many systems, classical or quantum, closed or open, exhibit universal statistical properties. Exciton–polariton condensates, being intrinsically driven-dissipative, offer a promising platform for observing nonequilibrium universal features. By conducting extensive numerical simulations of an incoherently pumped and interacting condensate coupled to an exciton reservoir we show that the effective nonlinearity of the condensate phase dynamics can be finely adjusted across a broad range, by varying the exciton–polariton interaction strength, allowing one to probe three main universal regimes with parameters accessible in current experiments: the weakly nonlinear Edwards-Wilkinson (EW) regime, where the phase fluctuations dominate, but the phase profile does not become rough, the strongly nonlinear Kardar-Parisi-Zhang regime, where the condensate phase fluctuations grow in a superdiffusive manner leading to roughening of the phase, and a vortex-dominated phase emerging at stronger interactions, where both density and phase dynamics play significant roles. Our results provide a unified picture of the phase diagram of two-dimensional exciton–polariton condensates under incoherent pumping, and shed light on recent experimental and numerical observations.

We develop a suitable technique to design zero-energy graphene models with radial electrostatic potentials capable of achieving electrostatic confinement. Using the Gaussian law for electrostatics, we derive the charge density associated with these potentials that correspond to concentric electrostatic rings. The technique is based on a modified supersymmetric transformation that allows us to design time-reversal invariant interaction terms and to find the corresponding zero-energy bound states in analytical form. Consequently, solutions with the same probability density but different angular momentum are characterized by circular probability currents flowing in opposite directions. The energies of the systems defined in two Dirac valleys (one-valley) have a fourfold (twofold) degeneracy. As an example of the technique, we construct a ring-decorated Coulomb potential that exhibits zero-energy collapse and bound states together.

Finding an exact ground state of a three-dimensional (3D) Ising spin glass is proven to be an NP-hard problem (i.e., at least as hard as any problem in the nondeterministic polynomial-time (NP) class). Given validity of the exponential time hypothesis, its computational complexity was proven to be no less than $2^{N^{2/3}}$, where $N$ is the total number of spins. Here, we report results of extensive experimentation with D-Wave 3D annealer with $N\le 5627$. We found exact ground states (in a probabilistic sense) for typical realizations of 3D spin glasses with the efficiency, which scales as $2^{N/\beta }$ with $\beta \approx {10}^3$. Based on statistical analysis of low-energy states, we argue that with an improvement of annealing protocols and device noise reduction, $\beta$ can be increased even further. This suggests that, for $N<{\beta }^3$, annealing devices provide most efficient way to find an exact ground state.

The moiré structure of AB-stacked ${\mathrm{MoTe}}_2/{\mathrm{WSe}}_2$ represents a natural platform to realize Kondo lattice models due to the discrepancy of the bandwidth between the individual layers. Here, we study this system at the commensurate filling of ${\nu }_{\mathrm{tot}}=2$. Our focus is on the $1+1$ filling setting of ${\nu }_{\mathrm{Mo}}={\nu }_{\mathrm{W}}=1$, which enables a Kondo lattice description. We find a Kondo semimetal due to the sizable intraorbital hopping among the electrons in the ${\mathrm{MoTe}}_2$ layer. The Kondo-driven (emergent) flat band is naturally pinned to the Fermi energy. When combined with the inherent topology of the electronic structure, a topological Kondo semimetal phase ensues. We calculate the valley Hall response, and due to the breaking of inversion symmetry we also identify a spontaneous Hall effect. There is a Berry curvature dodecapole that leads to a fourth-order spontaneous Hall effect in the perturbative regime of the electric field that is further amplified in the nonperturbative regime. As such, the system provides a tunable setting to simulate topological Kondo semimetals. Finally, we discuss the pathways that connect the physics realized here to the Weyl-Kondo semimetals and their proximate phases,which have been advanced in recent years in topological Kondo lattice models and materials.

A quantitative first-principles description of complex substitutional materials such as alloys is challenging due to the vast number of configurations and the high computational cost of solving the quantum mechanical problem. Therefore, materials properties must be modeled. The cluster expansion (CE) method is widely used for this purpose, but it struggles with properties that exhibit nonlinear dependencies on composition, often failing even in a qualitative description. By looking at CE through the lens of machine learning, we resolve this severe problem and introduce a nonlinear CE approach, yielding extremely accurate and computationally efficient results as demonstrated by distinct examples.

We investigate the real-time dynamics of a quenched quantum impurity immersed in a one-dimensional ultracold Fermi gas, focusing on the breakdown of the adiabatic Born-Oppenheimer approximation due to nonadiabatic effects. Despite a sizable impurity-bath mass imbalance, increasing interactions induce strong nonadiabatic couplings, disrupting adiabatic motion and enabling population transfer between the adiabatic potential energy curves. These transitions are governed by conical intersections arising from the pseudo Jahn-Teller effect, dynamically shaping the impurity's motion through the bath. Using ab initio simulations via the multilayer multiconfiguration time-dependent Hartree method and a multichannel Born-Oppenheimer framework, we track the impurity's evolution and directly prove the dynamical manifestation of the pseudo Jahn-Teller effect. We analyze two key scenarios: (i) a small initial shift, where a single avoided crossing drives transitions, and (ii) a large shift, where multiple avoided crossings lead to enhanced nonadiabaticity, self-trapping, and energy redistribution. Our findings establish ultracold fermionic few-body systems as tunable platforms for studying nonadiabatic quantum dynamics, opening new avenues for controlled impurity transport in strongly correlated environments.

One-dimensional (1D) flat bands in low-dimensional materials enable the study of exotic correlated phases like bond density waves, Luttinger liquids, and Mott insulators. However, the underlying mechanisms driving their formation remain elusive, and achieving well-isolated 1D flat bands in readily achievable systems remains a significant challenge. Here we present a versatile method for engineering tunable 1D flat bands in untwisted bilayer black phosphorus using asymmetric uniaxial strain to achieve differential strain in each layer. Our first-principles calculations reveal that both the highly anisotropic stacking pattern effect and the anisotropic intralayer orbital hybridization between moiré impurities (i.e., local stacking configurations) play critical roles in the formation of 1D flat bands. Notably, asymmetric armchair strain can generate 1D well-isolated flat bands at experimentally accessible strains owing to its pronounced stacking pattern effect. This configuration provides an opportunity to directly observe 1D flat band dispersion using angle-resolved photoemission spectroscopy. Furthermore, we demonstrate that transitioning from 1D to 2D flat bands is possible by applying asymmetric biaxial strain. Our work establishes asymmetric strain as a powerful tool for engineering flat bands in bilayer systems and opens new avenues for exploring 1D strongly correlated electron systems.