In the search for accurate approximate solutions of the many-body Schrödinger equation, reduced density matrices play an important role, as they allow one to formulate approximate methods with polynomial scaling in the number of particles. However, these methods frequently encounter the issue of $N$-representability, whereby in self-consistent applications of the methods, the reduced density matrices become unphysical. A number of algorithms have been proposed in the past to restore a given set of $N$-representability conditions once the reduced density matrices become defective. However, these purification algorithms either have ignored symmetries of the Hamiltonian related to conserved quantities or have not incorporated them in an efficient way, thereby modifying the reduced density matrix to a greater extent than is necessary. In this paper, we present an algorithm capable of efficiently performing all of the following tasks in the least invasive manner: restoring a given set of $N$-representability conditions, maintaining contraction consistency between successive orders of reduced density matrices, and preserving all conserved quantities. We demonstrate the superiority of the present purification algorithm over previous ones in the context of the time-dependent two-particle reduced density matrix method applied to the quench dynamics of the Fermi-Hubbard model.

Disorder, traditionally believed to hinder the propagation of waves, has recently been shown to prompt the occurrence of topological phase transitions. For example, when disorder strength continuously increases and surpasses a certain critical value, a transition from topologically trivial to nontrivial insulating phases can occur. However, in the nontrivial phase region, it remains unclear whether a finer phase diagram can be further classified by varying disorder strengths. Here, we present a successive topological phase transition driven by the disorder strength in a higher-order topological insulator with long-range couplings. As the disorder strength gradually increases, the real-space topological invariant of the system undergoes a consecutive change from 0 to 4, accompanied by a stepped increase in the number of boundary-localized corner states. Our work opens a pathway for utilizing disorder to induce phase transitions among different higher-order topological insulators.

We investigate the Hall response of hardcore bosonic atoms on a triangular ladder in a magnetic field. To access the dynamical properties of this many-body quantum system, we employ matrix product states numerical methods. We show that the behavior of the Hall polarization, both in its saturation value and in the short-time dynamics, correlates with the features of the underlying phase diagram, which stem from the interplay of interactions and geometric frustration. This paves the way to employ the Hall response as a sensitive probe of many-body chiral quantum phases in strongly correlated materials.

Building a practical quantum processor involves integrating millions of physical qubits along with the necessary components for individual qubit manipulation and readout. Arrays of gated silicon spins offer a promising route toward achieving this goal. Optimized radio frequency resonators with high internal quality factor are based on superconducting inductors and enable fast spin readout. All-electrical spin control and gate-dispersive readout remove the need for additional device components and simplify scaling. However, superconducting high-Q tank circuits are susceptible to crosstalk-induced ringup from electrical qubit control pulses, which causes fluctuations of the quantum dot potential and is suspected to degrade qubit performance. Here, we report on the coherent and all-electrical control of a hole spin qubit at $1.5\mathrm{K}$, integrated into a silicon fin field-effect transistor and connected to a niobium nitride nanowire inductor gate-sensor. Our experiments show that qubit control pulses with their broad range of higher harmonics ring up the tank when the control pulse spectrum overlaps with the tank resonance. This can cause a reduction of the readout visibility if the tank ringing amplitude exceeds the excited state splitting of the quantum dot, lifting Pauli spin blockade and thus leading to state preparation and measurement errors. We demonstrate how to circumvent these effects by engineering control pulses around the tank resonances. Importantly, we find that the ringup does not limit the spin coherence time, indicating that efficient high-Q resonators in gate-sensing are compatible with all-electrical spin control.

A Bloch point represents a three-dimensional hedgehog singularity of a magnetic vector field in which the magnetization vanishes. However, standard micromagnetic theory, developed for magnetic moments of fixed lengths, lacks full applicability in studying such singularities. To address this gap, we study a Bloch point in a quantum Heisenberg model for the case of spin-1/2 particles. Performing an exact diagonalization of the Hamiltonian as well as using density matrix renormalization group techniques, we obtain the ground state, which can be used to recover the corresponding magnetization profile. Our findings demonstrate a variation of the spin length in the quantum model, leading smoothly to zero magnetization at the Bloch point. Our results indicate the necessity of generalizing the classical micromagnetic model by adding the third degree of freedom of the spins: the ability to change their length. To this end, we introduce a phenomenological micromagnetic ${\mathbb{S}}^3$-model, which enables the description of magnets with and without Bloch point singularities.

