Entanglement entropy has been a powerful tool for analyzing phases and criticality in pure ground states via quantum Monte Carlo (QMC). However, mixed-state entanglement, relevant to systems with dissipation, finite temperature, and disjoint regions, remains less explored due to the lack of efficient numerical methods. In this work, we present a practical and easy-to-implement QMC method within the reweight-annealing framework, enabling efficient computation of the entanglement Rényi negativity by tracking its variation along given parameter paths. This method is scalable, parallelizable, and well suited for high-dimensional and large-scale simulations. Applying it to diverse scenarios, including one- and two-dimensional systems, ground and thermal states, and bipartite and tripartite partitions, not only is the information of the underlying conformal field theory achieved, but the role of entanglement in quantum and thermal phase transitions is revealed.

The aim of this study is to address the long-standing question of graphite melting and the nature of liquid carbon, a topic that has led to conflicting results since the late 1930s. In this study, graphite melting was performed using high-power CW-laser heating in an inert gas to a pressure of 6 kbar. Optical measurements such as high-speed pyrometry and spectropyrometry and high-speed video recording were used to capture and record the moment of liquid carbon formation. The pressure-dependent melting temperature and emissivity of the liquid carbon were measured and its density was estimated. All the obtained results showed strong correlation, resolving existing contradictions in the understanding of carbon's melting behavior, and providing insights into the nature of liquid carbon.

We investigated gram-scale macroscopic bulk acoustic wave (BAW) resonators manufactured from plates of piezoelectric lithium niobate. The intrinsic competing loss mechanisms were studied at cryogenic temperature through precision measurements of various BAW modes. Exceptional quality factors were measured for the longitudinal BAW modes in the 1–100 MHz range, with a maximum quality factor of 8.9 million, corresponding to a quality factor $\times$ frequency product of $3.8\times {10}^{14}$ Hz. Through measurements of the acoustic response to a strong drive tone, anomalous self-induced absorption and transparency effects are observed. We show that such observations can be explained by microscopic impurities and defect sites in the crystal bulk by the use of a nonlinear model of acoustic dissipation. The losses associated with these defects provide the ultimate limit of resonator performance, which could be improved in the future if more pure samples were available.

The new class of exactly solvable models of one-dimensional spin chains is found. Interactions of spins with crystalline electric fields (CEF) and spin-spin coupling between neighboring sites are taken into account for those models. Spin-spin coupling includes higher-order spin operators (the Stevens operators) and describes the interaction between $z\mathrm{th}$ components of the spins. We show that essential parts of the Hamiltonians of these models can be written in terms of exactly solvable transverse field Ising model (TFIM), in which certain combinations of the parameters of spin-spin interactions play the role of the TFIM exchange constant, and components of the CEFs play the role of external transverse magnetic field of the TFIM. The obtained results are valid for any values of spin (or total moments for rare-earth ions) and for the wide class of CEFs. The requirement for the exact solvability is that the space of single spin states should be split by the CEF into the subspaces with dimensions $\le 2$ (i.e., the only singlets and doublets are allowed). Cases of integer and half-integer spins are considered. For finite-size chains with integer spins and open ends we show numerically that energy spectra always contain the states whose energies do not depend on the CEF (the magnetic field for the TFIM). The energies (per spin) of these states decay as $L^{-1}$, where $L$ is the chain length. This behavior qualitatively distinguishes these states from known Majorana edge states and strong zero modes, where the energy decreases exponentially in $L$.

