The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in nonequilibrium setups. Therefore, it is vital to recognize states which are locally less complex and thus describable with (classical) effective theories. We use unsupervised learning with autoencoder neural networks to detect the local complexity of time-evolved states by determining the minimal number of parameters needed to reproduce local observations. The latter can be used as a probe of thermalization, to assign the local complexity of density matrices in open setups, and for the reconstruction of underlying Hamiltonian operators. Our approach is an ideal diagnostics tool for data obtained from (noisy) quantum simulators because it requires only practically accessible local observations.

We report results of magnetization, specific heat, and muon spin relaxation ($\mu \mathrm{SR}$) measurements on single crystals of disorder-free ${\mathrm{Yb}}^{3+}$ triangular lattice $\mathrm{Yb}{\left({\mathrm{BaBO}}_3\right)}_3$. The magnetization experiments show anisotropic magnetic properties with Curie-Weiss temperatures ${\theta }_{\perp }=-1.40\mathrm{K}$ ($H\perp c$) and ${\theta }_{\parallel }=-1.16\mathrm{K}$ ($H\parallel c$) determined from low-temperature data. The absence of both long-range antiferromagnetic order and spin freezing is confirmed down to 0.27 K at zero field. A two-level Schottky anomaly due to the opening of the ground-state Kramers doublet is observed from the low-temperature specific heat measurements when the applied magnetic fields ${\mu }_{0}H>0.7\mathrm{T}$. At zero field, the increase of both $C_{\mathrm{mag}}/T$ and the muon spin relaxation rate $\lambda$ below 1 K is due to the electronic spin excitations, which often exist in quantum magnets where dipole-dipole interactions create an anisotropy of magnetic properties. The spin excitation is also supported by the unusual maximum of the field dependence of $\lambda$ due to the field-induced increase in the density of excitations. We argue that dipolar interaction is dominant and induces the spin dynamics in the quantum magnet $\mathrm{Yb}{\left({\mathrm{BaBO}}_3\right)}_3$.

We have successfully manipulated the electronic properties of FeSe thin flakes based on a field-effect transistor with a solid proton conductor as the gate dielectric. The phase diagram as a function of gate voltage demonstrates three evident discrete superconducting phases with $T_{\mathrm{c}}$ corresponding to $\sim 8, \sim 34$, and $\sim 42$ K, respectively, which is similar to those observed in ${\mathrm{Li}}_x\mathrm{FeSe}$ and ${\mathrm{Na}}_x\mathrm{FeSe}$ by tuning Li or Na content with the solid-ion-conductor gating technique. In the protonation process, the final state with a saturation of the amount of hydrogen ions is reached at a moderately low gate voltage. It suggests that such a device based on a proton conductor can be used to modulate the physical properties by controlling the intercalated proton content and to explore the hydrogen storage capacity of materials.

Local measurements in quantum systems are projective operations which act to counteract the spread of quantum entanglement. Recent work has shown that local, random measurements applied to a generic volume-law entanglement generating many-body system are able to force a transition into an area-law phase. This work shows that projective operations can also force a similar classical phase transition; we show that local projections in a chaotic system can freeze information dynamics. In rough analogy with measurement-induced phase transitions, this is characterized by an absence of information spreading instead of entanglement entropy. We leverage a damage-spreading model of the classical transition to predict the butterfly velocity of the system both near to and away from the transition point. We map out the full phase diagram and show that the critical point is shifted by local projections, but remains in the directed percolation universality class. We discuss the implication for other classical chaotic many-body systems and the relation to synchronization transitions.

The magnetic spin Hall effect (MSHE) is an anomalous charge-to-spin conversion phenomenon that occurs in ferromagnetic materials. In contrast to the conventional spin Hall effect (SHE), being a time-reversal even effect, the magnetic counterpart is time-reversal odd. In this work, we use ab initio calculations to investigate the MSHE for the bulk ferromagnets Fe, Co, and Ni. The magnitudes of the MSHE of Fe and Co are comparable to those of the SHE, but the MSHE is strongly dependent on the electron lifetime and the MSHE and SHE can moreover have opposite signs. For Ni the MSHE is smaller than the SHE, but in general, the MSHE cannot be ignored for spin-orbit torques. Considering a charge current we analyze how both the MSHE and SHE contribute to a total Hall angle. We extend our analysis of the MSHE to its orbital counterpart, that is, the magnetic orbital Hall effect (MOHE), for which we show that the MOHE is in general smaller than the orbital Hall effect (OHE). We compute furthermore the thermal analogs, i.e., the spin and orbital Nernst effects, and their magnetic counterparts. Here our calculations show that the magnetic spin and orbital Nernst effects of Ni are substantially larger than those of Fe and Co.