Competing interactions in quantum magnets lead to a variety of emergent states, including ordered phases, nematic magnets, and quantum spin liquids. Among them, topological quantum magnets represent a promising platform to create topological excitations protected by the bulk many-body excitation gap. Here we establish the phase diagram of a breathing frustrated antiferromagnetic $J_1\text{−}{J}_2$-Heisenberg model, featuring both ordered states and a higher-order topological quantum magnet state. Using variational many-body methods based on neural network quantum states and tensor networks, we determine the existence of a first-order phase transition between stripe order and the topological quantum magnet and the second-order phase transition between the Néel order and quantum magnet phase, further corroborated by calculations of the many-body gap. Using an auxiliary fermion parton formalism, we show the emergence of topological spinon corner modes stemming from the breathing order parameter of the parent Heisenberg model. Our results establish the breathing frustrated square lattice Heisenberg model as a paradigmatic system to engineer topological quantum magnetism, as recently realized in Ti lattices at MgO.

In this paper, we investigate the local effects of a single impurity on the electron system of a short ballistic graphene Josephson junction. Within the Dirac–Bogoliubov–de Gennes approach, we systematically analyze the local electron density of states. Its behavior at subgap energies allows one to distinguish elastic and inelastic scattering processes and to identify the magnetic nature of the impurity. Moreover, the spatial dependence of the local density of states is a sensitive probe of microscopic processes yielding subgap impurity-induced bound states. The Fourier analysis allows one to recognize the wave vectors related to the momenta of the high-transmissive channels in ballistic graphene.

Superfluidity describes the ability of quantum matter to flow without friction. Due to its fundamental role in many transport phenomena, it is crucial to understand the robustness of superfluid properties to external perturbations. Here, we theoretically study the effects of speckle disorder on the propagation of sound waves in a two-dimensional Bose-Einstein condensate at zero temperature. We numerically solve the Gross-Pitaevskii equation in the presence of disorder and employ a superfluid hydrodynamic approach to elucidate the role of the compressibility and superfluid fraction in the propagation of sound. A key result is that disorder reduces the superfluid fraction and hence the speed of sound; it also introduces damping and mode coupling. In the limit of weak disorder, the predictions for the speed of sound and its damping rate are well reproduced by a quadratic perturbation theory. The hydrodynamic description is valid over a wide range of parameters, while discrepancies become evident if the disorder becomes too strong, the effect being more significant for disorder applied in only one spatial direction. Our predictions are well within the reach of state-of-the-art cold-atom experiments and carry over to more general disorder potentials.

Projected wave functions offer a means of incorporating local correlation effects in gapless electronic phases of matter, like metals. Although such wave functions can be readily specified formally, computing their associated physical observables is challenging. Tensor network approaches offer a modern numerical method for this task. In this paper, we develop and demonstrate a constructive tensor-network approach for obtaining physical quantities, like fermion two-point functions and density-density correlation functions, for one-dimensional projected Fermi sea states. We benchmark our method against exact analytical results for spin-$1/2$ electrons subjected to the Gutzwiller projection, and then present results on spinless fermions with nearest-neighbor repulsion. For a state with two pairs of Fermi points, we reveal a correlation-dependent tuning of the characteristic wave vector of the charge density modulation in the system.

In this work, the term “quantum chaos” refers to spectral correlations similar to those found in the random matrix theory. Quantum chaos can be diagnosed through the analysis of level statistics using, e.g., the spectral form factor, which detects both short- and long-range level correlations. The spectral form factor corresponds to the Fourier transform of the two-point spectral correlation function and exhibits a typical slope-dip-ramp-plateau structure (aka correlation hole) when the system is chaotic. We discuss how this structure could be detected through the quench dynamics of two physical quantities accessible to experimental many-body quantum systems: the survival probability and the spin autocorrelation function. The survival probability is equivalent to the spectral form factor with an additional filter. When the system is small, the dip of the correlation hole reaches sufficiently large values at times which are short enough to be detected with current experimental platforms. As the system is pushed away from chaos, the correlation hole disappears, signaling integrability or localization. We also provide a relatively shallow circuit with which the correlation hole could be detected with commercially available quantum computers.

