Determining the low-energy eigenspectra of quantum many-body systems is a long-standing challenge in physics. In this paper, we solve this problem by introducing two algorithms to determine low-energy eigenstates based on a compact matrix product state (MPS) representation of multiple targeted eigenstates. The first algorithm utilizes a canonicalization approach that takes advantage of the imaginary-time evolution of multitarget MPSs, offering faster convergence and ease of implementation. The second algorithm employs a variational approach that optimizes local tensors on the Grassmann manifold, capable of achieving higher accuracy. These algorithms can be used independently or combined to enhance convergence speed and accuracy. We apply them to the transverse-field Ising model and demonstrate that the calculated low-energy eigenspectra agree remarkably well with the exact solution. Moreover, the eigenenergies exhibit uniform convergence in gapped phases, suggesting that the low-energy excited eigenstates have nearly the same level of accuracy as the ground state. Our results highlight the accuracy and versatility of multitarget MPS-based algorithms for determining low-energy eigenspectra and their potential applications in quantum many-body physics.

While magnetic fields generally compete with superconductivity, a type II superconductor can persist to very high fields by confining the field within the topological defects, namely the vortices. We propose that a similar physics underlies the pseudogap phase in the cuprates, where the relevant topological defects—antiphase domain walls of an underlying antiferromagnetic (AFM) order—confine the excess charges. A key consequence of this scenario is that the termination of the pseudogap phase should be captured accurately by the underlying AFM model. We demonstrate that this picture can explain a number of key experimentally observed signatures of the pseudogap phase and how it collapses in the cuprates. Gap inhomogeneity is found to be necessary to produce the characteristic Fermi arcs.

In this paper, we consider an unconventional doping effect of strongly correlated cerium $4f$ electrons in layered intermetallic systems. The conduction electron part of the model is taken to reproduce the hole and electron pockets of iron-based superconductors (FeSCs), and the cerium contribution is studied through an effective tight-binding Hamiltonian arising from the slave-boson mean-field theory of the periodic Anderson model. We show how the consideration of the nonlocal Kondo coupling naturally present in real materials can lead to a pocket-selective doping effect from cerium $f$ electrons. The model is designed for paramagnetic materials of the ZrCuSiAs-type structure such as CeFeSiH, CeFePO, or the high-pressure phase of CeFeAsO. In certain conditions, the model shows a Lifshitz transition which can be induced by either doping or change in the hybridization strength between iron and cerium orbitals. We present some signatures of both pocket-selective doping and Lifshitz transition by means of the density of states at the Fermi level, the static spin susceptibility, the optical conductivity, and Raman spectroscopy.

Plasmons are fundamental excitations of metals which can be described in terms of electron dynamics, or in terms of the electromagnetic fields associated with them. In this work we develop a quantum description of plasmons in a double layer structure, treating them as confined electromagnetic modes of the structure. The structure of the resulting bosonic Hamiltonian indicates the presence of virtual plasmons of the individual layers which appear as quantum fluctuations in the ground state. For momenta smaller than the inverse separation between layers, these modes are in the ultrastrong coupling regime. Coherence terms in the Hamiltonian indicate that modes with equal and opposite momenta are entangled. We consider how in principle these entangled modes might be accessed, by analyzing a situation in which the conductivity of one of the two layers suddenly drops to zero. The resulting density matrix has a large entanglement entropy at small momenta, and modes at $\pm \mathbf{q}$ that are inseparable. More practical routes to releasing and detecting entangled plasmons from this system are considered.

Despite extensive studies, strong localization of electromagnetic waves in three dimensions has never been experimentally achieved. Stepping out of the paradigm of disordered systems, we carry out microwave transport experiments in planar aperiodic Vogel spiral arrays of cylinders with high dielectric permittivity. We characterize the electromagnetic modal structure in real space showing mixtures of long-lived modes with Gaussian, exponential, and power-law spatial decay. This unique modal structure, which cannot be found in traditional periodic or disordered photonic materials, is shown to be at the origin of strong localization of electromagnetic waves that survives even in a three-dimensional environment.

