Exploiting symmetries in tensor network algorithms plays a key role for reducing the computational and memory costs. Here we explain how to incorporate the Hermitian symmetry in double-layer tensor networks, which naturally arise in methods based on projected entangled-pair states. For real-valued tensors the Hermitian symmetry defines a ${\mathbb{Z}}_2$ symmetry on the combined bra and ket auxiliary level of the tensors. By implementing this symmetry, a speedup of the computation time by up to a factor 4 can be achieved, while expectation values of observables and reduced density matrices remain Hermitian by construction. Benchmark results based on the corner transfer matrix renormalization group and higher-order tensor renormalization group are presented. We also discuss how to implement the Hermitian symmetry in the complex case, where a similar speedup can be achieved.

Floating edge bands (FEB) have been identified in systems such as obstructed atomic insulators and layered nonsymmorphic semimetals, attracting considerable interest recently. Here we demonstrate that FEB can arise in a simplified model incorporating altermagnetism. By enhancing the Bernevig-Hughes-Zhang model on a square lattice with additional altermagnetic and Zeeman fields perpendicular to the two-dimensional plane, we uncover the emergence of FEB that are distinct from the bulk bands across the entire Brillouin zone and over broad parameter regimes. We calculate topological phase diagrams, highlighting the strong topological properties characterized by the Chern number and the weak topological properties marked by the winding number. Furthermore, we provide analytical results of the energy spectrum and the wave functions of the FEB. We also study the robustness of the FEB, showcasing its resilience against various perturbations such as geometric rotation, energy spectrum asymmetry, and spin coupling. Our findings advance our understanding of FEB and may pave new avenues for further exploration of topological phases in quantum materials.

Fermi surface reconstruction in cuprates can lead to an abrupt change in the Fermi momentum $k_F$ between different phases. This phenomenon remains a subject of debate and is at the heart of an ongoing discussion about the nature of the metallic state in the pseudogap regime. Here we study a minimal model of a $k_F$ changing crossover in the one-dimensional Fermi-Hubbard model, where a tuning of the on-site interaction leads to a crossover between a spin-$1/2$ Luttinger liquid with small Fermi momentum and a spinless chargon liquid with large Fermi momentum. We attribute this to an emergent $U\left(1\right)$ symmetry in the strongly correlated limit, which can be used to derive a modified Luttinger sum rule recovering the large Fermi momentum. We analyze Friedel oscillations at the edge of a system to directly probe the change of Fermi momentum at zero and nonzero temperature. This paves the way for a direct experimental observation of changes of the Fermi momentum using ultracold fermions in a quantum gas microscope, with possible extensions to higher dimensional systems.

The fractional quantum Hall effect is a well-known demonstration of strongly correlated topological phases in two dimensions. However, the extension of this phenomenon into a three-dimensional context has yet to be achieved. Recently, the three-dimensional integer quantum Hall effect based on Weyl orbits has been experimentally observed in a topological semimetallic material under a magnetic field. This motivates us to ask whether the Weyl orbits can give rise to the fractional quantum Hall effect when their Landau level is partially filled in the presence of interactions. Here we theoretically demonstrate that the fractional quantum Hall states based on Weyl orbits can emerge in a Weyl semimetal when a Landau level is one-third filled. Using concrete models for Weyl semimetals in magnetic fields, we project the Coulomb interaction onto a single Landau level from the Weyl orbit and find that the ground state of the many-body Hamiltonian is triply degenerate. We further show that the ground states exhibit the many-body Chern number of $1/3$ and the uniform occupation of electrons in both momentum and real space, implying that they are the fractional quantum Hall states. In contrast to the two-dimensional case, the states are spatially localized on two surfaces hosting Fermi arcs. Additionally, our findings suggest that the excitation properties of these states resemble those of the Laughlin state in two dimensions, as inferred from the particle entanglement spectrum of the ground states.

