Contradictory theoretical results for oxygen vacancies in ${\mathrm{SrTiO}}_3$ (STO) were often related to the peculiar properties of STO, which is a $d^0$ transition metal oxide with mixed ionic-covalent bonding. Here, we apply, for the first time, density functional theory (DFT) within the extended Hubbard $\mathrm{DFT}+U+V$ approach, including onsite as well as intersite electronic interactions, to study oxygen-deficient STO with Hubbard $U$ and $V$ parameters computed self-consistently via density-functional perturbation theory. Our results demonstrate that the extended Hubbard functional is a promising approach to study defects in materials with electronic properties similar to STO. Indeed, $\mathrm{DFT}+U+V$ provides a better description of stoichiometric STO compared to standard DFT or $\mathrm{DFT}+U$, the band gap and crystal field splitting being in good agreement with experiments. In turn, also the description of the electronic properties of oxygen vacancies in STO is improved, with formation energies in excellent agreement with experiments as well as results obtained with the most frequently used hybrid functionals, however, at a fraction of the computational cost. While our results do not fully resolve the contradictory findings reported in literature, our systematic approach leads to a deeper understanding of their origin, which stems from different cell sizes, STO phases, the exchange-correlation functional, and the treatment of structural relaxations and spin-polarization.

The existence or not of Landau poles is one of the oldest open questions in nonasymptotic quantum field theories. We investigate the Landau pole issue in two condensed matter systems whose long-wavelength physics is described by appropriate quantum field theories: the critical quantum magnet and Dirac fermions in graphene with long-range Coulomb interactions. The critical quantum magnet provides a classic example of a quantum phase transition, and it is well described by the ${\varphi }^4$ theory. We find that the irrelevant but symmetry-allowed couplings, such as the ${\varphi }^6$ potential, can significantly change the fate of the Landau pole in the emergent ${\varphi }^4$ theory. We obtain the coupled $\beta$ functions of a ${\varphi }^4+{\varphi }^6$ potential at both small and large orders. Already from the one-loop calculation, the Landau pole is replaced by an ultraviolet fixed point. A Lipatov analysis at large orders reveals that the inclusion of a ${\varphi }^6$ term also has important repercussions for the high-order expansion of the $\beta$ functions. We also investigate the role of the Landau pole in a very different system: Dirac fermions in $2+1$ dimensions with long-range Coulomb interactions, e.g., graphene. Both the weak-coupling perturbation theory up to two loops and a low-order large-$N$ calculation show the absence of a Landau pole. Furthermore, we calculate the asymptotic expansion coefficients of the $\beta$ function. We find that the asymptotic coefficient is bounded by that of a pure bosonic ${\varphi }^4$ theory, and consequently graphene is free from Landau poles if the pure ${\varphi }^4$ theory does not manifest a Landau pole. We briefly discuss possible experiments that could potentially probe the existence of a Landau pole in these systems. Studying Landau poles in suitable condensed matter systems is of considerable fundamental importance since the relevant Landau pole energy scales in particle physics, whether it is quantum electrodynamics or Higgs physics, are completely unattainable.

Linear atomic chains containing a single Kondo atom, Co, and several nonmagnetic atoms, Cu, were assembled atom by atom on Cu(111) with the tip of a scanning tunneling microscope. The resulting one-dimensional wires, ${\mathrm{Cu}}_m{\mathrm{CoCu}}_n$ ($0\le m,n\le 5$), exhibit a rich evolution of the single-Co Kondo effect with the variation of $m$ and $n$, as inferred from changes in the line shape of the Abrikosov-Suhl-Kondo resonance. The most striking result is the quenching of the resonance in ${\mathrm{CuCoCu}}_2$ and ${\mathrm{Cu}}_2{\mathrm{CoCu}}_2$ clusters. State-of-the-art first-principles calculations were performed to unravel possible microscopic origins of the remarkable experimental observations.

We study theoretically the effect of uniaxial deformation of ladder-type cuprate superconductors. Model construction based on first principles calculation shows that the rung-to-leg ratio of the nearest-neighbor hoppings counterintuitively increases when the lattice is compressed in the longitudinal (leg) direction. This leads to an enhancement of the superconducting transition temperature, which intuitively is expected when compressed in the rung direction. Such a trend is traced back to the on-site hybridization between $\mathrm{Cu}4s$ and $\mathrm{Cu}{d}_{x^2-y^2}$ orbitals, which varies and changes sign upon lattice deformation.

