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.

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)].

We show that three-dimensional (3D) Dirac semimetals (DSMs) can achieve highly efficient terahertz high-order harmonic generation (HHG) up to the 31st harmonic with input intensities $\approx 10\mathrm{M}\mathrm{W}/{\mathrm{cm}}^2$—over ${10}^5$ times lower than required in conventional terahertz HHG systems. Our theory reveals that this extreme nonlinearity is made possible by the existence of an operation regime that differs from previous demonstrations of lower order harmonic generation. We also reveal an unexpected regime in which emitted harmonics abruptly become negligible beyond the third order. This unprecedented vanishing of higher order nonlinearity has a geometrical origin related to the combination of conical dispersion and extra dimensionality in 3D DSMs, breaking the common notion that 3D DSMs share the essential physics of two-dimensional DSMs. Our findings pave the way to unlocking the full potential of 3D DSMs as efficient platforms for terahertz light sources and optoelectronics at moderate intensities.

We demonstrate the existence of universal features in the finite-time thermodynamics of quantum machines by considering a many-body quantum Otto cycle in which the working medium is driven across quantum critical points during the unitary strokes. Specifically, we consider a quantum engine powered by dissipative energizing and relaxing baths. We show that under very generic conditions, the output work is governed by the Kibble-Zurek mechanism; i.e., it exhibits a universal power-law scaling with the driving speed through the critical points. We also optimize the finite-time thermodynamics as a function of the driving speed. The maximum power and the corresponding efficiency take a universal form, and are reached for an optimal speed that is governed by the critical exponents. We exemplify our results by considering a transverse-field Ising spin chain as the working medium. For this model, we also show how the efficiency and power vary as the engine becomes critical.

We have investigated electron tunneling through an atomically smooth square potential barrier for both the dice lattice and graphene under a linearly polarized off-resonant and high-frequency dressing field. We have demonstrated Klein tunneling for a nonzero angle of incidence which is due to a nonalignment of optically controllable elliptical energy dispersions for the dressed states of Dirac particles and the direction of incoming kinetic particles. This finite angle of incidence has been found to depend on the light-induced anisotropy of energy dispersion, which is a function of the electron-light coupling strength, as well as the misalignment between directions of the light polarization and the electron beam incident on the potential barrier. Additionally, we have discovered much larger off-peak transmission amplitudes for dice lattices in contrast to graphene. We anticipate that the theoretical predictions could be applied to a wide range of Dirac materials and exploited for controlling both coherent tunneling and ballistic transport of electrons in the construction of novel electronic, optical, and valleytronic nanoscale switching devices.

Operator square roots are ubiquitous in theoretical physics. They appear, for example, in the Holstein-Primakoff representation of spin operators and in the Klein-Gordon equation. Often the use of a perturbative expansion is the only recourse when dealing with them. In this paper, we show that under certain conditions, differential equations can be derived which can be used to find perturbatively inaccessible approximations to operator square roots. Specifically, for the number operator $\widehat{n}=a^{†}a$ we show that the square root $\sqrt{\widehat{n}}$ near $\widehat{n}=0$ can be approximated by a polynomial in $\widehat{n}$. This result is unexpected because a Taylor expansion fails. A polynomial expression in $\widehat{n}$ is possible because $\widehat{n}$ is an operator, and its constituents $a$ and $a^{†}$ have a non trivial commutator $[a,a^{†}]=1$ and do not behave as scalars. We apply our approach to the zero-mass Klein-Gordon Hamiltonian in a constant magnetic field and, as a main application, the Holstein-Primakoff representation of spin operators, where we are able to find new expressions that are polynomial in bosonic operators. We prove that these new expressions exactly reproduce spin operators. Our expressions are manifestly Hermitian, which offers an advantage over other methods, such as the Dyson-Maleev representation.

We propose an effective field theory (EFT) of fractional quantum Hall systems near the filling fraction $\nu =5/2$ that flows to pertinent IR candidate phases, including non-Abelian Pfaffian, anti-Pfaffian, and particle-hole Pfaffian states (Pf, APf, and PHPf). Our EFT has a $(2+1)\text{D} \mathrm{O}{\left(2\right)}_{2,L}$ Chern-Simons gauge theory coupled to four Majorana fermions by a discrete charge-conjugation gauge field, with Gross-Neveu-Yukawa-Higgs terms. Including deformations via a Higgs condensate and fermion mass terms, we can map out a phase diagram with tunable parameters, reproducing the prediction of the recently proposed percolation picture and its gapless topological quantum phase transitions. Our EFT captures known features of both gapless and gapped sectors of time-reversal-breaking domain walls between Pf and APf phases. Moreover, we find that $\mathrm{Pf}\mid \mathrm{APf}$ domain walls have higher tension than domain walls in the PHPf phase. Then the former, if formed, may transition to the energetically favored PHPf domain walls; this could, in turn, help further induce a bulk transition to PHPf.