We report the crystal growth, magnetoresistance (MR) with low and high magnetic field applied along the crystallographic $c$ axis, and quantum Shubnikov–de Haas (SdH) and de Haas–van Alphen (dHvA) oscillations of the quasi-one-dimensional ternary telluride ${\mathrm{TaCo}}_2{\mathrm{Te}}_2$. The field-dependent MR at 2 K under magnetic field up to 9 T follows a ${\rho }_a\left(B\right)\sim B^{1.56}$ relation, which slightly differs from the ${\rho }_a\left(B\right)\sim B^{1.79}$ relation under high magnetic field up to 58.9 T without any signature of saturation. The SdH oscillations reveal two fundamental oscillation frequencies $F_{\alpha }=63.4 \mathrm{T}$ and $F_{\beta }=158.5 \mathrm{T}$, with the second- and third-harmonic frequencies of $F_{\beta }$, very close to the two major frequencies $F_{\alpha }=74.0 \mathrm{T}$ and $F_{\beta }=148.1 \mathrm{T}$ revealed by the more pronounced dHvA oscillations. A nontrivial Berry phase and small effective masses are extracted from the analyses of quantum oscillations, which provide the transport and magnetic evidence of the nontrivial band topology. The anisotropic character of the identified frequency is revealed by analyzing the angular dependence of dHvA oscillations. The two frequencies $F_{\alpha }$ and $F_{\beta }$ are expected to arise from the holelike Fermi surface sheets formed by the band which is part of the previously reported double Dirac cone and eightfold-degenerate Dirac point.

Many phenomena observed on the $\mathrm{Ti}{\mathrm{O}}_2$ surface under illuminations have been attributed to the formation of light-induced surface oxygen vacancies ($V_{\mathrm{O}}$), which were believed to act as electron donors and hole traps. However, direct experimental evidence supporting this explanation has been elusive, leading to a long-standing debate on the underlying mechanisms. Here, we employ first-principles calculations and defect theory under illumination to elucidate the underlying mechanisms governing diverse illumination effects on the rutile $\mathrm{Ti}{\mathrm{O}}_2$ (110) surface. We find that the illumination cannot directly create new surface defects under experimental conditions, while illumination can promote the ionization rate of Ti interstitials ($\mathrm{T}{\mathrm{i}}_{\mathrm{i}}$) and disrupt their original equilibrium distribution, thus triggering the associated defect dynamics. Specifically, under illumination, an increased number of subsurface $\mathrm{T}{\mathrm{i}}_{\mathrm{i}}$ become ionized, creating a concentration gradient relative to surface ionized $\mathrm{T}{\mathrm{i}}_{\mathrm{i}}$. Consequently, subsurface $\mathrm{T}{\mathrm{i}}_{\mathrm{i}}$ would diffuse towards the surface sites which not only provides a plausible explanation for the increased concentration of surface electron donors and hole traps, but also explains the time-dependent nature of illumination effects. After the removal of illumination, surface $\mathrm{T}{\mathrm{i}}_{\mathrm{i}}$ are temporarily retained, thereby extending the effects of illumination. Our proposed dynamics of $\mathrm{T}{\mathrm{i}}_{\mathrm{i}}$ are consistent with experimental observations, providing a picture for understanding the complex interplay between illumination and surface properties in rutile $\mathrm{Ti}{\mathrm{O}}_2$. Our findings not only resolve the historical debate but also offer a foundation for understanding illumination effects in a broader range of materials and systems.

Thermodynamic uncertainty relations (TURs) represent a benchmark result in nonequilibrium physics that allows to place fundamental lower bounds on the noise-to-signal ratio (precision) of currents in nanoscale devices. Originally formulated for classical time-homogeneous Markov processes, these relations, were shown to be violated in thermoelectric engines and photovoltaic devices supporting quantum-coherent transport. However, the extent to which these violations may occur still represents a missing piece of the puzzle. In this work, we provide such answer in a definitive way within the general Landauer-Büttiker formalism for noninteracting systems, beyond any perturbative regime, e.g., linear response. In particular, using analytical constrained-optimization techniques, we rigorously demonstrate that the transmission function which maximizes the reliability of thermoelectric devices (i.e., which minimizes the fluctuations of its steady-state currents) for fixed average power and efficiency is a collection of boxcar functions. This allows us to show that TURs can be violated by arbitrarily large amounts, depending on the temperature and chemical potential gradients, thus providing guidelines to the design of optimal devices.

