Within the framework of imaginary-time evolution for matrix product states, we introduce a cluster version of the infinite time-evolving block decimation algorithm for simulating quantum many-body systems, addressing the computational accuracy challenges in strongly correlated physics. By redefining the wave-function ansatz to incorporate multiple physical degrees of freedom, we enhance the representation of entanglement, thereby improving the accuracy of the ground states. Utilizing the Trotter-Suzuki decomposition and optimized truncation schemes, our method maintains roughly the same computational complexity while capturing more quantum correlations. We apply this approach to three nontrivial cases: the gapless spin-1/2 Heisenberg chain, the spin-1 anisotropic XXZD chain with a higher-order Gaussian-type phase transition, and a spin-1/2 twisted triangular prism hosting a magnetic plateau phase. Improved accuracy in physical quantities, such as magnetization, ground-state energy, and entanglement entropy, has been demonstrated. This method provides a scalable framework for studying complex quantum systems with high precision, making it suitable for situations where a pure increase in bond dimension alone cannot guarantee satisfactory results.

For strongly correlated quantum systems, fundamental questions about the formation and stability of Floquet-Bloch sidebands (FBs) upon periodic driving remain unresolved. Here, we investigate the impact of electron-electron interactions and perturbations in the coherence of the driving on the lifetime of FBs by directly computing time-dependent single-particle spectral functions using exact diagonalization (ED) and matrix product states (MPS). We study interacting metallic and correlated insulating phases in a chain of correlated spinless fermions. At high-frequency driving we obtain clearly separated, long-lived FBs of the full many-body excitation continuum. However, if there is significant overlap of the features, which is more probable in the low-frequency regime, the interactions lead to strong heating, which results in a significant loss of quantum coherence and of the FBs. Similar suppression of FBs is obtained in the presence of noise. The emerging picture is further elucidated by the behavior of real-space single-particle propagators, of the energy gain, and of the momentum distribution function, which is related to a quantum Fisher information that is directly accessible by spectroscopic measurements.

We theoretically explore Floquet engineering in few-layer black phosphorus (fBP) under time-periodic driving. Motivated by the ability of circularly polarized light to induce nontrivial topological states at Dirac nodes, we investigate the emergence of a photoinduced dc Hall effect in the Dirac semimetal phase of fBP. Starting from a low-energy continuum model, we derive the effective Floquet Hamiltonian and analytically calculate the Berry curvature, demonstrating the opening of a topological gap. We also perform lattice-model calculations incorporating a self-consistent Hartree method to compute Floquet band structures and dc Hall conductivity under a perpendicular electric field. Our results reveal that the dc Hall current in fBP can be effectively tuned via a periodic driving field and electrostatic gating.

The silicon vacancy $\left(V_{Si}\right)$ in $4H$-SiC at its cubic site (V2-center) has shown significant promise for quantum technologies, due to coherent spin states, the mature material system, and stable optical emission. In these SiC-based applications, doping plays a crucial role. It can be used to control the charge state of $V_{Si}$ and formation of different types of defects. Despite its importance, there has been little research on the effects of doping. In this work, we perform a study of the effects of nitrogen doping and annealing on the photoluminescence (PL), optically-detected magnetic resonance (ODMR) contrast, and dephasing times of ensembles of V2 in epilayers of $4H$-SiC. The results show an enhancement of PL that depends on the electron irradiation dose for a given electron concentration, supported by theoretical modeling of the charge state of $V_{Si}$ in the presence of nitrogen. Nitrogen substituted for carbon is shown to very efficiently donate one electron to $V_{Si}$. We also observe that the ODMR contrast can be increased from 0.5% in low doped SiC to 1.5% by nitrogen doping of ${10}^{17}$ to ${10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$ and annealing at $500-600{}^{\circ }\mathrm{C}$ for one hour, with only a 20% decrease in PL compared to unannealed. Some of the improvement in contrast is offset by a reduction in $T_2^{*}$ at these doping levels, but the estimated cw ODMR shot-noise limited sensitivity is still 1.6 times higher than that of undoped, unannealed SiC.

