A neural-network approach to optimize the selection of Slater determinants in configuration interaction calculations for condensed-matter quantum many-body systems is developed. We exemplify our algorithm on the discrete version of the single-impurity Anderson model with up to 299 bath sites. Employing a neural network classifier and active learning, our algorithm enhances computational efficiency by iteratively identifying the most relevant Slater determinants for the ground state wave function. We benchmark our results against established methods and investigate the efficiency of our approach compared to another basis truncation scheme without a neural network. Our algorithm demonstrates a substantial improvement in the efficiency of determinant selection, yielding a more compact and computationally manageable basis without compromising accuracy. Given the straightforward application of our neural-network-supported selection scheme to other model Hamiltonians of quantum many-body clusters, our algorithm can significantly advance selective configuration interaction calculations in the context of correlated condensed matter.

In this work, we applied first-principles calculations to address the problem of the electronic localization and the emergence of flat bands in one-dimensional boron nitride systems. We considered bilayer ribbons, hybrid bilayers formed by the stacking of a ribbon on top of an infinite sheet, and double-walled nanotubes. For the ribbon cases, we found results consistent with those reported for extended bilayer systems, with flat bands associated with specific stacking orders in the moiré patterns. The influence of the edge states in the moiré localizations is also described. For the double-walled nanotubes, we found a distinct phenomenology: The localization is also present in connection with the stacking orders; however, it shows up in the form of extended stripes along the tube axis, and not in the form of islands, as in the ribbon cases. A model to interpret this phenomenology is discussed.

The interplay between electron-electron and electron-phonon interactions is studied in a one-dimensional lattice model by means of a variational Monte Carlo method based on generalized Jastrow-Slater wave functions. Here, the fermionic part is constructed by a pair-product state, which explicitly depends on the phonon configuration, thus including the electron-phonon coupling in a backflow-inspired way. We report the results for the Hubbard model in the presence of the Su-Schrieffer-Heeger coupling to optical phonons, both at half filling and upon hole doping. At half filling, the ground state is either a translationally invariant Mott insulator, with gapless spin excitations, or a Peierls insulator, which breaks translations and has fully gapped excitations. Away from half filling, the charge gap closes in both Mott and Peierls insulators, turning the former into a conventional Luttinger liquid (gapless in all excitation channels). In the latter case, instead, a finite spin gap remains at small doping. Even though consistent with the general theory of interacting electrons in one dimension, the existence of such a phase (with gapless charge but gapped spin excitations) has never been demonstrated in a model with repulsive interaction and with only two Fermi points. Since the spin-gapped metal represents the one-dimensional counterpart of a superconductor, our results furnish evidence that a true off-diagonal long-range order may exist in the two-dimensional case.

The shift in the spectral weight distribution under doping is termed the spectral weight transfer (SWT) and is a key indicator of strongly correlated physics. The static SWT ($t=0$) for doping fraction $x$ scales as $x$ for semiconductors and as $2x$ for Mott insulators. The SWT receives corrections in $t/U$ due to the noncommutativity of the kinetic and interaction terms in the Hamiltonian, termed the dynamic SWT. We compute explicitly the low-energy spectral weight (LESW) in the lower Hubbard band using the orbital Hatsugai-Kohmoto (OHK) model. We show that the dynamical mixing enters the LESW with a universal slope independent of the number of orbitals. This independence on orbital number corroborates the rapid convergence of the OHK model to the Hubbard model. As a result, OHK is an effective simulator of Hubbard physics.

Understanding environmental effects in a topological Josephson junction is vital for identifying signatures of Majorana modes. We consider a planar Josephson junction formed on the surface of a three-dimensional topological insulator, which possesses Majorana modes inside the junction and boundary modes outside. We find that tunneling between the inner and outer modes gives rise to effective coupling between the inner Majorana modes and hence induces energy splitting of their states even in the absence of the direct spatial overlap of their wave functions. The energy splitting is obtained analytically in the weak tunneling limit and is numerically investigated for an arbitrary tunneling strength. We discuss in detail the evolution of the energy splitting with an external perpendicular magnetic field and its effect on the shape of the Fraunhofer pattern.

We investigate the nature of the quantum phase transition in modulated $\mathrm{SU}\left(N\right)$ Heisenberg spin chains. In the odd-$N$ case, the transition separates a trivial nondegenerate phase to a doubly degenerate gapped chiral $\mathrm{PSU}\left(N\right)$ symmetry-protected topological (SPT) phase which breaks spontaneously the inversion symmetry. The transition is not an Ising transition associated to the breaking of the ${\mathbb{Z}}_2$ inversion symmetry, but is governed by the delocalization of the edge states of the SPT phase. In this respect, a modulated $\mathrm{SU}\left(N\right)$ Heisenberg spin chain provides a simple example in one dimension of a non-Landau phase transition which is described by the $\mathrm{SU}{\left(N\right)}_1$ conformal field theory. We show that the chiral SPT phase exhibits fractionalized spinon excitations, which can be confined by slightly changing the model parameters.