Spin reorientation transition (SRT)-induced electric polarization ($P$) is a striking manifestation of magnetoelectric coupling in type-II multiferroic materials. This phenomenon typically arises either from complex incommensurate magnetic structures that break spatial inversion symmetry or from changes in the magnetic point-group symmetry of commensurate spin structures during an SRT. In this study, we report an SRT-induced hidden $P$ in a commensurate magnetic arrangement on the background of a noncentrosymmetric lattice α-$\mathrm{FeP}{\mathrm{O}}_4$, which belongs to the berlinite-type structure stabilized in a nonpolar space group ($P{3}_{1}21$). The long-range antiferromagnetic ordering of α-$\mathrm{FeP}{\mathrm{O}}_4$ at $T_{\mathrm{N}}$ (∼24 K), followed by SRT at $T_{\mathrm{SR}}$ (∼17 K), is confirmed by magnetic susceptibility $\chi (H,T)$ and specific heat $C_{\mathrm{p}}(H,T)$ measurements. Interestingly, two significant dielectric (${\varepsilon }^{\prime }$) anomalies were observed at $T_{\mathrm{N}}$ and $T_{\mathrm{SR}}$, accompanied by a change in the sign of magnetodielectric (%), indicating a coupling between SRT and lattice ${\varepsilon }^{\prime }$ anomalies. Neutron powder diffraction analysis of the detailed spin structure correlated these ${\varepsilon }^{\prime }$ and $P$ with the magnetic lattice, where the change in in-plane anisotropy during the SRT results in a shift of the spin moment direction from the $ab$ plane to the $c$ axis supported by the density functional theory calculations. Furthermore, synchrotron x-ray diffraction and Raman scattering revealed a magnetostrictive effect and anomalous spin-phonon coupling at both $T_{\mathrm{N}}$ and $T_{\mathrm{SR}}$. The delicate interplay between magnetic anisotropy, magnetic exchange interactions, and crystal field effects at $\mathrm{F}{\mathrm{e}}^{3+}$ ions within a narrow $T$ window (Δ$T$ = 5 K) establishes α-$\mathrm{FeP}{\mathrm{O}}_4$ as a unique multiferroic material.

The movement of magnetic flux quanta (Abrikosov vortices) in superconductors leads to dissipation and is influenced by various ordering effects arising from vortex-vortex, vortex-defect, and vortex-edge interactions. Under combined dc and ac stimuli, when the distance traveled by fluxons during an ac cycle corresponds to an integer multiple of the vortex lattice period, the superconductor's current-voltage ($I\text{−}V$) curve displays synchronization (Shapiro) steps. However, in planar constrictions, frequency-locking effects rely on a perfectly ordered vortex lattice and are typically observed when periodic vortex pinning arrays dominate over intrinsic uncorrelated disorder. Here, we propose 3D superconducting open nanotubes as systems free of periodic disorder, where the $I\text{−}V$ curves are expected to display pronounced Shapiro steps. Using the time-dependent Ginzburg-Landau equation, we attribute the predicted effect to a reduction in the dimensionality of vortex motion. Namely, rolling a planar film into a tube causes the 2D vortex array, which initially moves throughout the film, to evolve into quasi-1D vortex chains that are restricted to areas where the normal component of the magnetic field is near its maximum. The discussed effects are relevant for superconducting devices, where vortex nucleation frequency and voltage stabilization by an external ac stimulus can enhance their operation.

Non-Hermitian skin effect allows the bulk states to collapse toward the boundaries, which originates from the nontrivial energy spectral topology described by nonzero spectral windings. Recent theoretical studies have revealed that the spectral windings do not accurately predict the skin effect in some cases, which has not yet been confirmed in the experiment. Here, we find that this abnormal phenomenon can also exist in a bilayer Hatono-Nelson chain, which is caused by the unidirectional coupling between two chains, where the energies are decoupled, but the wave functions are not. We implement this theoretical model in electric circuits and observe anomalous skin effects by measuring the localized voltage distributions. Our findings deepen the understanding of the skin effect in multichain systems and may inspire a more complete non-Hermitian theory.

