Machine-learning algorithms thrive on large data sets of good quality. Here we show that they can also excel in a typical research setting with little data of limited quality, through an interplay of insights coming from machine and human researchers. The question we address is the unsolved problem of ordering out of a spin-liquid phase described by an emergent rank-2 $\text{U}\left(1\right)$ gauge theory, as described by H. Yan et al. [Phys. Rev. Lett. 124, 127203 (2020)]. Published Monte Carlo simulations for this problem are consistent with a strong first-order phase transition, but were too noisy for the form of low-temperature order to be identified. Using a highly interpretable machine-learning approach based on a support vector machine with a tensorial kernel, we reanalyze these Monte Carlo data, gaining new information about the form of order that could in turn be interpreted by traditionally trained physicists. We find that the low-temperature ordered phase is a form of magnetic order analogous to a smectic liquid crystal. This arises due to a subtle thermal order-by-disorder mechanism, that can be understood from the fluctuations of the tensor electric field of the parent rank-2 gauge theory. These results were obtained by a back-and-forth process which closely resembles a collaboration between human researchers and machines. We argue that this “collaborative” approach may provide a blueprint for solving other problems that have not yielded to human insights alone.

We investigate the hollowing transition of a shell-shaped Bose-Einstein condensate using collective excitations. The shell is created using an immiscible dual-species Bose-Einstein condensate mixture, with its hollowness controlled by tuning the repulsive interspecies interaction via a Feshbach resonance. Our results reveal two distinct monopole modes in which the two condensates oscillate either in phase or out of phase. The spectrum of the out-of-phase mode exhibits a nonmonotonic dependence on the interspecies interaction, providing a clear signature of the topology change from a filled to a hollow condensate. Furthermore, we find that the critical point of the hollowing transition depends strongly on the number ratio of the two species. Our findings provide a detailed understanding of the topology change in shell-shaped quantum gases and pave the way for future study of quantum many-body phenomena in curved spaces.

We investigate the ergodicity-to-localization transition in interacting fermion systems subjected to a spatially uniform electric field. For that, we employ the recently proposed tensorflow equations (TFE), a type of continuous unitary flow equations. This enables us to iteratively determine an approximate diagonal basis of the quantum many-body system. We present improvements to the method, which achieves good accuracy at small to intermediate interaction strengths, even in the absence of an electric field or disorder. Then, we examine two quantities that reveal the fate of Stark MBL in 1D and 2D. First, we investigate the structure of the resulting basis to determine the crossover between ergodic and localized regimes with respect to electric field strength. Second, we simulate long-time dynamics at infinite temperature. Our results in 1D show a localization transition at nonzero field for finite interaction that vanishes with increasing system size leading to localization at infinitesimally small field even in the presence of interactions. In 2D, we find less clear signatures of localization and strong finite-size effects. We establish that the TFE work accurately up to intermediate times but cannot capture higher order effects in interaction strength that lead to delocalization at longer times in finite-size Stark MBL systems.

We observed magnetocapacitance oscillations in InAs/GaSb quantum wells separated by a $20\mathrm{nm}$ AlSb middle barrier. By realizing independent ohmic contacts for electrons in InAs and holes in the GaSb layer, we found an out-of-plane oscillatory response in capacitance representing the density of states of this system. We were able to tune the charge carrier densities by applying a DC bias voltage, identifying the formation of beating signatures for forward bias. The coexistence of two distinguishable two-dimensional ($2\mathrm{D}$) charge carrier systems of unequal densities was verified. By developing a theory to describe the magnetocapacitance response of the system, we were able to validate that we have an electron-hole bilayer system. The Landau phase diagram presents distinct features originating from the bilayer channel with the additional presence of a $2\mathrm{D}$ electron system at the surface of the InAs layer.

The dc conductivity tensor of two-dimensional one-band metals with weak pointlike disorder and magnetic field is studied in the self-consistent Born approximation, with special emphasis on the regime of low carrier density. In this theory, the Kubo conductivity is a functional of the electron dispersion and local (momentum-independent) electron self-energy, which is itself a causal functional of the dispersion and disorder strength. We obtain closed expressions for the asymptotic low-density conductivities at zero temperature in the form of power laws of the density and disorder strength with universal exponents. The crossover to the semiclassical regime of high density is studied numerically, as well as the temperature dependence. Our model and results may be relevant to interpret linear magnetotransport experiments performed in the metallic regime of gated two-dimensional semiconductors.