Competition between superconductivity and charge order is a recurring theme in contemporary condensed matter physics. This is quintessentially captured in the attractive Hubbard model, a simple theoretical model where the competition can be directly tuned. In previous studies by the current authors, it has been suggested that the Hubbard model maps to an $SO\left(3\right)$ nonlinear sigma model, where the phase competition becomes manifest. In this article, we rigorously demonstrate this mapping and use it to study thermal disordering of a supersolid. Starting with the attractive Hubbard model in the presence of an orbital field, we take the limit of strong coupling where a pseudospin description emerges. The in-plane pseudospin components represent superconducting pairing while the out-of-plane component encodes charge density wave order. We obtain an effective spin-$1/2$ Hamiltonian with ferromagnetic in-plane couplings and antiferromagnetic z-z couplings. In addition, the orbital field gives rise to a textured Dzyaloshinskii-Moriya interaction that has the same periodicity as the magnetic unit cell. In order to examine the nature of ordering in this spin model, we consider it in the classical limit. We assume slowly varying fields, leading to the $SO\left(3\right)$ nonlinear sigma model description. As an application of these ideas, we study the nature of ordering using simulated annealing. The ground state represents a supersolid with coexisting superconductivity and charge order. It can be viewed as a “meron crystal,” a regular arrangement of superconducting vortices with charge-ordered cores. The overlap of core regions gives rise to coherent long-ranged charge order. We study the effect of thermal fluctuations using classical Monte Carlo simulations. We find a sharp phase transition in the Ising universality class where charge order is lost.

We study the effects of quenched disorder and a dissipative Coulomb interaction on an anyon gas in a periodic potential undergoing a quantum phase transition. We use a $(2+1)\text{−}\mathrm{dimensional}$ low-energy effective description that involves $N_f=1$ Dirac fermion coupled to a $U\left(1\right)$ Chern-Simons gauge field at level $(\theta -1/2)$. When $\theta =1/2$ the anyons are free Dirac fermions that exhibit an integer quantum Hall transition; when $\theta =1$ the anyons are bosons undergoing a superconductor-insulator transition in the universality class of the three-dimensional XY model. Using the large $N_f$ approximation we perform a renormalization-group analysis. We find the Coulomb interaction to be an irrelevant perturbation of the clean fixed point for any $\theta$. The dissipative Coulomb interaction allows for two classes of IR stable fixed points in the presence of disorder: those with a finite nonzero Coulomb coupling and dynamical critical exponent $z=1$ and those with an effectively infinite Coulomb coupling and $1<z<2$. At $\theta =1/2$ the clean fixed point is stable to charge-conjugation preserving (random mass) disorder, while a line of diffusive fixed points is obtained when the product of charge-conjugation and time-reversal symmetries is preserved. At $\theta =1$ we find a finite disorder fixed point with unbroken charge-conjugation symmetry whether or not the Coulomb interaction is present. Other cases result in runaway flows. We comment on the relation of our results to other theoretical studies and the relevancy to experiment.

Strongly correlated systems are often associated with an underlying quantum critical point which governs their behavior in the finite-temperature phase diagram. Their thermodynamical and transport properties arise from critical fluctuations and follow universal scaling laws. Here, we develop a microscopic theory of thermal transport in the quantum critical regime expressed in terms of a thermal sum rule and an effective scattering time. We explicitly compute the characteristic scaling functions in a quantum critical model system, the unitary Fermi gas. Moreover, we derive an exact thermal sum rule for heat and energy currents and evaluate it numerically using the nonperturbative Luttinger-Ward approach. For the thermal scattering times we find a simple quantum critical scaling form. Together, the sum rule and the scattering time determine the heat conductivity, thermal diffusivity, Prandtl number, and sound diffusivity from high temperatures down into the quantum critical regime. The results provide a quantitative description of recent sound attenuation measurements in ultracold Fermi gases.

