We present a general symmetry-based framework for obtaining many-body Hamiltonians with scarred eigenstates that do not obey the eigenstate thermalization hypothesis. Our models are derived from parent Hamiltonians with a non-Abelian (or $q$-deformed) symmetry, whose eigenspectra are organized as degenerate multiplets that transform as irreducible representations of the symmetry (“tunnels”). We show that large classes of perturbations break the symmetry, but in a manner that preserves a particular low-entanglement multiplet of states, thereby giving generic, thermal spectra with a shadow of the broken symmetry in the form of scars. The generators of the Lie algebra furnish operators with “spectrum-generating algebras” that can be used to lift the degeneracy of the scar states and promote them to equally spaced “towers.” Our framework applies to several known models with scars, but we also introduce models with scars that transform as irreducible representations of symmetries such as SU(3) and $q$-deformed SU(2), significantly generalizing the types of systems known to harbor this phenomenon. Additionally, we present examples of generalized Affleck-Kennedy-Lieb-Tasaki (AKLT) models with scar states that do not transform in an irreducible representation of the relevant symmetry. These are derived from parent Hamiltonians with enhanced symmetries, and bring AKLT-type models into our framework.

We establish the theory of critical transport in amorphous Chern insulators and show that it lies beyond the current paradigm of topological criticality epitomized by the quantum Hall transitions. We consider models of Chern insulators on percolation-type random lattices where the average density determines the statistical properties of geometry. While these systems display a two-parameter scaling behavior near the critical density, the critical exponents and the critical conductance distributions are strikingly nonuniversal. Our analysis indicates that the amorphous topological criticality results from an interpolation of a geometric-type transition at low density and an Anderson localization-type transition at high density. Our work demonstrates how the recently discovered amorphous topological systems display unique phenomena distinct from their conventionally studied counterparts.

We analyze the topological properties of a chiral $p+ip$ superconductor for a two-dimensional metal and semimetal with four Dirac points. Such a system has been proposed to realize second-order topological superconductivity and host corner Majorana modes. We show that with an additional ${\mathsf{C}}_4$ rotational symmetry, the system is in an intrinsic higher-order topological superconductor phase, and with a lower ${\mathsf{C}}_2$ symmetry, is in a boundary-obstructed topological superconductor phase. The boundary topological obstruction is protected by a bulk Wannier gap. However, we show that the well-known nested Wilson loop is in general unquantized despite the particle-hole symmetry, and thus fails as a topological invariant. Instead, we show that the higher-order topology and boundary-obstructed topology can be characterized using an alternative defect classification approach, in which the corners of a finite sample are treated as a defect of a space-filling Hamiltonian. We establish “$\mathrm{Dirac}+(p+ip)$” as a sufficient condition for second-order topological superconductivity.

We reveal polaron signatures in the spectral function of $n$-doped ${\mathrm{SrTiO}}_3$ and ZnO through first-principles interacting Green's function calculations. In ${\mathrm{SrTiO}}_3$ we observe a clear replica band at 94 meV below the conduction band, which shows that the observed replica in recent angle-resolved photoemission spectroscopy experiment is an intrinsic feature from electron-phonon coupling in ${\mathrm{SrTiO}}_3$. In contrast, we observe an elongated tail in the spectral function for ZnO but no well-separated replicas. By increasing the electron doping level, we identify kinks in the spectral function at phonon frequencies and a decreasing intensity of the tail structure. We find that the curvature of the conduction band bottom vanishes due to additional electron-phonon scattering channels enabled by increased occupied states at high-enough doping levels, beyond which the spectral function becomes a stronger quasiparticle one with a single peak structure. We further compare the spectral function computed from the Migdal-Dyson approach and the cumulant method, and show that the cumulant method can correctly reproduce the polaronic features observed in experiments.

Ion-specific interactions with materials are important for the design of ion-based energy and information devices, which are studied here with a focus on alkali-earth-metal and transition-metal ions in the context of carbon nanofluidics. Density functional theory calculations show that for the alkali-earth-metal ions, the nature of interaction is ionic, with charge transfer to and from graphene determined by the change in work function. In contrast, covalent bonding is identified for transition-metal ions adsorbed on graphene, showing hybridization near the Dirac point. The ion-graphene interaction is significantly stronger than van der Waals interactions and shows much higher contrast among the ions. We find that, surprisingly, these features are robust even with the presence of water solvation, where alkali-earth-metal ion-graphene interaction remains ionic with modified charge transfer, while covalent interaction with transition-metal ions turns into ionic. These understandings imply that the ion-wall interaction can be notably tuned by the external electric field, as verified by our calculations, and opens an avenue for the development of nanofluidics where the channel width is comparable with the range of ion-wall interaction.