In this work, we report a ubiquitous presence of topological Floquet time crystal ($\mathrm{TFTC}$) in one-dimensional periodically driven systems. The rigidity and realization of spontaneous discrete time-translation symmetry ($\mathrm{DTS}$) breaking in our $\mathrm{TFTC}$ model require necessarily coexistence of anomalous topological invariants (0 modes and $\pi$ modes), instead of the presence of disorders or many-body localization. We found that in a particular frequency range of the underlying drive, the anomalous Floquet phase coexistence between 0 and $\pi$ modes can produce the period doubling ($2T$, two cycles of the drive) that breaks the $\mathrm{DTS}$ spontaneously, leading to the subharmonic response ($\omega /2$, half the drive frequency). The rigid period-$2T$ oscillation is topologically protected against perturbations due to both nontrivially opening of 0 and $\pi$ gaps in the quasienergy spectrum, thus, as a result, can be viewed as a specific “Rabi oscillation” between two Floquet eigenstates with certain quasienergy splitting $\pi /T$. Our modeling of the time-crystalline “ground state” can be easily realized in experimental platforms such as topological photonics and ultracold fields. Also, our work can bring significant interest to explore topological phase transition in Floquet systems and to bridge the gap between Floquet topological insulators and photonics, and period-doubled time crystals.

We improve the efficiency of the minimally entangled typical thermal states (METTS) algorithm without breaking the Abelian symmetries. By adding the operation of Trotter gates that respects the Abelian symmetries to the METTS algorithm, we find that a correlation between successive states in Markov-chain Monte Carlo sampling decreases by orders of magnitude. We measure the performance of the improved METTS algorithm through the simulations of the canonical ensemble of the Bose-Hubbard model and confirm that the reduction of the autocorrelation leads to the reduction of computation time. We show that our protocol using the operation of Trotter gates is effective also for the simulations of the grand canonical ensemble.

We consider a mesoscopic superconducting island hosting multiple pairs of Majorana zero-energy modes. The Majorana island consists of multiple $p$-wave wires connected together by a trivial ($s$-wave) superconducting backbone and is characterized by an overall charging energy $E_C$; the wires are coupled to normal-metal leads via tunnel junctions. We calculate the average charge on the island as well as nonlocal conductance matrix as a function of a $p$-wave pairing gap ${\mathrm{\Delta }}_P$, charging energy $E_C$, and dimensionless junction conductances $g_i$. We find that the presence of a topological ground-state degeneracy in the island dramatically enhances charge fluctuations and leads to the suppression of Coulomb blockade effects. In contrast with conventional ($s$-wave) mesoscopic superconducting islands, we find that Coulomb blockade oscillations of conductance are suppressed in Majorana islands regardless of the ratio $E_C/{\mathrm{\Delta }}_P$ or the magnitude of the conductances $g_i$. We also discuss our findings in relation to the so-called topological Kondo effect.

Magnon emission and excitation by a relativistic domain wall at a constant velocity in antiferromagnets is theoretically studied. A pair emission due to a quadratic magnon coupling is shown to be dominant. The emission corresponds in the comoving frame to a vacuum polarization induced by a zero-energy instability of the Lorentz-boosted anomalous response function. The emission rate is sensitive to the magnon dispersion and wall profile, and is significantly enhanced for a thin wall with velocity close to the effective light velocity. The Ohmic damping constant due to magnon excitation at low velocity is calculated.

We propose a minimal lattice model for two-dimensional class DIII superconductors with $C_2$-protected higher-order topology. Although this class of superconductors cannot be topologically characterized by symmetry eigenvalues at high-symmetry momenta, we propose a simple Wannier-orbital-based real-space diagnosis to unambiguously capture the corresponding higher-order topology. We further identify and characterize a variety of conventional topological phases in our minimal model, including a weak topological superconductor and a nodal topological superconductor with chiral-symmetry protection. The disorder effect is also systematically studied to demonstrate the robustness of higher-order bulk-boundary correspondence. Our theory lays the groundwork for predicting and diagnosing $C_2$-protected higher-order topology in class DIII superconductors.

Pd-intercalated ${\mathrm{ErTe}}_3$ is studied as a model system to explore the effect of “intertwined” superconducting and charge density wave (CDW) orders. Despite the common wisdom that superconductivity emerges only when CDW is suppressed, we present data from STM and ac susceptibility measurements that show no direct competition between CDW order and superconductivity. Both coexist over most of the intercalation range, with uniform superconductivity over length scales that exceed the superconducting coherence length. This is despite persisting short-range CDW order and increased scattering from the Pd intercalation. While superconductivity is insensitive to local defects in either of the bidirectional CDWs, vestiges of the Fermi-level distortions are observed in the properties of the superconducting state.