Competition between magnetism and superconductivity can lead to unconventional and topological superconductivity. However, the experimental confirmation of the presence of Majorana edge states and unconventional pairing poses a major challenge. Here, we consider a two-dimensional lattice model for a superconductor with spin-orbit coupling and exchange coupling to randomly distributed magnetic impurities. Depending on parameters of the model, this system may display topologically trivial or nontrivial edge states. We map out the phase diagram by computing the Bott index, a topological invariant defined in real space. We then use machine learning (ML) algorithms to predict the Bott index from the local density of states (LDOS) at zero energy, obtaining high-accuracy results. We also train ML models to predict the amplitude of odd-frequency pairing in the anomalous Green's function at zero energy. Once the ML models are trained using the LDOS, which is experimentally accessible via scanning tunneling spectroscopy, our method could be applied to predict the number of Majorana edge states and estimate the magnitude of odd-frequency pairing in real materials.

Exploration of multiphase coexistence has always been an important topic in condensed matter physics, which can produce rich physics to meet the needs of modern science and technology. In this work, by means of first-principles calculations, we successfully predicted the ferroelectricity in the charge density wave (CDW) material $1T\text{−}\mathrm{Ti}{X}_2$ ($X$ = S, Se, and Te) bilayers by stacking two van der Waals (vdW) monolayers. Because the CDW transition occurring at low temperatures is accompanied by a metal-insulator transition (MIT), the ferroelectric (FE) polarization also changes. Taking $1T\text{−}{\mathrm{TiSe}}_2$ as an example, its bilayer behaves as an FE metal in the high-temperature normal phase, in which ferroelectricity and metallicity can coexist due to the dispersed spatial distribution of polarized and conducting electrons, with vertical polarization up to 0.38 pC/m. After the CDW transition, these bilayers exhibit semiconductivity as a result of the periodic lattice distortion. Meanwhile, the shielding effect of electrons is removed, and the polarization is approximately tripled. Interestingly, we found four polarization states in the CDW phase and confirmed that multistate modulation can be achieved by interlayer sliding with low energy consumption. Our findings link the CDW transition to ferroelectricity, which has potential applications in functional nanodevices and provides a new route to design polarization multistate for developing next-generation memory devices.

Single-photon detection is an energy quantum limit detection (EQLD) of extremely weak electromagnetic waves. Given that the sensitivity of the conventional electromagnetic induction microwave receiver working at room temperature is very limited, as a result of the significantly strong thermal noise, here we analyze the possibility of approaching the EQLD of the weak microwave signal by using a current-biased Josephson junction (CBJJ) detector. By numerically simulating the dynamics for the phase particle of the CBJJ, we propose an approach to describe the discriminability between the probabilistically escaped events of the phase particle with and without the microwave current driving, by measuring the minimum $d_{\mathrm{KC}}$ index. Our predictions indicate that the experimentally demonstrated CBJJ detector possesses the ability to resolve about a dozen photons. Furthermore, with the minimum detectable signal strength and the saturation threshold, we discuss how to determine the dynamic range of the proposed CBJJ detector. The feasibility of using the proposed CBJJ detector to achieve the EQLD in a microwave band is also discussed.