The out-of-time-ordered correlator (OTOC) is a popular probe for quantum information spreading and thermalization. In systems with local interactions, the OTOC defines a characteristic butterfly light cone that separates a regime unperturbed by chaos from one where time-evolved operators and the OTOC approach equilibrium. This relaxation has been shown to proceed in two stages. The first stage exhibits an extensive timescale and a decay rate known as the “phantom eigenvalue”, which is slower than the gap of the transfer matrix. In this paper, we investigate the two-stage relaxation of the OTOC towards its equilibrium value in various local quantum circuits. We apply a systematic framework based on an emergent statistical model, where the dynamics of two single-particle modes—a domain wall and a magnon—govern the decay rates. We show that a configuration with coexisting domain wall and magnon modes generates the phantom rate in the first stage, while competition between these two modes determines the second stage. We also examine this relaxation within the operator cluster picture. The magnon modes translate into a bound state of clusters, and the domain wall into a random operator, giving consistent rates. Finally, we extend our findings from random-in-time circuits to a broad class of Floquet models.

In quantum mechanics, measurements are dynamical processes and thus they should be capable of inducing currents. The symmetries of the Hamiltonian and measurement operator provide an organizing principle for understanding the conditions for such currents to emerge. The central role is played by the inversion and time-reversal symmetries. We classify the distinct behaviors that emerge from single and repeated measurements, with and without coupling to a dissipative bath. While the breaking of inversion symmetry alone is sufficient to generate currents through measurements, the breaking of time-reversal symmetry by the measurement operator leads to a dramatic increase in the magnitude of the currents. We consider the dependence on the measurement rate and find that the current is nonmonotonic. Furthermore, nondegenerate measurements can lead to current loops within the steady state even in the Zeno limit.

Nonreciprocity of supercurrents may exist when both spatial inversion and time-reversal symmetries are broken, leading to the supercurrent diode effect (SDE). The spatial inversion symmetry may be broken by chiral structures in nanotubes where the SDE is expected when a magnetic flux passes through the tube. While such an effect has been predicted based on a phenomenological theory, a microscopic and quantitative study with a concrete lattice model is missing. Here, we investigate the SDE in chiral nanotubes made of carbon and those made of transition-metal dichalcogenides (TMDs) with tight-binding models. We obtain the SDE efficiency as a function of the nanotube radius, the chiral angle, the magnetic flux, the temperature, the chemical potential, etc., and find that sign flipping happens in various parameter dependencies. In TMD nanotubes, the SDEs with and without the spin-orbit coupling are compared. We also simulate chiral nanotubes made from square-lattice materials for comparison and discuss the effects of strain. Besides qualitative consistency with previous phenomenological theory, new features are found and the microscopic origins are clarified.

A family of nanographene molecules called phenalenyl-tessellation molecules (PTMs) exhibits two types of zero modes: a $\sqrt{3}\times \sqrt{3}$ type that spreads over the entire molecule and a vacancy-localized type. A periodic system of PTMs is expected to have low-energy bands that strongly reflect the properties of the zero modes of PTMs as effective atoms. In this study, we show that the low-energy Dirac bands in a class of honeycomb PTMs (H-PTM) can be represented by an effective honeycomb model which is determined only by the connections between neighboring effective atoms. The hopping parameters of H-PTM in each direction take positive integer ratios according to the connection order between two PTMs. By structurally designing each PTM, we can change the connection order of the PTMs and hence modulate the energy gap and the Fermi velocity of the Dirac band of the H-PTM. Moreover, we confirm that Dirac bands coexist with vacancy-localized zero modes in the H-PTM with vacancies. The result indicates that the nanographene structure arranging PTMs as effective atoms extends material design freedom that effectively generates a modulated Dirac electron system with coexisting localized electron spins for graphene-based electronic and quantum devices.