Bethe-Salpeter equation (BSE) in the self-consistent Hartree-Fock (HF) basis is often used for describing complex many-body effects in material science applications. Its numerically exact solution on the real-frequency axis at finite temperature for polarization using the diagrammatic Monte Carlo method [I. S. Tupitsyn and N. V. Prokof'ev, Phys. Rev. B 109, 045152 (2024)] captures effects of multiple Coulomb scattering of a single particle-hole excitation, but does not account for multiple pair excitations important for studying dielectric loses in metals at frequencies comparable to the plasmon mode. In this paper we report technical developments which allow one to efficiently compute the dielectric response in a wide frequency range from zero to a few Fermi energies without systematic bias at finite $T$. By applying it to the homogeneous electron gas we demonstrate how at small momenta the gap in the spectral density between the electron-hole and plasmon excitations, existing within the HF-BSE approach, is filled with two particle-hole excitations and is completely washed out already at temperature $T\sim {\varepsilon }_F/10$.

Stabilizing exotic quantum phases of matter, e.g., spin liquid, is an attractive topic in condensed matter. Here, by a Monte Carlo study of a two-orbital spin-fermion model on a honeycomb lattice, we show that the cooperative effects of the orbital degeneracy of itinerant electrons and the exchange interaction of localized spins can significantly suppress both ferromagnetic and antiferromagnetic orders by generating topological defects, and give rise to an intermediate spin-liquid state via continuous phase transitions. This phase competition can also be achieved by tuning the electron filling. These results shed light on realizing spin liquids on geometrically nonfrustrated lattices.

Distinct atomic nonpolar/polar ordering is determined at long, intermediate, and short ranges using synchrotron x-ray diffraction, Raman scattering, and pair distribution function data in ${\mathrm{K}}_{0.5}{\mathrm{Na}}_{0.5}{\mathrm{NbO}}_3$-doped ${\mathrm{BaTiO}}_3$-based relaxor ferroelectrics, viz., $(1-x){\mathrm{Ba}}_{0.9}{\mathrm{Sr}}_{0.1}{\mathrm{TiO}}_3\text{−}x\mathrm{KNN}50$. Two different polar phases with distinct symmetries are identified at short/intermediate ranges for $x=0.10$, where a monoclinic phase at short ranges gradually transforms into a rhombohedral phase at intermediate ranges. In contrast, a nonpolar phase with average cubic symmetry is found to be stable at long ranges for a wide temperature range ($100\le T \le 500$  K). The polar behavior of short/intermediate-range ordering is quantified in terms of the amplitude of ferroelectric phonon mode ${\mathrm{\Gamma }}_4^{-}$ ($q=0,0,0$) (which corresponds to the zone center of the cubic Brillouin zone). The amplitude of the ${\mathrm{\Gamma }}_4^{-}$ phonon mode increases with decreasing temperature, suggesting the enhancement of ferroelectric polarization at short/intermediate ranges on lowering temperatures. Enhanced ferroelectric polarization at low temperature is also visible and evident by ferroelectrostriction and is quantified by the increase in magnitude of spontaneous volume ferroelectrostriction. Consequently, Zero thermal expansion is observed at low temperatures.

In this work, we investigate the Stark localization near the Aubry-André (AA) critical point. We perform careful studies for reporting system-dependent parameters, such as localization length, inverse participation ratio (IPR), and energy gap between the ground and first excited state, for characterizing the localization-delocalization transition. We show that the scaling exponents possessed by these key descriptors of localization are quite different from that of a pure AA model or Stark model. Near the critical point of the AA model, in the presence of Stark field of strength $h$, the localization length $\zeta$ scales as $\zeta \propto h^{-\nu }$ with $\nu \approx 0.29$, which is different from both the pure AA model $(\nu =1)$ and Stark model $(\nu \approx 0.33)$. The IPR in this case scales as IPR $\propto h^s$ with $s\approx 0.096$, which is again significantly different from both the pure AA model $(s\approx 0.33)$ and Stark model $(s\approx 0.33)$. The energy gap, $\mathrm{\Delta }$, scales as $E\propto h^{\nu z}$, where $z\approx 2.37$, which is however the same as the pure AA model. Finally, we discuss how invoking a criticality-inducing additional control parameter may help in designing better many-body quantum sensors. Quantum critical sensors exploit the venerability of the wave function near the quantum critical point against small parameter shifts. By incorporating a control parameter in the form of the quasiperiodic field, i.e., the AA potential, we show a significant advantage can be drawn in estimating an unknown parameter, which is considered here to be the Stark weak field strength, with high precision. We compute and extract the scaling exponent associated with the quantum Fisher information, $F_Q$, which provides a bound on the uncertainty associated with measuring an unknown parameter. We demonstrate that by a control field in the form of the quasiperiodic potential, and setting it at AA criticality, $F_Q$ scales with the system size as $F_Q\propto L^{\beta }$, where $\beta \approx 6.7$, which is greater in comparison to the pure Stark case, for which $\beta$ is known to be 5.8. We, thus, pitch a generic idea of invoking quantum-criticality-inducing additional control parameters for obtaining enhanced quantum advantage in many-body critical sensors.