Nematic orders emerge nearly universally in iron-based superconductors, but elucidating their origins is challenging because of intimate couplings between orbital and magnetic fluctuations. The iron-based ladder material ${\mathrm{BaFe}}_2{\mathrm{S}}_3$, which superconducts under pressure, exhibits antiferromagnetic order below $T_{\mathrm{N}}\sim 117$ K and a weak resistivity anomaly at $T^{*}\sim 180$ K, whose nature remains elusive. Here we report angle-resolved magnetoresistance (MR) and elastoresistance (ER) measurements in ${\mathrm{BaFe}}_2{\mathrm{S}}_3$, which reveal distinct changes at $T^{*}$. We find that MR anisotropy and ER nematic response are both suppressed near $T^{*}$, implying that an orbital order promoting isotropic electronic states is stabilized at $T^{*}$. Such an isotropic state below $T^{*}$ competes with the antiferromagnetic order, which is evidenced by the nonmonotonic temperature dependence of nematic fluctuations. In contrast to the cooperative nematic orders in spin and orbital channels in iron pnictides, the present competing orders can provide an alternative platform to identify the separate roles of orbital and magnetic fluctuations.

We propose a quantum-classical hybrid algorithm to simulate the nonequilibrium steady state of an open quantum many-body system, named the dissipative-system variational quantum eigensolver (dVQE). To employ the variational optimization technique for a unitary quantum circuit, we map a mixed state into a pure state with a doubled number of qubits and design the unitary quantum circuit to fulfill the requirements for a density matrix. This allows us to define a cost function that consists of the time evolution generator of the quantum master equation. Evaluation of physical observables is, in turn, carried out by a quantum circuit with the original number of qubits. We demonstrate our dVQE scheme by both numerical simulation on a classical computer and actual quantum simulation that makes use of the device provided in Rigetti quantum cloud service.

Electrons in type II Weyl semimetals display one-way propagation, which supports totally reflecting behavior at an endpoint, as one has for black hole horizons viewed from the inside. Junctions of type I and type II lead to equations identical to what one has near black hole horizons, but the physical implications, we suggest, are quite different from expectations which are conventional in that context. The time-reversed, “white hole” configuration is also physically accessible.

We present a scheme comprising a one-dimensional system with repulsive interactions, in which the formation of bound pairs can take place in an easily tunable fashion. By capacitively coupling a primary electronic quantum wire of interest to a secondary strongly correlated fermionic system, the intrinsic electron-electron repulsion may be overcome, promoting the formation of bound electron pairs in the primary wire. The intrinsic repulsive interactions tend to favor the formation of charge density waves of these pairs, yet we find that superconducting correlations are dominant in a limited parameter regime. Our analysis shows that the paired phase is stabilized in an intermediate region of phase space, encompassed by two additional phases: a decoupled phase, where the primary wire remains gapless, and a trion phase, where a primary electron pair binds a charge carrier from the secondary system. Tuning the strength of the primary-secondary interaction, as well as the chemical potential of the secondary system, one can control the different phase transitions. Our approach takes into account the interactions among the secondary degrees of freedom and strongly relies on their highly correlated nature. Extension of our proposal to two dimensions is discussed, and the conditions for a long-range superconducting order from repulsion only are found. Our physical description, given by a simple model with a minimal amount of ingredients, may help to shed some light on pairing mechanism in various low-dimensional strongly correlated materials.

We show that in superfluids with fermionic imbalance and uniform ground state, there are stable solitons. These solutions are formed of radial density modulations resulting in nodal rings. We demonstrate that these solitons exhibit nontrivial soliton-soliton and soliton-vortex interactions and can form complicated bound states in the form of “soliton sacks.” In a phase-modulating (Fulde-Ferrell) background, we find different solitonic states, in the form of stable vortex-antivortex pairs.