Displacement field control of elecronic bands in low-dimensional systems is a promising route toward engineering emergent quantum phases. Here, we report displacement-field-induced band inversion and modulation of the Berry phase of low-energy quasiparticles in high-mobility Bernal-stacked trilayer graphene (TLG). Using quantum oscillations, we track the evolution of the Fermi surface and topological properties of Dirac-like “gully” bands that emerge under a finite interlayer potential. We observe a striking sequence of transitions: at low displacement field $D$, the gullies are characterized by a Berry phase of $2\pi$ and large effective mass, indicating massive fermions. As $D$ increases, the Berry phase abruptly shifts to $\pi$ and the effective mass reaches a minimum, signaling the onset of massless Dirac behavior. At higher $D$, the Berry phase returns to $2\pi$, and the effective mass increases again, consistent with a band inversion. These findings demonstrate a rare, reversible topological phase transition—massive $\to$ massless $\to$ massive—driven entirely by an external displacement field. Despite robust theoretical predictions [Phys. Rev. B 87, 085424 (2013), Phys. Rev. B 87, 115422 (2013), and Phys. Rev. B 101, 245411 (2020)], this evolution of the band topology had escaped experimental detection. Our results establish TLG as a tunable platform for nanoscale control of band topology. They establish a means to tune between massive and Dirac-like dispersions dynamically providing a foundation for exploring field-switchable topological phenomena in layered two-dimensional systems.

The decrease in the Seebeck coefficient with increasing magnetic field and the rapid enhancement of thermal conductivity in longitudinal thermoelectric transport are often regarded as hallmark responses of the chiral anomaly. In this work, we investigate the thermoelectric responses of bulk topological insulators using the semiclassical Boltzmann transport equation. Our findings reveal that the Berry curvature can also induce a quadratic suppression of thermopower and a significant enhancement of thermal conductivity in systems without chirality, particularly when the chemical potential is near the band edge. These conclusions are broadly applicable to various topological insulators. Compared with ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, the pronounced band inversion in the conduction band of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ results in a distinct kink structure near the Van Hove singularity. Additionally, the sign of the $g$ factor has a strong influence on the signs of the thermoelectric coefficients. Our study highlights new challenges in identifying transport signatures of the chiral anomaly in topological semimetals and provides deeper insights into the thermoelectric transport behavior of topological materials influenced by Berry curvature.

We investigated the charge density wave (CDW) gap in $1T\text{−}{\mathrm{TiSe}}_2$ using scanning tunneling microscopy/scanning tunneling spectroscopy (STM/STS). We found that the tunneling spectra for the two types of Se atoms, differentiated due to the CDW, had different shapes near 0 mV, and the two normalized spectra crossed at about 180 mV. These results indicate that the CDW gap opens at about 180 meV above the Fermi energy $\left(E_{\mathrm{F}}\right)$. The STM measurement results are consistent with the CDW pattern expected from the Bardeen-Cooper-Schrieffer-like mean field theory with a CDW gap at $E_{\mathrm{F}}+180 \mathrm{meV}$. From our findings regarding the CDW gap, we suggest that the driving mechanism for the CDW in ${\mathrm{TiSe}}_2$ is the nesting of the isoenergetic surfaces at about $E_{\mathrm{F}}+180 \mathrm{meV}$.

The valley transport of electrons can carry not only charge but also spin angular momentum and orbital angular momentum (OAM). However, investigations on thermoelectric transport of OAM manipulated by valley degrees of freedom remain limited. Here, using the ferromagnetic transition metal dichalcogenides ${\mathrm{RuCl}}_2$ as an example, we investigate valley-contrasting Berry curvature and demonstrate its role in generating valley-dependent anomalous and orbital Nernst effects. The thermoelectric transport of OAM is shown to be modulated by intrinsic spin polarization and exhibits characteristics of valley-orbital coupling. Furthermore, we show that spin-valley coupling plays a crucial role in controlling the orbital Nernst effect and distinguishing it from the anomalous Nernst effect. Based on these findings, we propose a thermoelectric transport mechanism for generating pure orbital currents.