Bound states and scattering resonances in the unoccupied continuum of a two-dimensional crystal, as predicted in [Phys. Rev. B 87, 041405(R) (2013)], are considered within an exactly solvable model. A close connection of the observed resonances with those arising in the Fano theory is revealed. The resonance occurs when the lateral scattering couples the layer-perpendicular incident electron wave to a strictly bound state. The coupling strength determines the location of the pole in the scattering amplitude in the complex energy plane, which is analytically shown to lead to a characteristic Fano lineshape of the energy dependence of the electron transmissivity through the crystal. The implications for the temporal characteristics of the resonance scattering are discussed. The analytical results are illustrated by ab initio calculations for a graphene monolayer.

We have investigated the surface and bulk electronic structures of the superconducting type-II Dirac semimetal 1T-PdSeTe. The superconducting transition temperature $T_{\text{c}}=3.2$ K was almost twice as high as $T_{\text{c}}=1.6$ K in 1T-${\mathrm{PdTe}}_2$. Scanning transmission electron microscopy measurements showed homogeneously mixed Se and Te atoms in the chalcogen layers, consistent with the ${\mathrm{CdI}}_2$-type crystal structure. Angle-resolved photoemission spectroscopy measurements and density functional theory calculations indicated the existence of the topological surface states, and the overall band structures were similar to those of 1T-${\mathrm{PdTe}}_2$. These results suggest that the ${\mathrm{CdI}}_2$-type lattice symmetry dictates the band dispersion, regardless of atomic disorder in the chalcogen layers. As the electronic band dispersion and the local structures were persistent upon substitution, the enhancement of $T_{\text{c}}$ is likely associated with the chemical pressure. Our results provide insight into the effects of the solid solution on the surface and bulk electronic states as well as the superconducting transition temperature.

Concepts from non-Hermitian quantum mechanics have proven useful in understanding and manipulating a variety of classical systems, such as those encountered in optics, classical mechanics, and metamaterial design. Recently, the non-Hermitian analog of the Berry phase for adiabatic processes was experimentally measured. In non-Hermitian systems, the Berry phase can have an imaginary part, which contributes to the amplification or decay of the total wave intensity. When the imaginary part of the Berry curvature is zero, this geometric amplification factor is determined solely by the initial and final points of the adiabatic path in parameter space, and it does not depend on how these points are connected by the path. We list classes of non-Hermitian Hamiltonians where this path independence is guaranteed by suitable symmetries, and we find that, for some of these classes, the amplification factor can be written only in terms of the Petermann factors of the initial and final points. Our result can, in turn, be used to experimentally obtain the Petermann factor by observing how the norm of the wave function changes under adiabatic processes. We validate our theory using a couple of concrete examples of physical relevance.

We investigate the relationship between the K-edge fine structure of isolated single-wall carbon nanotubes (SWCNTs) and the Van Hove singularities (VHSs) in the conduction-band density of states. To this end, we model x-ray absorption spectra of SWCNTs using the final-state approximation and the Bethe-Salpeter equation (BSE) method. Both methods can reproduce the experimental fine structure, where the BSE results improve on peak positions and amplitude rations compared to the final-state approximation. When the fine structure in the modeled spectra is related to the VHSs, significant differences are found. We suggest that these differences arise due to modifications of the core exciton wave functions induced by the confinement along the circumference. Additionally, we analyze the character of core excitons in SWCNTs, and we find that the first bright excitons are Frenkel excitons, while higher-lying excitons are charge resonance states. Finally, we suggest that the qualitative picture based on VHSs in the density of states holds when there is a large energy gap between successive VHSs.

In the low-energy regime, the Su-Schrieffer-Heeger (SSH) model's key characteristics are encapsulated by a Dirac-type Hamiltonian in continuum space, i.e., localized states emerge at the boundaries. Building on this, we have developed an effective Hamiltonian to model ultracold interacting bosons on an SSH-like lattice through variational minimization under the mean-field approximation. To pinpoint the boundary states, we have developed an algorithm by generalizing the imaginary time propagator, where an initial state evolves under the squared Hamiltonian to converge to the targeted state. This algorithm has broader applicability, enabling the identification of specific eigenstates in various contexts. Furthermore, we draw a parallel to an experimentally physical setup involving a gas of ultracold bosons confined to an array of potential wells with alternating depths. By establishing the system's analogy with the SSH system, we apply our algorithm to investigate boundary states in the presence of interactions, demonstrating how these findings align with those of the continuous system.