A deep neural network is a parametrization of a multilayer mapping of signals in terms of many alternatively arranged linear and nonlinear transformations. The linear transformations, which are generally used in the fully connected as well as convolutional layers, contain most of the variational parameters that are trained and stored. Compressing a deep neural network to reduce its number of variational parameters but not its prediction power is an important but challenging problem toward the establishment of an optimized scheme in training efficiently these parameters and in lowering the risk of overfitting. Here we show that this problem can be effectively solved by representing linear transformations with matrix product operators (MPOs), which is a tensor network originally proposed in physics to characterize the short-range entanglement in one-dimensional quantum states. We have tested this approach in five typical neural networks, including FC2, LeNet-5, VGG, ResNet, and DenseNet on two widely used data sets, namely, MNIST and CIFAR-10, and found that this MPO representation indeed sets up a faithful and efficient mapping between input and output signals, which can keep or even improve the prediction accuracy with a dramatically reduced number of parameters. Our method greatly simplifies the representations in deep learnin, and opens a possible route toward establishing a framework of modern neural networks which might be simpler and cheaper, but more efficient.

A Rashba nanowire is subjected to a magnetic field that assumes opposite signs in two sections of the nanowire, and, thus, creates a magnetic domain wall. The direction of magnetic field is chosen to be perpendicular to the Rashba spin-orbit vector such that there is only a partial gap in the spectrum. Nevertheless, we prove analytically and numerically that such a domain wall hosts a bound state whose energy is at bottom of the spectrum below the energy of all bulk states. Thus, this magnetically confined bound state is well-isolated and can be accessed experimentally. We further show that the same type of magnetic confinement can be implemented in two-dimensional systems with strong spin-orbit interaction. A quantum channel along the magnetic domain wall emerges with a nondegenerate dispersive band that lies energetically below the bulk states. We show that this magnetic confinement is robust against disorder and various parameter variations.

1T-${\mathrm{TaS}}_2$ is a prototypical charge-density-wave system with a Mott insulating ground state. Usually, a Mott insulator is accompanied by an antiferromagnetic state. However, the antiferromagnetic order had never been observed in 1T-${\mathrm{TaS}}_2$. Here, we report the stabilization of the antiferromagnetic order by the intercalation of a small amount of Fe into the van der Waals gap of 1T-${\mathrm{TaS}}_2$, i.e., forming 1T-${\mathrm{Fe}}_{0.05}{\mathrm{TaS}}_2$. Upon cooling from 300 K, the electrical resistivity increases with a decreasing temperature before reaching a maximum value at around 15 K, which is close to the Néel temperature determined from our magnetic susceptibility measurement. The antiferromagnetic state can be fully suppressed when the sample thickness is reduced, indicating that the antiferromagnetic order in ${\mathrm{Fe}}_{0.05}{\mathrm{TaS}}_2$ has a non-negligible three-dimensional character. For the bulk ${\mathrm{Fe}}_{0.05}{\mathrm{TaS}}_2$, a comparison of our high pressure electrical transport data with that of 1T-${\mathrm{TaS}}_2$ indicates that, at ambient pressure, ${\mathrm{Fe}}_{0.05}{\mathrm{TaS}}_2$ is in the nearly commensurate charge-density-wave phase near the border of the Mott insulating state. The temperature-pressure phase diagram thus reveals an interesting decoupling of the antiferromagnetism from the Mott insulating state.

Parafermion zero modes are exotic emergent excitations that can be considered as ${\mathbb{Z}}_n$ generalizations of Majorana fermions. Present in fractional quantum Hall-superconductor hybrid systems, among others, they can serve as potential building blocks in fault-tolerant topological quantum computing. We propose a system that reveals noise and current signatures indicative of parafermion zero modes. The system is comprised of the edge excitations (“quasiparticles”) of a fractional quantum Hall bulk at filling factor $\nu =1/m$ (for odd integer $m$) incident upon the interface of a superconductor, and in the presence of backscattering. Using perturbative calculations, we derive the current that propagates away from this structure, and its corresponding noise correlation function. Renormalization group analysis reveals a flow from an ultraviolet fixed point of perfect normal reflection towards an infrared fixed point of perfect Andreev reflection. The power law dependence of the differential conductance near these fixed points is determined by $m$. We find that behavior at these two limits is physically distinguishable; whereas near perfect Andreev reflection, the system deviates from equilibrium via tunneling of Cooper pairs between the two edges, near perfect normal reflection this is done via tunneling of a single quasiparticle to an emergent parafermion zero mode at the superconductor interface. These results are fortified by an exact solution.