The theoretical quest for flat-band tight-binding models usually relies on lattice structures on which electrons reside. Typical examples of candidate lattice structures include the Lieb-type lattices and the line graphs. Meanwhile, there can be accidental flat-band systems that belong to neither of such typical classes and deriving flat-band energies and wave functions for such systems is not straightforward. In this work, we investigate the characteristic band structure for the tight-binding model on a network composed of pentagonal rings, which is inspired by the theoretically predicted carbon-based material. Although the lattice does not belong to conventional classes of flat-band models, the exact flat bands appear only for fine-tuned parameters. We analytically derive the exact eigenenergies and eigenstates of the flat bands. By using the analytic form of the Bloch wave function, we construct the corresponding Wannier function and reveal its characteristic real-space profile. We also find that, even away from the exact-flat-band limits, the nearly flat band exists near the Fermi level for the half-filled systems, which indicates that the present system will be a suitable platform for the quest for flat-band-induced correlated electron physics if it is realized in a real material. This is supported by the density functional theory calculations for the carbon-based materials where we find the ferromagnetic state.

The deconfined phase of ($2+1$)-dimensional ${\mathbb{Z}}_k$ gauge theory exhibits topological order, with $e$ and $m$ anyons that have a $2\pi /k$ braiding phase. Proliferating either $e$ or $m$ drives Higgs or confinement transitions, respectively. At the multicritical point where these transitions meet, the theory enjoys an additional duality symmetry that exchanges $e$ and $m$ anyons. This symmetry forces anyons with nontrivial braiding to close their gaps simultaneously, giving rise to a critical theory that mixes strong interactions with mutual statistics. We propose an effective $\mathrm{U}\left(1\right)\times \mathrm{U}\left(1\right)$ gauge theory with a mutual Chern-Simons term at level $k$ to describe the vicinity of the multicritical point for $k\ge 4$. The emergence of a global $\mathrm{U}{\left(1\right)}^{\mathrm{top}}\times \mathrm{U}{\left(1\right)}^{\mathrm{top}}$ symmetry at the critical point imposes powerful constraints on universal properties of the phase transition. In particular, we show that (1) the lattice magnetic flux operator embeds as a conserved U(1) current with protected scaling dimension; (2) the first-order line emanating from the critical point for $k=2$ disappears generically for sufficiently large $k$; (3) the correlation length exponent approaches that of the three-dimensional XY model with corrections of order $1/k^2$ in the large-$k$ limit. These predictions can be tested in near-term numerical simulations and pave the way for a more general exploration of topological quantum criticality enriched with anyon-permuting symmetries.

The interplay between non-Hermitian systems and topological insulators has garnered significant attention in recent years. In the presence of gain and loss contrast, the topological chiral boundary states exhibit the non-Hermitian skin effect (NHSE). A widely accepted perspective is that the NHSE is intrinsically linked to the nontrivial winding of the point gap in the complex spectrum. In this study, we identify an anomalous NHSE in a Chern insulator subjected to a gain-loss domain wall. Specifically, we demonstrate that the chiral boundary states induced by the gain-loss domain wall transition into corner states—exhibiting the NHSE—under open boundary conditions. Intriguingly, this NHSE is not associated with a nontrivial point-gap topology. As evidence, we show that a projective twofold rotational symmetry ensures the absence of nontrivial spectral winding. We have also investigated the size-dependent decaying length of this anomalous NHSE and its hybridization with other typical NHSEs. The discovery of this anomalous NHSE sheds new insights into the underlying mechanism of NHSEs.