Understanding the interplay among magnetism, electron correlations, and complex electronic structures in rare-earth materials requires both high-quality single crystals and systematic investigation of their electronic properties. In this study, we have successfully grown a single crystal of ${\mathrm{SmAg}}_2{\mathrm{Ge}}_2$ and investigated its anisotropic physical properties and de Haas-van Alphen (dHvA) quantum oscillations through experimental and theoretical approaches. ${\mathrm{SmAg}}_2{\mathrm{Ge}}_2$ crystallizes in the well-known ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type tetragonal structure with lattice parameters, $a=4.226$ Å and $c=11.051$ Å. Electrical transport and magnetization measurements indicate that it is metallic and exhibits antiferromagnetic ordering below the Néel temperature, $T_{\mathrm{N}}=9.2\mathrm{K}$. ${\mathrm{SmAg}}_2{\mathrm{Ge}}_2$ exhibits a linear nonsaturating magnetoresistance, reaching $\sim 97$% at $2\mathrm{K}$ for applied magnetic field $B\parallel \left[001\right]$ and a significant anomalous Hall effect with an anomalous Hall angle of $0.10–0.14$. Additionally, magnetization measurements reveal dHvA quantum oscillations for magnetic fields greater than 8 T. Our calculated electronic structure, quantum oscillations, and anomalous Hall effect in the canted antiferromagnetic state closely align with experimental results, underscoring the role of complex electronic structure and spin-canting-driven nonzero Berry curvature in elucidating the physical properties of ${\mathrm{SmAg}}_2{\mathrm{Ge}}_2$.

We have drawn connections between the Sachdev-Ye-Kitaev model and the multi-orbit Hatsugai-Kohmoto model, emphasizing their similarities and differences regarding chaotic behaviors. The features of the spectral form factor, such as the dip-ramp-plateau structure and the adjacent gap ratio, indicate chaos in the disordered orbital Hatsugai-Kohmoto model. One significant conclusion is that the plateau value of the out-of-time-order correlator, whether in the Hatsugai-Kohmoto model, Sachdev-Ye-Kitaev model with two- or four-body interactions, or a disorder-free Sachdev-Ye-Kitaev model, does not effectively differentiate between integrable and chaotic phases in many-body systems. This observation suggests a limitation in using out-of-time-order correlator plateau values as a diagnostic tool for chaos. Our exploration of these ideas provides a deeper understanding of how chaos arises in non-Fermi-liquid systems and the tools we use to study it. It opens the door to further questions, particularly about whether there are more effective ways to distinguish between chaotic and integrable phases in these complex systems.

The interplay between nontrivial topology, magnetism, and strong correlation has generated considerable research interest in condensed matter physics. The topological $R\text{Al}X$ ($R$ = rare earth; $X$ = Si and Ge) family has provided an excellent platform for exploring these complex interactions. Here, we performed infrared spectroscopy measurements on the ferromagnetic (FM) topological semimetal PrAlSi, in order to investigate the impact of FM orderings on the topological band structure. We find that the optical conductivity associated with the Dirac/Weyl cones exhibits two segments of linearly increasing parts in the normal state, connected by a kink feature at around 1960 ${\mathrm{cm}}^{-1}$. By entering the FM state, however, an additional linear-growing segment shows up in between the original ones, suggesting that the band structure is reconstructed. We propose that these observations can be effectively explained by a scenario where the Dirac/Weyl nodes are split into pairs of Weyl nodes with lower degeneracy, due to the time reversal symmetry breaking induced by the FM ordering. This band structure reconstruction also leads to a sudden enhancement of the itinerant carrier density. In addition, the effective mass of the itinerant carriers are estimated to be three orders of magnitude smaller than the free electron mass, providing a rare case where nearly all the free carriers exhibit behaviors characteristic of relativistic Dirac or Weyl fermions. Our results demonstrate a compelling example of the strong interaction between magnetic order and topological band structures, which opens up new avenues for exploring novel topological materials and their potential applications.