Studying magnetic properties of ${\mathrm{LiTmF}}_4$, a recognized insulating Van Vleck paramagnet, can hold promise for advancements in quantum computing, MRI, spintronics, material design, and potentially, single-photon technologies. This study may be pivotal due to challenges in simulating noncollinear magnetism using density functional theory (DFT), requiring more sophisticated spin configurations and time-consuming spin relaxations or embedded dynamical mean field theory. Instead, we utilize two distinct efficient and reliable schemes— ab initio DFT and a semiempirical superposition model, both integrated with crystal field (CF) theory (including Zeeman effect) and underpinned by statistical mechanics—to analyze noncollinear paramagnetic properties. At the core of this investigation is the ${\mathrm{S}}_4$ site symmetry of the ${\mathrm{Tm}}^{3+}$ ion, which admits several sets of six (seven) independent CF parameters (CFPs) under the reduced (complete) approach generated by suitable rotations of the coordinate system. By applying the Noether theorem, we show that these numerically distinct sets are physically equivalent. This is evidenced by computing the several conserved CFP quantities predicted by the Noether theorem, which exhibit notable coherence across different data sets. Using one of these equivalent sets of 7 CF parameters, as computed in [Phys. Rev. B 102, 045120 (2020)] under the complete approach, this study explores the theoretical analysis of multiplet splitting induced by the CF and the external magnetic field within the ${\mathrm{Tm}}^{3+}$ ion lattice in ${\mathrm{LiTmF}}_4$. We investigate the magnetic moment per ion and the temperature dependencies of magnetic susceptibility, utilizing a Hamiltonian, including the free ion, CF terms, and Zeeman interaction. The agreement of our findings with existing experimental data accentuates the efficacy of the proposed approach in reproducing magnetic properties in ${\mathrm{LiTmF}}_4$, providing a significant analytical tool for the analysis of EPR spectra in terms of the defined Zeeman $\mathit{g}$ tensor. This research may stand as a pivotal guide in the accurate determination of magnetic properties, potentially influencing significant advancements in technology and materials science.

Employing first-principles modeling and many-body methods, the magnetic properties of the spin-1/2 chain compound ${\mathrm{NaVOPO}}_4$ are explored. The extensive first-principles calculations establish an intricate three-dimensionally-coupled model that consists of weakly alternating $J-J^{\prime }$ antiferromagnetic chains running along cris-cross directions between two consecutive $ab$ planes, connected via two subleading couplings: a ferromagnetic exchange along the $c$ direction ($J_c$) and a weaker antiferromagnetic exchange ($J_a$) along the body-diagonal direction. The exact diagonalization and density matrix renormalized group study has been carried out on a two-dimensional spin model with $J-J^{\prime }-J_c$ and effective $J_d$ couplings, constructed based on the full model, for numerical ease. The $J_c-J_d$ phase diagram is found to host a disorder phase with a finite spin gap for comparable values of $J_c$ and $J_d$, arising out of the competing nature of these two interactions, other than two ordered phases. The calculated thermodynamic properties of this model provide a fair description of experimentally measured data. The predominant manifestation of $J_c$ and $J_d$ in the disorder phase happens in the stabilization of a multimagnon condensed phase upon gap closing by application of an external magnetic field. We further explore the effect of tensile uniaxial strain, which is found to drive the system from a gapful to a gapless ground state.

Spinon-magnon mixing was recently reported in botallackite ${\mathrm{Cu}}_2{\left(\mathrm{OH}\right)}_3\mathrm{Br}$ with a uniaxially compressed triangular lattice of ${\mathrm{Cu}}^{2+}$ quantum spins [H. Zhang et al., Phys. Rev. Lett. 125, 037204 (2020)]. Its nitrate counterpart rouaite, ${\mathrm{Cu}}_2{\left(\mathrm{OH}\right)}_3{\mathrm{NO}}_3$, has a highly analogous structure and might be expected to exhibit similar physics. To lay a foundation for research on this material, we clarify rouaite's magnetic phase diagram and identify both low-field phases. The low-temperature magnetic state consists of alternating ferromagnetic and antiferromagnetic chains, as in botallackite, but with additional canting, leading to net moments on all chains which rotate from one chain to another to form a ${90}^{\circ }$ cycloidal pattern. The higher-temperature phase is a helical modulation of this order, wherein the spins rotate from one Cu plane to the next. This extends to zero temperature for fields perpendicular to the chains, leading to a set of low-temperature field-induced phase transitions. Rouaite may offer another platform for spinon-magnon mixing, while our results suggest a delicate balance of interactions and high tunability of the magnetism.