We show that a composite quantum system described by the tensor product of multiple systems each with a leading-order exceptional point (a non-Hermitian degeneracy at which not only eigenvalues but also eigenstates coalesce) exhibits a single leading-order exceptional point, whose order surpasses the order of any constituent exceptional point. The formation of such higher-order exceptional points does not require coupling among the subsystems. We determine explicitly the order and the spectral response strength of this exceptional point. Moreover, we observe that the energy eigenstates that do not merge are entangled. Finally, we demonstrate that general initial states disentangle during time evolution due to the presence of the higher-order exceptional point of the composite system.

In kagome metals, flat electronic bands induced by frustrated hopping are a platform for strong electron correlations. Here, we investigate the superconductivity in the kagome system ${\mathrm{LaRu}}_3{\left({\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x\right)}_2$ by chemical pressure tuning while preserving the Ru-$4d$ states that constitute the kagome flat bands. We observe a sizable enhancement in the density of states up to $x=0.07$, as determined by the specific heat, with a concomitant increase in the superconducting transition temperature $T_{\mathrm{c}}$. Ge dopants induce a uniaxial lattice expansion along the $c$ axis. Our first-principles calculations suggest that this mitigates the detrimental effect of hybridization between kagome layers and reduces the dispersion of the Ru-$d_{x^2-y^2}$ flat band. The calculated chemical potential moves closer to the maximum in the energy-dependent density of states. Our result is consistent with a theoretical prediction of tunable flat-band superconductivity in ${\mathrm{LaRu}}_3{\mathrm{Si}}_2$ by mode-selective coupling between specific kagome phonons and the Ru-$d_{x^2-y^2}$ orbitals.

We construct an observable mixed-state topological order parameter for symmetry-protected free-fermion matter. It resolves the entire table of topological insulators and superconductors, relying exclusively on the symmetry class, but not on unitary symmetries. It provides a robust, quantized signal not only for pure ground states, but also for mixed states in or out of thermal equilibrium. Key ingredient is a unitary probe operator, whose phase can be related to spectral asymmetry, in turn revealing the topological properties of the underlying state. This is demonstrated analytically in the continuum limit, and validated numerically on the lattice. The order parameter is experimentally accessible via either interferometry or full counting statistics, for example, in cold-atom experiments.

The orbital angular momentum (OAM) of electron states is an essential ingredient for topological and quantum geometric quantities in solids. For example, Dirac surface states with helical spin- and orbital-angular momenta are a hallmark of a 3D topological insulator. Angle-resolved photoemission spectroscopy (ARPES) with variable circular light polarization, known as circular dichroism (CD), has been assumed to be a direct probe of OAM and, by proxy, of the Berry curvature of electronic bands in energy- and momentum-space. Indeed, topological surface states have been shown to exhibit angle-dependent CD (CDAD), and more broadly, CD is often interpreted as evidence of spin-orbit coupling. Meanwhile, it is well-established that CD originates from the photoemission matrix elements, which can have extrinsic contributions related to the experimental geometry and the inherently broken inversion symmetry at the sample surface. Therefore, it is important to broadly examine CD-ARPES to determine the scenarios in which it provides a robust probe of intrinsic material physics. We performed CD-ARPES on the canonical topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ over a wide range of incident photon energies. Not only do we observe angle-dependent CD in the surface states, as expected, but we also find CD of a similar magnitude in virtually all bulk bands. Since OAM is forbidden by inversion symmetry in the bulk, we conclude this originates from symmetry-breaking in the photoemission process. Comparison with theoretical calculations supports this view and suggests that “hidden” OAM—localized to atomic sites within each unit cell—contributes significantly. Additional effects, including inter-atomic interference and final-state resonances, are responsible for the rapid variation of the CDAD signal with photon energy.

We have measured the magneto-optical Kerr effect (MOKE) in an orthorhombic organic antiferromagnet $\kappa \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{Cu}\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]\mathrm{Cl}$ (κ-Cl), which is a candidate for an altermagnet. From the Maxwell equations, we derived matrix-type general formulae describing the optical propagation and reflection for arbitrary crystals. These formulae enabled us to correctly measure and obtain the off-diagonal optical responses of κ-Cl. The MOKE of κ-Cl appeared at around the Néel temperature and exhibited a nonlinear field dependence in the antiferromagnetic phase. This nonlinear field dependence eliminates a simple origin due to the net canted magnetization. The obtained off-diagonal optical conductivity spectra for the entire π-electron band clearly show three features. One is the large peaks at the spectral ends due to the magnetic origin with the large energy scale compared to the very small spin-orbit interaction in κ-Cl. The others are the middle region spectra proportional to the diagonal conductivities, possibly related to the symmetric piezomagnetic effect and the standard antisymmetric origins. These results suggest the altermagnetic response of κ-Cl. We also discuss the analogy between the magnetization in ferromagnets and the net magnetization and Néel vector with respect to the magneto-optical configurations.