By gauging a higher-moment polynomial degree global symmetry and a discrete charge conjugation (i.e., particle-hole) symmetry coupled to matter fields (two symmetries mutually noncommutative), we derive a class of higher-rank tensor non-Abelian gauge field theory with dynamically gauged fractonic matter fields: Non-Abelian gauged fractons interact with a hybrid class of higher-rank (symmetric or generic nonsymmetric) tensor gauge theory and antisymmetric tensor topological field theory, generalizing work by Wang and Xu (arXiv:1909.13879) and by Wang, Xu, and Yau (arXiv:1911.01804). We also apply a quantum phase transition similar to that between insulator and superfluid/superconductivity [U(1) symmetry disordered phase described by a topological gauge theory or a disordered sigma model vs U(1) global/gauge symmetry-breaking ordered phase described by a sigma model with a U(1) target space underlying Goldstone modes]: We can regard our tensor gauge theories as disordered phases, and we transition to their ordered phases by deriving sigma models in continuum field theories. While one low energy theory is captured by degrees of freedom of rotor or scalar modes, another side of low energy theory has vortices and superfluids; we explore non-Abelian vortices (two types of vortices mutually interacting noncommutatively beyond an ordinary group structure) and their Cauchy-Riemann relation.

Unlike anomalous quantum Hall insulators, clean single-band chiral superconductors do not exhibit intrinsic Hall effect at the one-loop approximation. Finite ac Hall conductance was found to emerge beyond one loop, such as with vertex corrections associated with extrinsic random impurity scatterings. In this paper, we investigate the effect of impurities embedded in single-band chiral superconductors in a superlattice pattern, instead of in random distributions. The impurity-induced Bogoliubov quasiparticle bound states hybridize to form subgap bands, constituting an emergent low-energy effective theory whose Hall effect can be studied with ease. We demonstrate that the occurrence of the Hall effect depends on the superlattice geometry and on the parity of the chiral pairing. In particular, due to the mixed particle-hole character of the subgap states, the Hall conductance may arise at the one-loop level of the current-current correlator in our effective model. Our theory provides an insight into the impurity-induced anomalous Hall effect in chiral superconductors.

We report the influence of the excitation conditions on the emission behavior of a carbon-nanodot-based microcavity. The emission properties under nanosecond excitation indicate room-temperature lasing with a lasing threshold of $0.1{\mathrm{Jcm}}^{-2}$. The input-output characteristic is also dependent on the repetition rate of the excitation source. Higher repetition rates generate more heat in the gain medium, which increases the losses in the cavity and has a negative impact on the emission characteristics.

We propose to induce a time-crystalline state in a high-$T_c$ superconductor, by optically driving a sum resonance of the Higgs mode and a Josephson plasma mode. The generic cubic process that couples these fundamental excitations converts driving of the sum resonance into simultaneous resonant driving of both modes, resulting in an incommensurate subharmonic motion. We use a numerical implementation of a semiclassical driven-dissipative lattice gauge theory on a three-dimensional layered lattice, which models the geometry of cuprate superconductors, to demonstrate the robustness of this motion against thermal fluctuations. We demonstrate this light-induced time-crystalline phase for mono- and bilayer systems and show that this order can be detected for pulsed driving under realistic technological conditions.

The phenomenon of metastability can shape dynamical processes on all temporal and spatial scales. Here, we induce metastable dynamics by pumping ultracold bosonic atoms from the lowest band of an optical lattice to an excitation band, via a sudden quench of the unit cell. The subsequent relaxation process to the lowest band displays a sequence of stages, which include a metastable stage, during which the atom loss from the excitation band is strongly suppressed. Using classical-field simulations and analytical arguments, we provide an explanation for this experimental observation, in which we show that the transient condensed state of the atoms in the excitation band is a dark state with regard to collisional decay and tunneling to a low-energy orbital. Therefore the metastable state is stabilized by destructive interference due the chiral phase pattern of the condensed state. Our experimental and theoretical study provides a detailed understanding of the different stages of a paradigmatic example of many-body relaxation dynamics.

We show that chiral (nearly) flat band superconductivity can develop and host novel Majorana fermions at a time-reversal pair of symmetry-protected three-band crossing points. Based on symmetry analysis, mean-field study, and superfluid stiffness calculation, we determine and analyze the irreducible pairing channels with flat band pairings in the low-energy spin-1 fermion theory. Flat band pairing can enhance superconductivity dramatically, where the critical temperature scales linearly in the interaction strength. While fully gapped flat band pairing states develop in the single-component pairing channels, we find chiral $\overline{p}\pm i\overline{p}$ flat band superconductivity in the multicomponent pairing channels. Three-dimensional itinerant Majorana fermions arise at the bulk nodal points, whereas Majorana arcs appear on the surface.