We consider the vestigial phase with broken time reversal symmetry above the superconducting transition temperature of a two-component superconductor in two spatial dimensions. We show that, in contrast to three dimensions, a vestigial phase is in general allowed within Ginzburg-Landau theory. The vestigial phase occupies an increasing temperature region if the parameters in the Ginzburg-Landau theory give a larger energy difference between the broken time reversal symmetry phase and the other ordered phase.

We have investigated the effect of 2.6-GeV U irradiation on the superconductivity of $\mathrm{Cs}{\mathrm{V}}_3\mathrm{S}{\mathrm{b}}_5$ and $\mathrm{Cs}{\left({\mathrm{V}}_{0.93}\mathrm{N}{\mathrm{b}}_{0.07}\right)}_3\mathrm{S}{\mathrm{b}}_5$ single crystals by using resistivity and magnetization measurements. The critical transition temperature for $\mathrm{Cs}{\mathrm{V}}_3\mathrm{S}{\mathrm{b}}_5$ crystal is enhanced up to 4.3 K after irradiation with a dose of $B_{\mathrm{\Phi }}=2.0\mathrm{T}$, while the critical current density is increased up to $\sim 0.8\times {10}^4\mathrm{A}/\mathrm{c}{\mathrm{m}}^2$ after irradiation with a dose of $B_{\mathrm{\Phi }}=0.5\mathrm{T}$ under self-field at 2.0 K, which is about four times larger than that for the pristine crystal under the same condition. For $\mathrm{Cs}{\left({\mathrm{V}}_{0.93}\mathrm{N}{\mathrm{b}}_{0.07}\right)}_3\mathrm{S}{\mathrm{b}}_5$ crystal, the critical transition temperature remains almost constant up to $B_{\mathrm{\Phi }}=2.0\mathrm{T}$, followed by monotonic suppression with further increase of dose. Besides the enhanced critical current density, we observe an anomalous peak effect in the magnetic hysteresis loop close to zero field at low irradiation doses, which can be interpreted by the matching effect in irradiated $\mathrm{Cs}{\left({\mathrm{V}}_{0.93}\mathrm{N}{\mathrm{b}}_{0.07}\right)}_3\mathrm{S}{\mathrm{b}}_5$ crystals.

The structure of solid oxygen has been studied at pressures from 50 to 140 GPa using static structure search methods and molecular dynamics simulations with density functional theory and a hybrid exchange functional. Several crystalline structures with space group symmetries Pnma, $P$ $2_1$/m, Pm, and $P$ $6_3$/mmc have been identified as candidates for the $\zeta$ phase of oxygen at 0 K. Within the hybrid exchange functional framework and at 300 K temperature, $\mathit{Pm}$ is shown to be energetically most favorable above 111 GPa. A comparison with experimental x-ray diffraction, spectroscopic, and superconductivity measurements is provided for all competing structures.

Understanding the mechanism of negative thermal expansion (NTE) and controlling the thermal expansion properties of materials at the atomistic level have long captured the attention of scholars. In this regard, the NTE mechanism of fluorides such as monometallic $\mathrm{Sc}{\mathrm{F}}_3$ and bimetallic fluorides like $\mathrm{CaZr}{\mathrm{F}}_6$ is particularly interesting; despite sharing similar crystal structure, $\mathrm{CaZr}{\mathrm{F}}_6$ exhibits a thermal expansion coefficient twice that of $\mathrm{Sc}{\mathrm{F}}_3$. Why is this so? Here, we investigate the structural vibrations of these two substances in real and reciprocal space at atmospheric and zero pressure, respectively, using machine-learning based deep potentials in combination with density-functional theory. Our study reveals that the structural flexibility of $\mathrm{CaZr}{\mathrm{F}}_6$ results in a greater number of vibration modes exhibiting negative Grüneisen parameters. Moreover, the combined impact of octahedral distortion and tilt vibration leads to a substantially greater NTE for $\mathrm{CaZr}{\mathrm{F}}_6$ compared to $\mathrm{Sc}{\mathrm{F}}_3$. This work offers insights into understanding and tailoring NTE by considering polyhedral distortion in other open-framework materials.