We investigate a system of two coupled qubits interacting with an Ohmic bath as a physical model for the implementation of one logical qubit. In this model, the interaction with the other qubit represents unitary noise, while the Ohmic bath is responsible for finite temperature. In the presence of a one-dimensional decoherence-free subspace (DFS), we show that, while this is not sufficient to protect a qubit from decoherence, it can be exploited to encode one logical qubit with greater performance than the physical one. We show different possible strategies for the optimal encoding of a logical qubit through a numerical analysis based on matrix product states. This method reproduces faithfully the results of perturbative calculations, but it can be extended to cases of crucial interest for physical implementations, e.g., in the case of strong coupling with the bath. As a result, a logical qubit encoded in the subspace which is the direct sum of the antiferromagnetic states in the Bell basis, namely the DFS and the antiferromagnetic state in the triplet, is the optimally robust one, as it takes advantage of both the anchoring to the DFS and the protection from the antiferromagnetic interaction.

The lattice thermal conductivity (LTC) of ${\mathrm{ZrSe}}_2$, a typical layered transition metal disulfide, has been calculated using a hybrid approach that combines force field molecular dynamics (MD) simulation and Boltzmann transport equation (BTE). In this approach, the phonon quasiparticle picture of each normal mode can be obtained directly by the velocity autocorrelation function and its power spectrum projected in $q$ space. By employing the retarded one phonon Green's function method, the phonon quasiparticle frequency and lifetime of each independent normal mode are effectively determined. On-the-fly machine learning force fields combine the precision of quantum mechanics and the scale of classical MD to analyze sizable supercells with long-wavelength phonons. This yields accurate LTC by using sufficient $q$ samples in the Brillouin zone, which cannot be achieved at the ab initio molecular dynamics scale. The convergent LTC tensor of bulk and monolayer ${\mathrm{ZrSe}}_2$ decays faster with increasing temperature than the well-known $\frac{1}{T}$ scale, which is typically observed when considering only three phonon scattering. The phonon lifetime and mean free path exhibit significant dependence on temperature. MD simulations encompass all orders of anharmonic effects, thereby enabling an accurate description of anharmonic interactions between phonons at finite temperatures. Moreover, this approach respects the contribution of each normal mode to the LTC based on the BTE, which facilitates the quantitative analysis of phonon anharmonic properties and the role of specific normal modes.

An extended domain wall (DW) in the presence of the Dzyaloshinskii-Moriya interaction can harbor a nontrivial spin texture inside it, which is called the DW skyrmion due to its topological equivalence to skyrmions in chiral magnets. In this study we develop a theory for the dynamics of the DW skyrmion and demonstrate, using micromagnetic simulations, that the DW skyrmion exhibits the skyrmion Hall effect akin to conventional skyrmions. Notably, we find that, distinct from the conventional skyrmion Hall effect induced by the current, the DW skyrmion Hall effect can be induced not only by a current, but also by a uniform magnetic field. We also find that, by exploiting the fact that the spin-transfer torque and magnetic field result in the skyrmion Hall effect in different directions, it is possible to adjust the net skyrmion Hall angle, including elimination of the skyrmion Hall angle. Our work shows that the DW skyrmion can exhibit topological dynamics that are absent in conventional skyrmions, which leads us to envision that skyrmionics may benefit from further investigations of its properties.

Based on the first-principles linear response method and Monte Carlo simulation, we investigate the magnetic properties of single-layer transition metal dihalides $M{X}_2$ $(M=\mathrm{V}, \mathrm{Cr}, \mathrm{Mn}, \mathrm{Fe}, \mathrm{Co}, \mathrm{Ni}; X=\mathrm{Cl}, \mathrm{Br}, \mathrm{I})$. We calculate the magnetic exchange interactions using the first-principles linear response method and find that the third-nearest-neighbor interaction of most dihalides is very important. When spin-orbit coupling is included, $\mathrm{Fe}{X}_2$ and $\mathrm{Cr}{X}_2$ $(X=\mathrm{Cl}, \mathrm{Br}, \mathrm{I})$ are predicted to be insulators. Using the parameters of the exchange interactions and magnetic anisotropy, the magnetic ground states of transition metal dihalide monolayers are obtained by Monte Carlo simulation. Moreover, we find that the magnetic ground states of ten $M{X}_2$ monolayers are independent of the $U$ value. Among them, the magnetic ground state of ${\mathrm{CrI}}_2$ is ferromagnetic, the magnetic ground state of ${\mathrm{CrCl}}_2$ is collinear antiferromagnetic, the magnetic ground states of ${\mathrm{VCl}}_2$, ${\mathrm{FeI}}_2$, and $\mathrm{Co}{X}_2$ $(X=\mathrm{Br}, \mathrm{I})$ are ${120}^{\circ }$ antiferromagnetic, and the magnetic ground states of ${\mathrm{FeCl}}_2$ and $\mathrm{Ni}{X}_2$ $(X=\mathrm{Cl}, \mathrm{Br}, \mathrm{I})$ are helimagnetic.