Quantum fluctuations are pivotal in driving quantum phase transitions, exemplified by the quantum melting of Wigner crystals into Fermi liquids in electron systems. However, their impact on superconducting systems near zero temperature, particularly in the superconductor-insulator/metal transition, remains an open question. In this study, through electric transport measurements on the two-dimensional (2D) superconductor ${\left(\mathrm{SnS}\right)}_{1.17}{\mathrm{NbS}}_2$, we demonstrate that quantum fluctuations induce vortex displacement from their mean position, leading to the quantum melting of vortex solid near zero temperature. Quantitative analysis suggests the magnetic field-induced anomalous metal originates from this quantum melting transition, with energy dissipation governed by quantum fluctuations-driven vortex displacements. Remarkably, further extending this analysis to various 2D superconductors yields the same results, and many properties of anomalous metal can be qualitatively understood within the framework of quantum melting. The connection between the quantum melting of vortex solids and dissipative anomalous metal opens a pathway toward understanding quantum phase transitions through vortex dynamics, providing insights on both fields.

We investigate the role of interlayer interaction terms in the competition between different superconducting gap symmetries in the bilayer nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ under high pressure. We study a two-layer, two-orbital electron model that encompasses both intra- and interlayer Coulomb interaction terms within the matrix random-phase approximation. We find that interlayer interactions favor a $d_{xy}$-wave superconducting pairing symmetry over the $s^{\pm }$-wave symmetry, which has been found to prevail when interlayer interactions are disregarded. Moreover, our findings indicate that interlayer interactions enhance the interorbital pairing, incorporating contributions from all three electron pockets, arising from both $d_{3z^2-r^2}$ and $d_{x^2-y^2}$ orbital characters, resulting in nodes within the gap function (not present in the $s^{\pm }$-wave state) and consequently favoring the $d_{xy}$-wave pairing.

We consider the spreading of a local operator $A$ in one-dimensional many-body systems with Hamiltonian $H$ by calculating the $k$-fold commutator $[H,[H,[...,[H,A\left]\right]\left]\right]$. We derive bounds for the operator norm of this commutator in free and interacting systems with and without disorder thus directly connecting the operator growth hypothesis with questions of localization. We analytically show, in particular, that an almost-factorial growth of the operator norm—as recently proven for the random Ising model and strongly suggested here to also hold for the Heisenberg model with random fields—is inconsistent with an exponential localization of $A$. Assuming there exists a quasilocal unitary $U$ which maps $H$ onto an effective Hamiltonian $\tilde{H}=UH{U}^{†}={\sum }_n{E}_n{\tau }_n^z+{\sum }_{i,j}{J}_{ij}{\tau }_i^z{\tau }_j^z+\cdots$, we show that $\tilde{A}=UA{U}^{†}$ is a quasilocal operator which, in contrast to the Anderson case, indeed does not remain exponentially localized in the general many-body case, leading to an almost-factorial growth of the commutator norm. Therefore, either the unitary $U$ in many-body systems with maximal norm growth does not exist, and such systems are always ergodic, or unusual nonergodic phases described by $\tilde{H}$ exist which violate the operator growth hypothesis and in which local operators spread over the entire lattice, implying that transport will eventually set in. To investigate this issue further, we concentrate on the XXZ chain with random magnetic fields. We analytically and symbolically verify our general results for the noninteracting Anderson and Aubry-André models. For the XXX case, the symbolic calculations are consistent with a maximal norm growth. Furthermore, we find no indication of a weakened exponential localization of $A$, expected for strong disorder and low commutator orders if the unitary $U$ does exist. Finally, we study the differences between the interacting and noninteracting cases when trying to perturbatively construct $U$ by consecutive Schrieffer-Wolff transformations. While it is straightforward to show that this construction converges in the Anderson case, we find no indications for a convergence in the interacting case, suggesting that $U$ does not exist and that many-body localization is absent.