${RT}_{12}$ materials continue to attract attention due to their potential use as “rare-earth-lean” permanent magnets, but converting their promising intrinsic properties into practical high performance remains an elusive goal. Sophisticated experimental characterization techniques are providing unprecedented insight into the structure of these materials at the atomistic scale. Atomistic spin dynamics or micromagnetics simulations could help unravel the links between these structures and resultant magnet performance, but require input data describing the intrinsic magnetic properties. Here, first-principles calculations based on density functional theory are used to determine these properties for two model interface structures which have been derived from recently reported high-resolution electron microscopy images. One model structure is a stoichiometric twin formed by mirroring the ${RT}_{12}$ structure in the (101) plane, and the other model structure is a “stacking fault” involving the insertion of a ${RT}_4$ plane and a displacement along the [100] axis. Magnetic moments and crystal field coefficients have been calculated for the optimized structures. The interfaces modify the magnetic properties at the sub-nm scale. In particular, in the $R$-rich region of the “stacking fault,” the local easy axis of magnetization rotates by ${49}^{\circ }$ from its bulk direction, which may lead to reduced coercivity through the easier nucleation of reverse domains.

Ternary hydrides have recently been predicted to exhibit exceptional superconducting properties under high pressure, positioning them as promising candidates for room-temperature superconductivity. In this work, we perform a systematic investigation of the Th-B-H system at 100 and 200 GPa using state-of-the-art structural prediction method combined with first-principles calculations. Our results identified seven thermodynamically stable compounds, namely ThBH, ${\mathrm{ThBH}}_7$, ${\mathrm{ThB}}_2{\mathrm{H}}_{10}$, ${\mathrm{ThB}}_2{\mathrm{H}}_3$, ${\mathrm{ThB}}_2{\mathrm{H}}_{13}$, ${\mathrm{Th}}_2{\mathrm{BH}}_{16}$, and ${\mathrm{ThB}}_6{\mathrm{H}}_6$, in which B atoms are bonded with H atoms, giving rise to diverse structural motifs, including ${\mathrm{BH}}_4$ tetrahedra, ${\mathrm{B}}_2{\mathrm{H}}_8$ (${\mathrm{H}}_4\mathrm{B}\text{−}{\mathrm{BH}}_4$) units, ${\mathrm{BH}}_6$ octahedra, an interpenetrating framework constructed from orthogonal zigzag ${\mathrm{BH}}_3$ chains and corrugated B-H layers. In addition to the existence of conventional atomic H, we uncover exotic hydrogen species, such as isolated ${\mathrm{H}}_5$ planar pentagons and ${\mathrm{H}}_4$ pyramidal units. Further electron-phonon coupling calculations reveal that nonclathrate hydride ${\mathrm{Th}}_2{\mathrm{BH}}_{16}$ exhibits a $T_c$ of 72 K at 200 GPa, which increases to 102 K upon decompression to 120 GPa. Moreover, the further results show hole doping could enhance superconductivity, leading to an increased $T_c$ of 115 K in the isostructural ${\mathrm{Th}}_2{\mathrm{BH}}_{15}$. These findings provide valuable insights for the design and synthesis of ternary hydrides with high-temperature superconductivity, particularly in rare-earth metal hydrides under high pressure.

A solid transparent medium with randomly positioned, immobile impurity atoms is a promising candidate for observation of Anderson localization of light in three dimensions. It can have low losses and allows for mitigation of the detrimental effect of longitudinal optical fields by an external magnetic field, but it has its own issues: thermal oscillations of atoms around their equilibrium positions and inhomogeneous broadening of atomic spectral lines due to random local electric fields. Our calculations suggest that these complications should not impede observation of Anderson localization of light in such materials provided that a sufficiently high number densities of impurities can be reached. The thermal oscillations hardly affect light propagation whereas the inhomogeneous broadening can be compensated for by increasing the number density of impurities.