We consider a pair of identical fermions with a short-range attractive interaction on a finite lattice cluster in the presence of strong site disorder. This toy model imitates a low-density regime of the strongly disordered Hubbard model. In contrast to spinful fermions, which can simultaneously occupy a site with minimal energy and thus always form a bound state resistant to disorder, for the identical fermions the probability of pairing on neighboring sites depends on the relation between the interaction and the disorder. The complexity of “brute-force” calculations (both analytical and numerical) of this probability grows rapidly with the number of sites even for the simplest cluster geometry in the form of a closed chain. Remarkably, this problem is related to the old mathematical task of computing the volume of a polyhedron, known as NP-hard. However, we have found that the problem in the chain geometry can be exactly solved by the transfer matrix method. Using this approach, we have calculated the pairing probability in the long chain for an arbitrary relation between the interaction and the disorder strengths and completely describe the crossover between the regimes of coupled and separated fermions.

The delocalization-localization (DL) transition in non-Hermitian systems is a fascinating phenomenon with distinct characteristics compared to their Hermitian counterparts. In our study, we deal with the DL transition in a generalized non-Hermitian lattice. The non-Hermitian behavior arises due to asymmetry in the hoppings and the complex nature of the quasiperiodic (QP) potentials. We demonstrate that the interplay between these two leads to more diverse and intricate phases. For identical modulation of the real and the complex parts of the QP potential, we obtain the analytical expression of the critical point that precisely captures the DL transition for systems with periodic boundary conditions (PBC). Our numerical investigations reveal that the critical point remains unchanged even with open boundary conditions (OBC). One particularly fascinating aspect of our findings is the emergence of a mixed phase between the delocalized and localized regions in systems with nonidentical modulation of the real and complex parts of the QP potential. This mixed phase presents a remarkable coexistence of skin modes and localized states for systems with OBC, while systems with PBC exhibit a coexistence of delocalized and localized states within the mixed phase. To provide further insights into the underlying physics, we construct comprehensive phase diagrams, shedding light on the crucial role of various parameters in a broad range of non-Hermitian QP lattices.

Large valley polarization and perpendicular magnetocrystalline anisotropy energy (PMAE) in room-temperature ferrovalley materials has been pursued for a long time because PMAE not only stabilizes long-range ferromagnetic (FM) order but also ensures spontaneous valley polarization. Herein, valley polarization and MAE of monolayer $M{X}_2$ ($M=\mathrm{Ru},\mathrm{Os}$; $X=\mathrm{Cl},\mathrm{Br}$) are investigated based on first-principles calculations, Wannier functions, and Monte Carlo simulations. It is found that $\mathrm{Os}{\mathrm{Br}}_2$ has a giant valley polarization of 327.158 meV and PMAE of 10.354 meV, ascribing to the strong spin-orbital coupling. The physical mechanism of valley polarization and PMAE are analyzed both qualitatively and quantitatively on the basis of perturbation theory, which shows that the valley polarization induces the distribution of MAE at $K$ and $K^{\prime }$ valley points with opposite signs, and the couplings between $d_{z^2}$ and $d_{yz}, d_{xz}$ and $d_{xy}$, and $d_{x^2\text{−}{y}^2}$ and $d_{yz}$ in opposite spin channels through orbital angular momentum operator ${\widehat{L}}_x$ have a dominant contribution to the total MAE. Moreover, doping of a few holes and biaxial compressive strain both remarkably improve the PMAE of $\mathrm{Os}{\mathrm{Br}}_2$. Meanwhile, the compressive strain can enhance FM exchange coupling of $\mathrm{Os}{\mathrm{Br}}_2$, increasing the Curie temperature $T_c$ far beyond the room temperature. Additionally, doping of a few electrons can significantly increase the PMAE of room-temperature ferrovalley $\mathrm{Os}{\mathrm{Cl}}_2$ to reach ∼40 meV. In this paper, we elucidate the physical mechanism of the valley polarization and MAE and indicate that monolayer $\mathrm{Os}{\mathrm{Cl}}_2$ and $\mathrm{Os}{\mathrm{Br}}_2$ are promising for application in valleytronic and magnetic storage devices at room-temperature condition.