Quantum simulation of lattice gauge theories (LGTs) provides a powerful framework for understanding nonperturbative phenomena. However, to realize the hope of answering challenging physics questions on near-term devices it is crucial to develop resource-efficient formulations, in particular for non-Abelian LGTs and beyond (1+1) dimensions. In this work, we address this issue by focusing on the difficulty of simulating fermionic degrees of freedom and on mitigating the Hilbert space redundancy, i.e., the presence of exponentially many nonphysical states that do not obey gauge invariance. First, we show a procedure that removes the matter and improves the hardware-resource efficiency. We demonstrate it for the simplest non-Abelian group addressable with this procedure, ${\mathbb{D}}_8$, in the cases of both one and two spatial dimensions. Then, with the objective of running a variational quantum simulation on real quantum hardware, we map the ${\mathbb{D}}_8$ LGT onto qudit systems with local interactions. We propose a variational scheme for the qudit system with a local Hamiltonian, which can be implemented on a universal qudit quantum device. Our results show the effectiveness of the matter-removing procedure, solving the redundancy problem, and reducing the amount of quantum resources. This approach can serve as a way of simulating LGTs in high spatial dimensions, with non-Abelian gauge groups, and including dynamical fermions.

Open dissipative systems of quantum fluids have been well studied numerically. In view of a complementary analytical description, we extend here the variational optimization method for Bose-Einstein condensates of closed systems to open-dissipative condensates. The resulting projection optimization method is applied to a complex Gross-Pitaevskii equation, which models a photon Bose-Einstein condensate. Together with known methods from hydrodynamics, we obtain an approximate vortex solution, which depends on the respective open system parameters and has the same properties as obtained numerically in the literature.

The study of charge current fluctuations (noise) can give useful insights into the properties of nanoscale systems. In this work, the peculiar properties of noise in multiterminal hybrid normal-superconducting systems are explored in the thermal out-of-equilibrium regime, i.e., when temperature biases are present ($\mathrm{\Delta }T$-noise). Using the Landauer-Büttiker approach, we identify two contributions: background noise and excess noise, analyzing them when both electrical and thermal biases are applied. When temperature biases are present, and superconducting terminals are grounded, we find that the first contribution depends not only on the electrical conductance, as the Johnson-Nyquist at equilibrium, but also on a quantity strictly related to the heat conductance. This is our first main result. On the other hand, the second contribution shows, as expected, additional terms originating from the partitioning of currents into different transport channels, including the ones associated with Andreev reflection processes. However, noise induced by the temperature differences unveils also interference terms that cannot be present either in voltage bias or in the absence of any Andreev processes. Finally, we apply the results obtained to two different specific physical situations. The first is a generic three-terminal normal-superconductor-normal system and the second is a device based on spin-resolved copropagating chiral channels in the integer quantum Hall regime with a superconducting region. In these example setups, we investigate mainly the shot-noise regimes, when high-voltage or high-temperature biases are applied. We find remarkable differences between the two limits, which ultimately show the different nature of electrically and thermally induced charge current fluctuations.

Time-dependent Wannier functions were initially proposed as a means for calculating the polarization current in crystals driven by external fields. In this work, we present a simple gauge where Wannier states are defined based on the maximally localized functions at the initial time, and are propagated using the time-dependent Bloch states obtained from established first-principles calculations, avoiding the costly Wannierization at each time step. We show that this basis efficiently describes the time-dependent polarization of the laser-driven system through the analysis of the motion of Wannier centers. We use this technique to analyze highly nonlinear and nonperturbative responses such as high-harmonic generation in solids, using hexagonal boron nitride as an illustrative example, and we show how it provides an intuitive picture for the physical mechanisms.

We consider one-dimensional, interacting spinless bosons on a tight-binding lattice described by the Bose-Hubbard model. Besides attractive onsite two-body interactions, we include a three-body repulsive term such that the competition between these two forces allows the formation of self-bound liquid states. We investigate the properties of this system using the Gutzwiller approximation, showing that, indeed, this mean-field approach also supports liquid states. We find that for densities lower than the equilibrium density, the Gutzwiller method and other mean-field approaches—such as the Gross-Pitaevskii theory—feature a sharp transition to the vacuum state. This, however, is avoided by considering local minima of the functional in the standard manner. We also study the excitation spectrum, and calculate the speed of sound, in full agreement with the usual expression obtained from the thermodynamic equation of state. We study their corresponding quantum droplets variationally and find that the results behave in accordance with the one-dimensional liquid-drop model.