We investigate magnetic properties of ${\mathrm{CrTe}}_2$ within the density functional theory (DFT) approach in ferromagnetic phase and the combination of the DFT and the dynamical mean field theory ($\mathrm{DFT}+\mathrm{DMFT}$) approach in the paramagnetic phase. We show that a few-layer ${\mathrm{CrTe}}_2$ possesses well-formed local magnetic moments. In the monolayer ${\mathrm{CrTe}}_2$, we find the most preferable antiferromagnetic exchange with the ${120}^{\circ }$ antiferromagnetic structure. In the bilayer and trilayer systems, electronic correlations in the $\mathrm{DFT}+\mathrm{DMFT}$ approach yield ferromagnetic exchange interaction within each layer, but the interaction between the layers is antiferromagnetic, such that alternation of the direction of magnetization between the layers is expected. In bulk ${\mathrm{CrTe}}_2$ we find the tendency toward ferromagnetic order at low temperature, but with an increase in temperature, antiferromagnetic correlations between the layers dominate. Determination of the critical number of layers at which the interlayer antiferromagnetic order changes to ferromagnetic likely requires consideration of the nonlocal Coulomb interactions.

Tensor network quantum states are powerful tools for strongly correlated systems, tailored to capture local correlations such as in ground states with entanglement area laws. When applying tensor network states to interacting fermionic systems, a proper choice of the basis or orbitals can reduce the bond dimension of tensors and provide physically relevant orbitals. We introduce such a change of basis with unitary gates obtained from compressing fermionic Gaussian states into quantum circuits corresponding to various tensor networks. These circuits can reduce the ground-state entanglement entropy and improve the performance of algorithms such as the density matrix renormalization group. We study the Anderson impurity model with one and two impurities to show the potential of the method for improving computational efficiency and interpreting impurity physics. Furthermore, fermionic Gaussian circuits can also suppress entanglement during the time evolution out of low-energy state. Last, we consider Gaussian multiscale entanglement renormalization ansatz (GMERA) circuits which compress fermionic Gaussian states hierarchically. The emergent coarse-grained physical models from these GMERA circuits are studied in terms of their entanglement properties and suitability for performing time evolution.

The electronic structure and phonon dispersion of $X{\text{S}}_2$ with $X$ = Co, Tc, Ti, Ru, Nb, and Rh in the monolayer ${\mathrm{MoS}}_2$ structure with trigonal-prismatic coordination are studied from first principles. Although each $X{\text{S}}_2$ is dynamically unstable, ${\mathrm{CoS}}_2, {\mathrm{TcS}}_2, {\mathrm{RuS}}_2$, and ${\mathrm{RhS}}_2$ can be stabilized by developing charge density waves in the ($2\times 2$) supercell, leading to metal-insulator transitions. Without necessitating the metal-insulator transitions and large atomic distortions, the total energy may be lowered by mixing different transition metal elements to create multicomponent combinations for $X=\mathrm{Mo}$, Co, Tc, Ti, Ru, Nb, and Rh in the ($2\times 2$) supercell mentioned previously, which offers deeper insight into the stability mechanism of two-dimensional complex-concentrated materials and presents a wide range of $X{\text{S}}_2$ compounds that exhibit a variety of band structures, including direct- and indirect-gap semiconductors, metals, and semimetals. In addition, nonmagnetic ${\mathrm{MoS}}_2, {\mathrm{CoS}}_2, {\mathrm{TiS}}_2$, and ${\mathrm{RuS}}_2$ become magnetic after being mixed to form ${\mathrm{MoCoTiRuS}}_8$, showing great potential for spintronics applications.