An intense terahertz pulse has the potential to control the polarization of ferroelectrics at the subpicosecond time scale. In some ferroelectrics, it has been reported that irradiation with a terahertz pulse on the order of 100 kV/cm modulates the polarization in a manner proportional to the electric field. If a stronger electric field is applied, it may be possible to alter the polarization nonlinearly or even cause it to disappear. However, such attempts have not been reported to date. In this paper, we aim to nonlinearly control ferroelectric polarization by irradiating an organic molecular compound tetrathiafulvalene-$p$-chloranil (TTF-CA), a typical electronic-type ferroelectric, with a terahertz pulse having an electric-field amplitude of up to 2.2 MV/cm. When the temperature is reduced, TTF-CA undergoes a neutral (N) to ionic (I) phase transition at $T_{\mathrm{c}}=81\mathrm{K}$, and the degree of charge transfer $\rho$ from CA to TTF changes from 0.3 to 0.6. In the I phase, it shows the ferroelectricity owing to the collective intermolecular charge transfer at $T_{\mathrm{c}}$. Therefore, if the I-to-N conversion is induced by a strong electric field, the ferroelectric polarization $P$ may change significantly. To investigate the changes in $\rho$ and $P$ along the electric-field waveform of the terahertz pulse in the ferroelectric I phase of TTF-CA, in this paper, a terahertz pump-optical reflectivity probe and second harmonic generation (SHG) probe measurements are performed. For the terahertz electric-field amplitudes $E_{\mathrm{THz}}<0.5\mathrm{MV}/\mathrm{cm}$, the changes in $\rho$ and $P$ are proportional to $E_{\mathrm{THz}}$. When $E_{\mathrm{THz}}>0.5\mathrm{MV}/\mathrm{cm}$ is applied parallel to $P$, the increases in $\rho$ and $P$ tend to become saturated. The increase in P is only ∼10% at a maximum electric-field amplitude of 2.2 MV/cm. In contrast, when $E_{\mathrm{THz}}$ is antiparallel to $P$, the decreases in $\rho$ and $P$ are proportional to $E_{\mathrm{THz}}$ up to 1.5 MV/cm. When $E_{\mathrm{THz}}$ is further increased to values >1.5 MV/cm, a partial I-to-N conversion occurs via quantum electron tunneling processes, and $P$ decreases in a nonlinear manner. The decrease in P reaches ∼30% at 2.2 MV/cm. These nonreciprocal changes in $\rho$ and $P$ are discussed while considering the valence instability characteristic of TTF-CA. Furthermore, several coherent oscillations are observed in the changes of reflectivity and SHG, which reflect the modulations of $\rho$ and $P$ due to molecular vibrations (lattice modes), respectively. A detailed analysis of the amplitudes and phases of these coherent oscillations reveals that a molecular vibration with a frequency of ∼90 $\mathrm{c}{\mathrm{m}}^{-1}$ is driven by changes in $\rho$ induced by a terahertz electric field and modulates $P$ significantly through the changes in the dimeric molecular displacements along the molecular stacking axis, that is, the polarization direction.

Itinerant ferromagnetism is one of the most-studied quantum phase transitions, the transition point and the nature of this phase transition being widely discussed. In dilute Fermi liquids, this analysis has been carried out up to second order in the gas parameter, where the results for any spin degeneracy are universal in terms of only the $s$-wave scattering length $a_0$. We extend this analysis to third order, where energies depend not only on $a_0$, but also on the $s$-wave effective range $r_0$ and the $p$-wave scattering length $a_1$. The introduction in the theory of these new parameters changes the transition point, with respect to the second-order estimation, and also can modify the nature of the phase transition itself. We analyze these interaction effects on the phase transition for different spin values. The emerging phase diagram shows that the type of ferromagnetic transition changes dramatically as a function of $r_0$ and $a_1$ and, importantly, that this classification is not solely determined by the spin value, as happens at second order.

We study a two-terminal Josephson junction with conventional superconductors and a normal region with a Rashba spin-orbit interaction, characterized by two Aharonov-Casher (AC) fluxes. When the superconducting phase difference equals $\pi$, the Andreev subgap spectrum may host zero-energy Weyl singularities associated with a vanishing normal-state reflection eigenvalue. With one of the AC fluxes playing the role of a quasimomentum, the junction can be viewed as an artificial one-dimensional chiral topological insulator. Its topological phase can be tuned by crossing a Weyl singularity by means of varying the remaining AC flux. By associating an additional component of the quasimomentum with the superconducting phase difference, an artificial Chern insulator is realized.