${\mathrm{ReS}}_2$ and ${\mathrm{ReSe}}_2$ are less frequently studied transition metal dichalcogenides. They appear in the $1T^{\prime }$ phase with a significantly reduced symmetry compared with, for example, ${\mathrm{MoS}}_2$, while inversion symmetry is preserved. Several broad peaks have been observed in previous experimental measurements. The interpretation of their physical origin and properties is a challenging task without the help of theoretical insights. Here, we employ ab initio $GW$-Bethe-Salpeter equation calculations to investigate the optical properties of neutral and charged monolayers. We present a detailed analysis of the low-energy excitons and trions. In agreement with experiment, we find that the neutral excitons are strongly bound. In contrast, only a tiny trion binding energy of <10 meV is found. By artificially manipulating the spin-orbit coupling (SOC), we demonstrate its importance for the internal structure of the transitions. Interestingly, we find two optically active low-energy excitons. Both stem from transitions between the same valence and conduction bands. In the absence of SOC, only one peak (singlet) can be bright. Therefore, additional peaks are a direct manifestation of SOC on the optical properties.

The interplay of Kondo screening and magnetic ordering in strongly correlated materials containing local moments is a subtle problem. Usually the number of conduction electrons per unit cell matches or exceeds the number of moments, and a Kondo-screened heavy Fermi liquid develops at low temperatures. Changing the pressure, magnetic field, or chemical doping can displace this heavy Fermi liquid in favor of a magnetically ordered state. Alternatively, Kondo singlet formation can be suppressed when the number of conduction electrons is small compared to the number of magnetic moments, known as the Kondo exhaustion scenario. Here we report the discovery of such an “exhausted” Kondo lattice material, ${\mathrm{YbIr}}_3{\mathrm{Si}}_7$, where the bulk electrical conductivity tends to zero in the antiferromagnetic state below the Néel temperature $T_{\mathrm{N}}=4.1\mathrm{K}$, as all the free carriers are consumed in the formation of Kondo singlets. By contrast, the surface is conducting, as the ${\mathrm{Yb}}^{3+}$ ions relax into larger nonmagnetic ${\mathrm{Yb}}^{2+}$ in the presence of reduced chemical pressure, which shifts the chemical potential.

Charged domain walls in ferroelectric materials exhibit nontrivial electronic and transport properties, which have promising application in many electronic devices, such as high-density nonvolatile memories. Taking advantage of oxygen vacancy engineering, charged domain walls are introduced into the $\mathrm{PbTi}{\mathrm{O}}_3/\mathrm{LaCo}{\mathrm{O}}_{2.5}$ superlattice system, and the quasi-two-dimensional electron gas is formed near the domain walls, featuring an intrinsic $n$-type conductive characteristic. The charged domain walls can be erased by eliminating oxygen vacancies in the $\mathrm{LaCo}{\mathrm{O}}_{2.5}$, resulting in an insulating state. The proposed scheme of writing and erasing of charged domain walls may facilitate the development of domain wall based devices.

We study two-dimensional electron systems confined in wide quantum wells whose subband separation is comparable with the Zeeman energy. Two $N=0$ Landau levels from different subbands and with opposite spins are pinned in energy when they cross each other and electrons can freely transfer between them. When the disorder is strong, we observe clear hysteresis in our data corresponding to the instability of the electron distribution in the two crossing levels. When the intralayer interaction dominates, multiple minima appear when a Landau level is $\frac{1}{3}$ or $\frac{2}{3}$ filled and the fractional quantum Hall effect can be stabilized.

We present a detailed study of mechanically compliant, photonic crystal based microcavities featuring a quasibound state in the continuum. Such systems were recently predicted to reduce the optical loss in Fabry-Pérot-type optomechanical cavities. However, they require two identical photonic crystal slabs facing each other, which poses a considerable challenge for experimental implementation. We investigate how such an ideal system can be simplified and still exhibit a quasibound state in the continuum. We find that a suspended photonic crystal slab facing a distributed Bragg reflector realizes an optomechanical system with a quasibound state in the continuum. In this system, the radiative cavity loss can be eliminated to the extent that the cavity loss is dominated by dissipative loss originating from material absorption only. These proposed optomechanical cavity designs are predicted to feature optical quality factors in excess of ${10}^5$.