This investigation covers the effects of variable exchange interactions on the spin dynamics of the zigzag honeycomb lattice. Using a Holstein-Primakoff expansion of the Heisenberg Hamiltonian with easy-axis anisotropy, we characterize the effects of multiple nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions with asymmetry within the context of a frustrated and nonfrustrated zigzag magnetic configuration. By building the model term by term, we directly observe the behavioral contributions from each interaction, how the system changes with anisotropy, and how asymmetric terms transform the system from a nonfrustrated to a frustrated state. By analyzing geometric frustration, we are able to demonstrate the role that NN and NNN interactions play within an asymmetric honeycomb lattice, show the emergence of direction-dependent Dirac nodes, and postulate that the standard Heisenberg interaction has a notable contribution to the behavior observed in the spin excitation behavior within the high-symmetry pathway $\mathrm{\Gamma }$-M. Furthermore, to examine the efficacy of our model, we compare it to known inelastic neutron scattering data for $\alpha \text{−}{\mathrm{RuCl}}_3$, which has been established to host a zigzag honeycomb ground state dominated by anisotropic interactions.

The exploitation of piezoelectric ferromagnetism in two-dimensional (2D) materials with large out-of-plane piezoelectric response is motivated not only by technological applications but also scientific interest. In this study, the $\mathrm{CrO}NM$ monolayer family $(N=\text{F,}\text{Cl};$ $M=\text{Br,}\text{Cl})$ was investigated using first-principles calculations, revealing that the Janus CrOFBr monolayer exhibits intrinsic ferromagnetic semiconductor behavior along with a significant out-of-plane piezoelectric effect. The calculated out-of-plane piezoelectric strain coefficients $d_{31}$ and $d_{32}$ are up to 1.21 and 0.63 pm/V, respectively. These values are greater than those of the majority of 2D materials. Furthermore, our findings demonstrate that applying tensile strain can enhance the out-of-plane piezoelectric response, leading to a respective 27% and 67% augmentation in the piezoelectric strain coefficients $d_{31}$ and $d_{32}$ compared to the unstrained configurations. This discovery holds great potential for propelling the field of nanoelectronics forward and facilitating the development of multifunctional semiconductor spintronic applications. Finally, by comparing $d_{31}$ and $d_{32}$ of the $\mathrm{CrO}NM$ monolayer family $(N=\text{F,}\text{Cl};$ $M=\text{Br,}\text{Cl})$, we find that the magnitudes of $d_{31}$ and $d_{32}$ are correlated with the electronegativity difference ratio. These findings provide valuable insights for the design of 2D piezoelectric materials with enhanced vertical piezoelectric responses.

The synthesis, structural, magnetic, thermal, and transport properties are reported for polycrystalline $\mathrm{PrI}{\mathrm{r}}_3$. At room temperature $\mathrm{PrI}{\mathrm{r}}_3$ displays the rhombohedral space group $R\text{−}3m$ and a ${\mathrm{PuNi}}_3$-type structure. At around 70 K a phase transition to a monoclinic $C2/m$ structure is observed and continued cooling reveals temperature independent behavior of the unit cell volume. Further, $\mathrm{PrI}{\mathrm{r}}_3$ undergoes a paramagnetic to ferromagnetic transition with $T_c=7.5\mathrm{K}$. The temperature dependent magnetic susceptibility follows the Curie-Weiss law with a positive Curie-Weiss temperature, and an effective moment that is close to the theoretical effective moment for a free $\mathrm{P}{\mathrm{r}}^{+3}$ ion. The structural transition introduces further complexity into the behavior of ${\mathrm{PuNi}}_3$-type materials and highlights the importance of temperature-dependent structural studies to complement physical property measurements in intermetallic compounds.

We investigate the pairing tendencies in the hole-doped Haldane spin-1 chain. To allow for doping, we extend the original spin chain Hamiltonian into a fermionic model involving a two-orbital Hubbard chain at intermediate or strong repulsive interaction strengths $U$ and for degenerate orbitals. At half filling and large $U$, the ferromagnetic Hund's coupling, $J_{\mathrm{H}}$, generates effective spin-1 moments, with antiferromagnetic correlations between sites. Using large-scale density matrix renormalization group calculations, we accurately study the system's behavior under light hole-doping. For $U=1.6$ in units of the noninteracting bandwidth and for $J_{\mathrm{H}}/U\gtrsim 0.275$, we find that singlet pairing dominates the long-distance physics, establishing this system as a promising platform for repulsively mediated superconductivity. We provide concrete examples of materials that could realize the physics described here. We also provide evidence that the system approaches a Luther-Emery liquid state at large system sizes, reminiscent of the behavior of doped one-orbital two-leg ladders at weak coupling, which also have superconducting tendencies. The numerically calculated central charge approaches one in the thermodynamic limit, indicating a single gapless mode as is expected for the Luther-Emery state. Exponents characterizing the power-law decays of singlet pair-pair and charge density-density correlations are determined, and found to approximately satisfy the Luther-Emery identity.