We study the response of ideal spin systems which are interacting with both a strong oscillating magnetic field, and a thermal environment, to a weak probing magnetic field. We demonstrate that even the sign of the resulting mean magnetization depends on the amplitude of the driving field and that its absolute value can be significantly larger than the equilibrium magnetization in the absence of time-periodic forcing. Since the underlying Floquet-state occupation probabilities are determined by the precise form of the system-bath coupling, future measurements of such effects have the potential to establish a particularly innovative line of research, providing information on nonequilibrium thermodynamics and giving access to quantities which usually remain hidden when probing equilibrium systems.

We predict the existence of non-Hermitian topologically protected end states in a one-dimensional exciton-polariton condensate lattice, where topological transitions are driven by the laser pump pattern. We show that the number of end states can be described by a Chern number and a topological invariant based on the Wilson loop. We find that such transitions arise due to enforced exceptional points which can be predicted directly from the bulk Bloch wave functions. This allows us to establish a new type of bulk-boundary correspondence for non-Hermitian systems and to compute the phase diagram of an open chain analytically. Finally, we demonstrate topological lasing of a single end mode in a realistic model of a microcavity lattice.

Two-dimensional van der Waals crystals and their heterostructures provide an exciting alternative to bulk wide-band-gap semiconductors as hosts of single-photon emitters. Among different layered materials, bright and robust defect-based single-photon emitters have been observed within hexagonal boron nitride, a layered wide-band-gap semiconductor. Despite research efforts to date, the identities of the deep defects responsible for quantum emissions in hexagonal boron nitride remain unknown. In this theoretical work, I demonstrate that the strain-induced changes in emission frequencies depend on (i) the detailed nature of the defect states involved in the optical excitations, and (ii) the rich boron chemistry that results in complex interactions between boron atoms. As each defect shows a distinct response to the strain, it can be used not only to tune emission frequencies but also to identify the quantum emitters in hexagonal boron nitride.

Coupling a many-body system to a thermal environment typically destroys the quantum coherence of its state, leading to an effective classical dynamics at the longest time scales. We show that systems with anyonlike defects can exhibit universal late-time dynamics that is stochastic, but fundamentally nonclassical, because some of the quantum information about the state is topologically protected from the environment. Our coarse-grained model describes one-dimensional systems with domain-wall defects carrying Majorana modes. These defects undergo Brownian motion due to coupling with a bath. Since the fermion parity of a given pair of defects is nonlocal, it cannot be measured by the bath until the two defects happen to come into contact. We examine how such a system anneals to zero temperature via the diffusion and pairwise annihilation of Majorana defects, and we characterize the nontrivial entanglement structure that arises in such stochastic processes. Separately, we also investigate simplified “quantum measurement circuits” in one or more dimensions, involving repeated pairwise measurement of fermion parities for a lattice of Majoranas. The dynamics of these circuits can be solved by exact mappings to classical loop models. They yield analytically tractable examples of measurement-induced phase transitions, with critical entanglement structures that are governed by nonunitary conformal fixed points. In the system of diffusing and annihilating Majorana defects, the relaxation to the ground state is analogous to coarsening in a classical one-dimensional Ising model via domain-wall annihilation (the classical “$A+A\to \varnothing$” reaction-diffusion process). Here, however, configurations are labeled not only by the defect positions but by a nonlocal entanglement structure. This “$\gamma +\gamma \to \varnothing$” process constitutes a universality class for the coarsening of topological domains walls that is distinct from those of classical reaction-diffusion processes. The universal properties of this process can be obtained from an exact mapping.