In this paper, we present a computationally efficient methodology that utilizes a local real-space formulation of the projector augmented wave (PAW) method discretized with a finite-element (FE) basis to enable accurate and large-scale electronic structure calculations. This real-space approach for DFT calculations combines the efficiency of PAW formalism involving smooth electronic fields with the ability of systematically improvable higher-order finite-element basis to achieve significant computational gains. In particular, we developed efficient strategies for solving the underlying FE discretized PAW generalized eigenproblem by employing the Chebyshev filtered subspace iteration approach to compute the desired eigenspace in each self-consistent field iteration. These strategies leverage the low-rank perturbation of the FE basis overlap matrix in conjunction with reduced order quadrature rules to invert the discretized PAW overlap matrix while also exploiting the sparsity of both the local and nonlocal parts of the discretized PAW Hamiltonian and overlap matrices. Further, we employ higher-order quadrature rules to accurately evaluate integrals in these matrices involving PAW-atomic data, allowing the use of coarser FE meshes for various electronic fields. Using the proposed approach, we benchmark the accuracy and performance of various representative examples involving periodic and nonperiodic systems with plane-wave-based PAW implementations. Furthermore, we also demonstrate a considerable computational advantage $(\sim 5\times -10\times )$ over state-of-the-art plane-wave methods for medium to large-scale systems ($\sim 6000-35000$ electrons). Finally, we show that our approach (PAW-FE) significantly reduces the degrees of freedom to achieve the desired accuracy, thereby enabling large-scale DFT simulations ($>50000$ electrons) at an order of magnitude lower computational cost compared to norm-conserving pseudopotential calculations using finite-element discretization.

The exploration of topological quantum phases and their transitions has become a focus of intense research. In this paper, we introduce a family of two-dimensional (2D) metal-organic frameworks (MOFs) that host various emergent 2D fermions and second-order topological insulators (SOTIs) while also exhibiting strain-tunable quantum phase transitions. Using first-principles calculations, we demonstrate that these MOFs can exhibit either a narrow-band-gap semiconductor or a zero-band-gap semimetal state, with three key bands in the low-energy region. Importantly, we find that applying biaxial strain can induce a semiconductor-to-semimetal quantum phase transition or vice versa. We further reveal that the semiconductor phase may possess nontrivial properties, including corner states, indicative of a second-order topological phase. At the critical strain point, a 2D triple point emerges, which transitions into a double-Weyl-fermion state under additional strain. We also construct effective models to describe these emergent 2D fermions. Our findings highlight the potential of MOFs as a versatile platform for studying quantum phases, emergent fermions, and SOTIs, paving the way for future applications in quantum materials and nanoscale technologies.

We report on neutron diffraction, magnetoresistance, magnetization and magnetic torque measurements under high magnetic field in the helical antiferromagnet ${\mathrm{CeVGe}}_3$. This compound exhibits Kondo lattice coherence and helical antiferromagnetic (AFM) ordering at ambient pressure, similar to the well-studied ${\mathrm{CeRhIn}}_5$. Our measurements reveal that ${\mathrm{CeVGe}}_3$ undergoes a magnetic transition from an incommensurate (ICM) AFM state to an up-up-down-down commensurate (CM) AFM structure, followed by a transition to a novel phase at higher fields. A quantum phase transition occurs around 21.3 T. This rich magnetic field phase diagram closely resembles that of ${\mathrm{CeRhIn}}_5$. Furthermore, angle-dependent magnetoresistance measurements reveal that all transitions in ${\mathrm{CeVGe}}_3$ occur from the field component along the $ab$ plane. These findings highlight the intricate interplay among exchange interactions, crystal field effects, ground state properties, and crystalline symmetries.

Maximally localized Wannier functions use the gauge freedom of Bloch wave functions to define the optimally smooth subspace with matrix elements that depend smoothly on crystal momentum. The associated Wannier functions are real-space localized, a feature often used to Fourier interpolate periodic observables in reciprocal space on ultradense momentum grids. However, Fourier interpolation cannot handle nonperiodic quantities in reciprocal space, such as the oscillator strength matrix elements, which are crucial for the evaluation of optical properties. We show that a direct multidimensional interpolation in the optimally smooth subspace yields comparable accuracy with respect to Fourier interpolation at a similar or lower computational cost. This approach can also interpolate and extrapolate nonperiodic observables, enabling the calculation of optical properties on ultradense momentum grids. Finally, we underline that direct interpolation in the optimally smooth subspace can be employed for periodic and nonperiodic tensors of any order without any information on the position of the Wannier centers in real space.