We study several models of $d$-dimensional fermions ($d=1,2,3$) with an emphasis on the properties of their gapless (metallic) phase. It occurs at $T=0$ as a continuous transition when zeros of the partition function reach the real range of parameters. Those zeros define the $(d-1)$-manifold of quantum criticality (Fermi surface). Its appearance or restructuring correspond to the Lifshitz transition. Such $(d-1)$-membrane breaks the symmetry of the momentum space, leading to gapless excitations, a hallmark of metallic phase. To probe quantitatively the gapless phase we introduce the geometric order parameter as $d$-volume of the Fermi sea. From analysis of the chain, ladder, and free fermions with different spectra, this proposal is shown to be consistent with scaling near the Lifshitz points of other quantities: correlation length, oscillation wavelength, susceptibilities, and entanglement. All the (hyper)scaling relations are satisfied. Two interacting cases of the Tomonaga-Luttinger ($d=1$) and the Fermi ($d=2,3$) liquids are analyzed, yielding the same universality classes as free fermions.

We define a measurable spin for the edge of a lowest Landau level and incompressible fractional quantum Hall state in the presence of an Abelian or non-Abelian bulk quasiparticle. We show that this quantity takes a fractional value inherited from the fractional spin of the bulk quasiparticle. We present a geometric picture that does not rely on global symmetries of the wave function, but is able to treat quasiparticles and edges with different shapes. We study finite-size many-body wave functions on the cylinder with circular quasiparticles and straight edges. Our results are supported by matrix-product-state calculations for the Laughlin and the $k=3$ Read-Rezayi states.

Janus transition metal dichalcogenide (JTMD) monolayers have broadened the family of two-dimensional (2D) materials. Despite numerous theoretical predictions of JTMDs, the underlying stability mechanisms at the electronic scale remain systematically underexplored. Here, we investigate the group-dependent stability of 1H-phase JTMDs, revealing its origin in the bonding mode competition, coupled with the antibonding orbital splitting at the Fermi level through $d$-orbitals repulsion. Three orbital splitting configurations are identified to explain the group-dependent stability and structural phase preferences. Guided by the electronic origin of stability, we design a family of stable 2D Janus transition metal halides with intrinsic ferrovalley properties. This work bridges the gap between stability predictions and electronic structures, and extends the design guidelines for synthesizing 2D Janus materials.

We introduce a practical and accurate strategy to capture light-matter interactions using the Floquet formalism in the velocity gauge in combination with realistic first-principle models of solids. The velocity gauge, defined by the linear coupling to the vector potential, is a standard method to capture the light-matter interaction in solids. However, its use with first-principle models has been limited by the challenging fact that it requires a large number of bands for convergence and its incompatibility with nonlocal pseudopotential plane wave methods. To improve its convergence properties, we explicitly take into account the truncation of Hilbert space in the construction of the Floquet Hamiltonian in the velocity gauge which leads to a series of nested commutators between the position operator and the material Hamiltonian. To avoid the incompatibility with the pseudopotentials and efficiently compute the nested commutators, we base our computations on generalized tight-binding Hamiltonians derived from first-principles through maximally-localized Wannier functions. We exemplify the approach by computing the non-equilibrium optical absorption spectra of laser-dressed trans-polyacetylene chain using realistic electronic structure. We show that, by proceeding in this way, Floquet consideration involving the truncated Hilbert spaces reproduces the full basis calculations with only a few bands and with significantly reduced computation time. The strategy has been implemented in FloqticS, a general code for the Floquet engineering of the optical properties of materials. Overall, this work introduces a useful theoretical tool to realize Floquet engineering of realistic solids in the velocity gauge.

We investigate the optical properties of bi-isotropic materials under the anomalous Hall effect (AHE) of axion electrodynamics. Four refractive indices associated with circularly polarized waves are achieved, implying circular birefringence with rotatory power endowed with double sign reversal, an exotic optical signature for chiral dielectrics. The Kerr rotation and ellipticity are analyzed, with an unusual observation of a giant rotation angle deprived of discontinuity. Anomalous enhanced reflectance ($R$ greater than unity) is also reported, associated with negative refraction stemming from the anomalous transport properties. These effects constitute the singular optical signature of a nonequilibrium bi-isotropic medium with the AHE.