In one spatial dimension, families of short-range entangled many-body quantum states, parameterized over some parameter space, can be topologically distinguished and classified by topological invariants built from the higher Berry phase—a many-body generalization of the Berry phase. Previous works identified the underlying mathematical structure (the gerbe structure) and introduced a multi-wave-function overlap, a generalization of the inner product in quantum mechanics, which allows for the extraction of the higher Berry phase and topological invariants. In this paper, building on these works, we introduce a connection, the higher Berry connection, for a family of parameterized matrix product states (MPS) over a parameter space. We demonstrate the use of our formula for simple nontrivial models.

We investigate the spin state stability of Mn in $\alpha \text{−}{\mathrm{Mn}}_2{\mathrm{O}}_3$ through the structural, insulator-to-metal transition under high pressure by x-ray emission spectroscopy (XES) and x-ray diffraction (XRD) up to 41 GPa. The XES spectra show a broadening of the main line and a weak shift of the satellite feature as pressure increases but no signature of spin transition while XRD confirms the full conversion to the $Cmcm$ phase at high pressure. Using multiplet calculations, we suggest that the XES spectral changes under pressure is driven by the increased Coulomb interaction in the compressed lattice. The absence of spin transition through the phase transition could be caused by Jahn-Teller distortions on the Mn sites, which stabilize the spin state, possibly leading to hopping conductivity owing to polaronic effects.

In this paper, the anomalous Hall effect of topologically nontrivial MXenes, $M_2{M}^{\prime }{\mathrm{C}}_2{\mathrm{O}}_2$, and the electronic structure in the presence of the magnetic proximity effect are theoretically investigated. The theoretical analysis is performed in two different ways: an effective model and a multi-orbital tight-binding model generated from the first-principles band structure. These two theoretical methods provide a similar profile of Berry curvature for electronic states near the bulk band gap, and they show an unconventional rise of hollowed-out peak in the profile with the tilt of the proximity magnetic potential. The anomalous Hall conductivity is also calculated as a function of the charge density and the tilt angle of the proximity magnetic order. Then, an unconventional enhancement of anomalous Hall conductivity by the tilt of magnetic order is theoretically predicted as a result of the variation of Berry curvature.

We construct a general theoretical framework for describing curvature-induced spin-orbit interactions on the basis of group theory. Our theory can systematically determine the emergence of spin splitting in the band structure according to symmetry in the wave number space and the bending direction of the material. As illustrative examples, we derive the curvature-induced spin-orbit coupling for carbon and silicon nanotubes. Our theory offers a strategy for designing valley-contrasting spin-orbit coupled materials by tuning their curvatures.

A magnetic Weyl semimetal presents the intriguing possibility of controlling topological properties through magnetic order. The kagome compound ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ has emerged as one of the most thoroughly characterized magnetic Weyl semimetals, yet the potential coexistence of a ferromagnetic state below $T_c$ = 172 K with a noncollinear antiferromagnetic phase or a glassy state remains unresolved. We employ ${}^{59}\mathrm{Co}$ NMR to gain a local perspective on the magnetic order. The magnetic and electric field gradient tensors at room temperature are determined by fitting the NMR spectra using evolutionary algorithms. Zero-field NMR measurements reveal that all Co sites are equivalent in the magnetic phase at low temperatures and up to 90 K. The local magnetic field follows in intensity the macroscopic magnetization as a function of temperature and is tilted from the $c$ axis by a few degrees toward the nearest triangle center. Above 90 K, a shoulder appears on the low-field side, which we attribute to a preferential tilting of the local field in one direction, breaking the equivalence between the three Co sites of the kagome structure. We rule out any coexistence with an in-plane antiferromagnetic phase and suggest instead that in-plane ferromagneticlike moments appear above 90 K and play an increasing role in the magnetic order up to the magnetic transition.

The Grüneisen ratio $\mathrm{\Gamma }$ and its magnetic analog, the magnetic Grüneisen ratio ${\mathrm{\Gamma }}_H$, are powerful probes to study the nature of quantum phase transitions. Here, we propose a Grüneisen parameter, the rotational Grüneisen ratio ${\mathrm{\Gamma }}_{\varphi }$, by introducing the orientation of the external field as a control parameter. We investigate ${\mathrm{\Gamma }}_{\varphi }$ of the highly anisotropic paramagnets CeRhSn and CeIrSn by measuring the rotational magnetocaloric effect in a wide range of temperatures and magnetic fields. We find that the ${\mathrm{\Gamma }}_{\varphi }$ data of both compounds are scaled by using the same critical exponents and the field-invariant critical field angle. Remarkably, the scaling function for the ${\mathrm{\Gamma }}_{\varphi }$ data reveals the presence of highly anisotropic quantum criticality that develops as a function of the easy-axis component of the magnetic field from the quantum critical line. This paper provides a thermodynamic approach to detect and identify magnetic quantum criticality in highly anisotropic systems.