We present a microscopic theory of heat and particle transport of an interacting, low-temperature Bose-Einstein condensate in a quantum point contact. We show that, in contrast to charged, fermionic superconductors, bosonic systems feature tunneling processes of condensate elements, leading to the presence of odd-order harmonics in the AC Josephson current. A crucial role is played by an anomalous tunneling process where condensate elements are coherently converted into phonon excitations, leading to even-order harmonics in the AC currents as well as a DC contribution. At a low bias, we find dissipative components obeying Ohm's law and bias-independent nondissipative components, in sharp contrast to fermionic superconductors. Analyzing the DC contribution, we find zero thermopower and Lorenz number at zero temperature, a breakdown of the bosonic Wiedemann-Franz law. These results highlight the importance of the anomalous tunneling process inherent to charge-neutral superfluids. The consequences could readily be observed in existing cold-atom transport setups.

There has been growing excitement over the possibility of employing artificial neural networks (ANNs) to gain new theoretical insight into the physics of quantum many-body problems. “Interpretability” remains a concern: can we understand the basis for the ANN's decision-making criteria in order to inform our theoretical understanding? “Interpretable” machine learning in quantum matter has to date been restricted to linear models, such as support vector machines, due to the greater difficulty of interpreting nonlinear ANNs. Here we consider topological quantum phase transitions in models of Chern insulator, ${\mathbb{Z}}_2$ topological insulator, and ${\mathbb{Z}}_2$ quantum spin liquid, each using a shallow fully connected feed-forward ANN. The use of quantum loop topography, a “domain knowledge”–guided approach to feature selection, facilitates the construction of faithful phase diagrams and semiquantitative interpretation of the criteria in certain cases. To identify the topological phases, the ANNs learn physically meaningful features, such as topological invariants and deconfinement of loops. The interpretability in these cases suggests hope for theoretical progress based on future uses of ANN-based machine learning on quantum many-body problems.

The existence of magnetostatic surface spin waves in ferromagnets, known as the Damon-Eshbach mode, was recently demonstrated to originate from the topology of the dipole-dipole interaction. In this work, we study the topological characteristics of magnons in easy-axis antiferromagnets with uniaxial anisotropy. The dipolar spin waves are found to be, driven by the dipole-dipole interaction, in a topological nodal-line semimetal phase, which hosts Damon-Eshbach-type surface modes due to the bulk-edge correspondence. The long-wavelength character of dipolar spin waves makes our proposal valid for any natural uniaxial easy-axis antiferromagnet and, thus, enriches the candidates of topological magnonic materials. In contrast to the nonreciprocal property in the ferromagnetic case, surface modes with opposite momentum coexist at each surface, but with different chiralities. Such chirality-momentum or spin-momentum locking, similar to that of electronic surface states in topological insulators, offers the opportunity to design novel chirality-based magnonic devices in antiferromagnets.

Topological insulators are materials with spectral bands associated with an integer-valued index, manifesting through quantized bulk phenomena and robust boundary effects. In this Rapid Communication, we demonstrate that higher-order topological insulators are descendants from a high-dimensional chiral semimetal. Specifically, we apply dimensional reduction to an ancestor four-dimensional Chern insulator, and obtain two-dimensional (2D) second-order topological insulators when the former becomes chiral. Correspondingly, we derive the quantized charge accumulation at the corners of the 2D descendants and relate it to the topological index—the second Chern number—of the ancestor model. Our results provide a clear connection between the boundary states of higher-order topological insulators and topological pumps—the latter being dynamical realizations of the quantum Hall effect in high dimensions.

Anderson localization in two-dimensional topological insulators takes place via the so-called levitation and pair annihilation process. As disorder is increased, extended bulk states carrying opposite topological invariants move towards each other in energy, reducing the size of the topological gap, eventually meeting and localizing. This results in a topologically trivial Anderson insulator. Here, we introduce the anomalous levitation and pair annihilation, a process unique to periodically driven, or Floquet, systems. Due to the periodicity of the quasienergy spectrum, we find it is possible for the topological gap to increase as a function of disorder strength. Thus, after all bulk states have localized, the system remains topologically nontrivial, forming an anomalous Floquet-Anderson insulator (AFAI) phase. We show a concrete example for this process, adding disorder via on-site potential “kicks” to a Chern insulator model. By changing the period between kicks, we can tune which type of (conventional or anomalous) levitation and annihilation occurs in the system. We expect our results to be applicable to generic Floquet topological systems and to provide an accessible way to realize AFAIs experimentally, without the need for multistep driving schemes.