We investigate strong coupling topological superconductivity in twisted moiré bilayer ${\mathrm{WSe}}_2$. Our approach is based on an effective $t\text{−}J$ model with displacement-field-dependent complex hoppings, which is treated with the variational Gutzwiller projection method. The calculated phase diagram contains domes of topologically nontrivial superconducting phases, with Chern numbers $C=\pm 2,\pm 4$. The order parameter is characterized by a mixed ($d+id$)-wave (singlet) and ($p\text{−}ip$)-wave (triplet) gap symmetry. We also report on the appearance of an additional topologically trivial extended $s$-wave and $f$-wave paired phases. As we show, by changing the electron density and displacement field, one can tune the singlet and triplet contributions to the pairing, as well as induce topological phase transitions between superconducting states characterized by different values of the Chern number. We analyze the physical origin of the reported effects and discuss it briefly in the view of new possibilities for designing unconventional superconductivity in moiré systems.

We propose a framework based on the concept of the semigroup to understand the fermion sign problem. By using properties of contraction semigroups, we obtain sufficient conditions for quantum lattice fermion models to be sign-problem-free. Many previous results can be considered as special cases of our new results. As a direct application of our new results, we construct a class of sign-problem-free fermion lattice models, which cannot be understood by previous frameworks. This framework also provides an interesting aspect in understanding related quantum many-body systems. We establish a series of inequalities for all the sign-problem-free fermion lattice models that satisfy our sufficient conditions.

The Seebeck effect consists in the induction of a voltage drop due to the temperature difference in a conductor. In the middle of the 19th century, Kelvin proposed a relation between the Seebeck coefficient and the derivative of the chemical potential over temperature in the broken circuit regime. This relation appears to be nearly universal as it equally well applies to metals, semimetals, and semiconductors. We show that it may fail, however, in graphene, due to the nonlocality effects in the ballistic electronic transport regime. The correction to Kelvin's formula emerges due to the coexistence of counterpropagating nondissipative currents of cold and hot electrons. The external magnetic field normal to the graphene sample allows separating hot and cold currents in real space. The developed formalism may help interpreting the recent experimental data on ballistic edge currents in graphene bilayers in the quantum Hall regime [J. Barrier et al., Nature (London) 628, 741 (2024)].

A many-body quantum system whose topological defects are conserved, abundant, and mobile is a correlated quantum liquid. Since topological defects can be classified by homotopy groups, each homotopy identifies a class of quantum liquids. Here we explore the quantum liquids based on the ${\pi }_3\left(S^2\right)$ homotopy group, i.e., Hopf fibration. Their topologically nontrivial dynamics emerges from the interlinking between magnetic flux or skyrmion loops in the charge and spin sectors respectively. We lay down a field theory foundation for analyzing such states by naturally incorporating the well-known framing regularization into the theory, and constructing the appropriate topological Lagrangian terms. We show that at least two strongly correlated phases of interlinked loops can exist in $d=3$ spatial dimensions at zero and low-finite temperatures. These phases are closely related to the chiral quantum anomaly and do not have an obvious topological order, but they are distinguished from the trivial disordered phase by a generalization of the Wilson loop operator. In $d=4$ spatial dimensions, interlinked loops are able to produce topological order at zero temperature, featuring charge, angular momentum, and braiding fractionalization. We discuss some possible experimental signatures of loop entanglement in the quantum noise of charge currents.

Interacting lattice Hamiltonians at high temperature generically give rise to energy transport governed by the classical diffusion equation; however, predicting the rate of diffusion requires numerical simulation of the microscopic quantum dynamics. For the purpose of predicting such transport properties, computational time evolution methods must be paired with schemes to control the growth of entanglement to tractably simulate for sufficiently long times. One such truncation scheme—dissipation-assisted operator evolution (DAOE)—controls entanglement by damping out components of operators with large Pauli weight. In this paper, we generalize DAOE to treat fermionic systems. Our method instead damps out components of operators with large fermionic weight. We investigate the performance of DAOE, the new fermionic DAOE (FDAOE), and another simulation method, density matrix truncation (DMT), in simulating energy transport in an interacting one-dimensional Majorana chain. The chain is found to have a diffusion coefficient scaling like interaction strength to the fourth power, contrary to naive expectations based on Fermi's Golden rule—but consistent with recent predictions based on the theory of weak integrability breaking. In the weak interaction regime where the fermionic nature of the system is most relevant, FDAOE is found to simulate the system more efficiently than DAOE.