We study a Kondo state that is strongly influenced by its proximity to an ${\omega }^{-1/2}$ singularity in the metallic host density of states. This singularity occurs at the bottom of the band of a one-dimensional chain, for example. We first analyze the noninteracting system: A resonant state ${\varepsilon }_d$, located close to the band singularity, suffers a strong renormalization, such that a bound state (Dirac $\delta$ function) is created below the bottom of the band in addition to a resonance in the continuum. When ${\varepsilon }_d$ is positioned right at the singularity, the spectral weight of the bound state is $\frac{2}{3}$, irrespective of its coupling to the conduction electrons. The interacting system is modeled using the single-impurity Anderson model, which is then solved using the numerical renormalization group method. We observe that the Hubbard interaction causes the bound state to suffer a series of transformations, including level splitting, transfer of spectral weight, appearance of a spectral discontinuity, changes in binding energy (the lowest state moves farther away from the bottom of the band), and development of a finite width. When ${\varepsilon }_d$ is away from the singularity and in the intermediate valence regime, the impurity occupancy is lower. As ${\varepsilon }_d$ moves closer to the singularity, the system partially recovers Kondo regime properties, i.e., higher occupancy and lower Kondo temperature $T_K$. The impurity thermodynamic properties show that the local-moment (LM) fixed point is also strongly affected by the existence of the bound state. When ${\varepsilon }_d$ is close to the singularity, the LM fixed point becomes impervious to charge fluctuations (caused by bringing ${\varepsilon }_d$ close to the Fermi energy), in contrast to the LM suppression that occurs when ${\varepsilon }_d$ is away from the singularity. We also discuss an experimental implementation that shows similar results to the quantum wire if the metallic host of the impurity is an armchair graphene nanoribbon.

The interplay among topology, crystal symmetry, magnetic order, and strong electron correlation can give rise to a plethora of exotic physical phenomena. The ZrSiS family is known as typical topological Dirac semimetals, among them $\mathit{Ln}\mathrm{SbTe}$ ($\mathit{Ln}$ denotes lanthanide) compounds exhibit intriguing characteristics due to the presence of $\mathit{Ln} 4f$ electrons, resulting in quantum states and unique properties. In this paper, the topological electronic structure of PrSbTe is systematically studied by angle-resolved photoemission spectroscopy (ARPES), combined with magnetic, specific heat measurements, and band structure calculations. The detailed three-dimensional electronic structure of PrSbTe has been obtained, and a diamond-shaped Fermi surface and multiple Dirac nodal lines have been observed, which are in remarkable agreement with theoretical calculations. Moreover, the $4f$ electrons in PrSbTe are rather localized, which can be revealed by on-resonant ARPES data and further confirmed by the rather small Sommerfeld coefficient of $\gamma =2.6231\mathrm{mJ}/\mathrm{mol}{\mathrm{K}}^2$. Our results provide more detailed information about the $\mathit{Ln}\mathrm{SbTe}$ family, which gives a deeper understanding of the interaction between $\mathit{Ln} 4f$ electrons and the topological states.

Linear carbon chains (LCCs) are the ultimate one-dimensional molecular system, and they show unique mechanical, optical, and electronic properties that can be tuned by altering the number of carbon atoms, strain, encapsulation, and other external parameters. In this work we probe the effects of quantum anharmonicity, strain, and finite size on the structural and vibrational properties of these chains using high-level density-functional-theory calculations. We find strong anharmonicity effects for infinite chains, leading to ground-state nuclear wave functions that are barely localized at each of the dimerized geometries, i.e., strong tunneling occurs between the two minima of the potential energy surface. This effect is enhanced for compressive strains. In addition, vibrational C-band frequencies deviate substantially from experimental measurements in long chains encapsulated in carbon nanotubes. On the other hand, calculations for finite chains suggest that quantum anharmonicity effects are strongly suppressed in finite systems, even in the extrapolation to the infinite case. For finite systems, vibrational C-band frequencies agree well with experimental values at zero pressure. However, these frequencies increase under compressive strain, in contradiction with recent results. This contradiction is not resolved by adding explicitly the encapsulating carbon nanotubes to our calculations. Our results indicate that LCCs embody an intriguing 1D system in which the behavior of very large, finite systems do not reproduce or converge to the behavior of truly infinite ones.