Understanding the mechanisms governing the optical activity of layered-stacked materials is crucial to the design of devices aimed at manipulating light at the nanoscale. Here, we show that both twisted and slid bilayer graphene are chiral systems that can deflect the polarization of linear polarized light. However, only twisted bilayer graphene supports circular dichroism. Our calculation scheme, which is based on the time-dependent Schrödinger equation, is particularly efficient for calculating the optical-conductivity tensor. Specifically, it allows us to show the chirality of hybridized states as the handedness-dependent bending of the trajectory of kicked Gaussian wave packets in bilayer lattices. We show that nonzero optical Hall conductivity is the result of the noncanceling manifestation of hybridized states in chiral lattices. We also demonstrate the continuous dependence of the conductivity tensor on the twist angle and the sliding vector.

Despite tremendous theoretical efforts to understand subtleties of the many-body localization (MBL) transition, many questions remain open, in particular concerning its critical properties. Here we make the key observation that MBL in one dimension is accompanied by a spin freezing mechanism which causes chain breaks in the thermodynamic limit. Using analytical and numerical approaches, we show that such chain breaks directly probe the typical localization length and that their scaling properties at the MBL transition agree with the Kosterlitz-Thouless scenario predicted by phenomenological renormalization group approaches.

We present a detailed study of the ground-state phase diagram of the classical frustrated Heisenberg model on the face-centered-cubic lattice. By considering exchange interactions to third nearest neighbors, we find commensurate, helimagnetic, as well as noncollinear, multi-Q orders which include noncoplanar and chiral spin structures. We reveal the presence of subextensively degenerate manifolds that appear at triple points and certain phase boundaries in the phase diagram. Within these manifolds, the spin Hamiltonian can be recast as a complete square of spins on finite motifs, permitting us to identify families of exact ground-state spin configurations in real space—these include randomly stacked ferro- or antiferromagnetically ordered planes and interacting ferromagnetic chains, among others. Finally, we critically investigate the ramifications of our findings on the example of the Ising model, where we exactly enumerate all the states numerically for finite clusters.

We study critical Fermi surfaces in generic dimensions arising from coupling finite-density fermions with transverse gauge fields by applying a dimensional regularization scheme developed previously [Phys. Rev. B 92, 035141 (2015)]. We consider the cases of $U\left(1\right)$ and $U\left(1\right)\times U\left(1\right)$ transverse gauge couplings and extract the nature of the renormalization group (RG) flow fixed points as well as the critical scalings. Our analysis allows us to treat a critical Fermi surface of a generic dimension $m$ perturbatively in an expansion parameter $\epsilon =\left(2-m\right)/\left(m+1\right).$ One of our key results is that although the two-loop corrections do not alter the existence of an RG flow fixed line for certain $U\left(1\right)\times U\left(1\right)$ theories, which was identified earlier for $m=1$ at one-loop order, the third-order diagrams do. However, this fixed line feature is also obtained for $m>1$, where the answer is one-loop exact due to UV/IR mixing.

We study positions of chiral hinge states in higher-order topological insulators (HOTIs) with inversion symmetry. First, we exhaust all possible configurations of the hinge states in the HOTIs in all type-I magnetic space groups with inversion symmetry by studying dependence of the sign of the surface Dirac mass on surface orientations. In particular, in the presence of glide symmetry, for particular surface orientations, the surface Dirac mass changes sign by changing the surface terminations. By applying this result to a layered antiferromagnet, we find a difference in the hinge states between the cases with an even and odd number of layers. In the case of an even number of layers, which does not preserve inversion symmetry, positions of hinge states are not inversion symmetric. Nonetheless, these inversion-asymmetric hinge states result from the bulk topology. We show that their inversion-asymmetric configurations are uniquely determined from the symmetries and the topological invariant.

We point out the emergence of magnetism from the interplay of electron quasi-itinerancy and quantum order by disorder in pyrochlore iridates. Like other Mott insulating iridates, the ${\mathrm{Ir}}^{4+}$ ion in pyrochlore iridates develops an effective $J=1/2$ moment from the on-site spin-orbit coupling. We consider the generic symmetry-allowed exchange between these local moments on a pyrochlore lattice and obtain the mean-field phase diagram. Assuming the superexchange is mediated by direct and/or indirect electron hopping via intermediate oxygens, we derive the exchange interactions in the strong-coupling regime from the Hubbard model. This exchange has a degenerate classical ground-state manifold, and quantum fluctuation selects a noncoplanar ground state, known as quantum order by disorder. Extending to the intermediate-coupling regime, the same noncoplanar order is selected from the degenerate manifold by the kinetic energy, which is dubbed “electron quasi-itinerancy.” We discuss the experimental relevance of our results and electron quasi-itinerancy among other iridates and $4d/5d$ magnets.

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.