Two-dimensional electron gas (2DEG) at complex oxide interfaces presents a unique platform to investigate various correlated electron phenomena in low-dimensional environments. While most previous research has focused on (001) oriented 2DEG grown by pulsed laser deposition, we report the fabrication of conducting interfaces between paramagnetic ${\mathrm{PrAlO}}_3$ (PAO) and ${\mathrm{SrTiO}}_3$ (STO) in both (001) and (110) orientations using the spin-coating technique. The 2DEGs exhibit high conductivity, with Hall mobilities of approximately 150 ${\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ and 826 ${\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ in the (001) and (110) orientations, respectively, at 2 K. Additionally, we observe evidence of the Kondo effect in both samples. Out-of-plane magnetoresistance (MR) analysis confirms the existence of electron-electron interaction in the high-magnetic-field regime, while in-plane MR shows a crossover from weak localization to weak antilocalization for both samples. Notably, we report strong out-of-plane and in-plane directional anisotropy in a spin-coated (110)-2DEG along the in-plane [001] and $\left[1\overline{1}0\right]$ crystallographic directions. The estimated Rashba spin splitting energy ($\mathrm{\Delta }$) for both [001] and $\left[1\overline{1}0\right]$ directions reveals a maximum difference of $\mathrm{\Delta }\left[001\right]-\left[1\overline{1}0\right]\sim 0.71$ meV at 2 K. Furthermore, spin relaxation in these interfaces follows the D'yakonov-Perel (Rashba spin-orbit coupling) mechanism ($\tau {}_{\mathrm{so}}\propto {\mu }^{-1}$). This study highlights the remarkable potential of the spin-coating method for producing high-quality oxide 2DEGs.

We study spin-orbit proximity effects in an armchair (4,4) carbon nanotube on the Pt(111) surface. By employing first-principles calculations, we show that the Dirac cone of the metallic nanotube is altered due to strong hybridization with the Pt substrate. Inserting a monolayer hexagonal boron nitride (hBN) between the nanotube and the substrate limits the hybridization effects leading to recovering the Dirac cone. The Dirac bands display asymmetric spin splitting, 0.7 meV for the right movers and 1.7 meV for the left movers at the $K$ valley, due to the proximity to the Pt substrate. We find that the Dirac states exhibit almost perfect spin polarization, transverse to the nanotube axis and to the stacking direction, forming a proper condition for a charge-to-spin conversion with coherent spin transport in the nanotube. We propose an effective Hamiltonian describing the proximity-induced effects on the Dirac electrons and their spin texture.

Controlling the magnetization direction of ferromagnets by utilizing the current-induced spin-orbit torque shows promising applications in low-energy spintronic devices. The magnetization dynamics of a honeycomb lattice with both Rashba and Ising spin-orbit couplings are studied by using the microscopic Landau-Lifshitz-Gilbert equation from a quantum transport perspective. In the honeycomb system with only Rashba spin-orbit coupling, the minimum magnetic field required for magnetization reversal decreases almost linearly with the increasing Rashba spin-orbit coupling strength. When Ising spin-orbit coupling is introduced, the critical magnetic field reduces significantly as Ising spin-orbit coupling strength increases. The magnetization switching is found to be determined by the cooperation of Rashba and Ising spin-orbit torques, which mainly behave as fieldlike and dampinglike torques, respectively. The reduction in the critical magnetic field due to Ising spin-orbit coupling is robust under low disorder strength. In addition, the critical magnetic field can also be reduced by the increase of bias voltages which can be attributed to the rise of Rashba spin-orbit torque. Our simulations provide an effective way to reduce the critical magnetic field for spin-orbit torque driven magnetization switching in future spintronic applications.