In a thin-film topological insulator (TI), the edge states on two surfaces may couple by quantum tunneling, opening a gap known as the hybridization gap. Controlling the hybridization gap and transport has a variety of potential uses in photodetection and energy-harvesting applications. In this paper, we report the effect of strain, and electric and magnetic field, on the hybridization gap and transport in a thin ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ film, investigated within the tight-binding theoretical framework. We demonstrate that vertical compression decreases the hybridization gap, as does tensile in-plane strain. Applying an electric field breaks the inversion symmetry and leads to a Rashba-like spin splitting proportional to the electric field, hence closing and reopening the gap. The influence of a magnetic field on thin-film TI is also discussed, starting from the role of an out-of-plane magnetic field on quantum Hall states. We further demonstrate that the hybridization gap can be controlled by an in-plane magnetic field, and that by applying a sufficiently strong field a quantum phase transition from an insulator to a semimetal can be achieved.

The low-energy excitation properties of the excitonic condensate in the semimetal and semiconducting materials are inspected in the extended Falicov-Kimball model. In the framework of the unrestricted Hartree-Fock approximation, we have released a set of self-consistent equations so the excitonic condensate order parameter and then the optical conductivity and the dynamical excitonic susceptibility function are evaluated. We find that the optical conductivity becomes significant and shows a sharp peak at a frequency that is twice as of the excitonic condensate order parameter once the system settles in the excitonic condensate. In the meanwhile, out of the excitonic condensation state, the dynamical excitonic susceptibility function in the semimetal state releases a dominant peak at low frequency if Coulomb interaction is sufficiently large. This character indicates the possibility of the resonance bound excitonic condensate even in high-temperature normal semimetals. The resonance is dramatically reinforced inside of the semiconducting state and that specifies the stability of the bound excitonic coherent state of the preformed excitons in the semiconducting materials.

Sign problems in fermion quantum Monte Carlo (QMC) simulation appears to be an extremely hard problem. Traditional lore passing around for years tells people that when there is a sign problem, the average sign in QMC simulation approaches zero exponentially fast with the space-time volume of the configurational space. We, however, analytically show this is not always the case and manage to find physical bounds for the average sign. Our understanding is based on a direct connection between the sign bounds and a well-defined partition function of the reference system and could distinguish when the bounds have the usual exponential scaling and when they are bestowed on an algebraic scaling at the low-temperature limit. We analytically explain such algebraic sign problems found in flat-band moiré lattice models at the low-temperature limit. At finite temperature, a domain-size argument based on sign bounds also explains the connection between sign behavior and finite-temperature phase transition. Sign bounds, as a well-defined observable, may have the ability to ease or even make use of the sign problem.

In the present paper we derive the general expressions for the differential entropy per particle near van Hove singularities (vHs) in the density of states. The dependence of entropy per particle on chemical potential and temperature demonstrates different behavior depending on the type of vHs, and distinguishes high-order vHs with different divergence exponents and flat bands. In addition, it allows one to test the “flatness” of the band in experiment. We compare the analytic predictions with the numerical calculation of the differential entropy for tight-binding models of graphene, the Lieb lattice, and the square-octagon lattice. Our results show that the obtained analytic expressions capture the main features of the differential entropy, thus serving as a good probe for details of the density of states structure.

Various types of topological phenomena at criticality are currently under active research. In this paper we suggest to generalize the known topological quantities to finite temperatures, allowing us to consider gapped and critical (gapless) systems on the same footing. It is then discussed that the quantization of the topological indices, also at critically, is retrieved by taking the low-temperature limit. This idea is explicitly illustrated on a simple case study of chiral critical chains where the quantization is shown analytically and verified numerically. The formalism is also applied for studying robustness of the topological indices to various types of disordering perturbations.

Proper consideration of anharmonicity is important for the calculation of thermal conductivity. However, how the anharmonicity influences the thermal conduction in amorphous materials is still an open question. In this work, we uncover the role of anharmonicity on the thermal conductivity of amorphous silica ($a\text{−}{\mathrm{SiO}}_2$) by comparing the thermal conductivity predicted from the harmonic theory and the anharmonic theory. Moreover, we explore the effect of anharmonicity-induced frequency shift on the prediction of thermal conductivity. It is found that the thermal conductivity calculated by the recently developed anharmonic theory (quasi-harmonic Green-Kubo approximation) is higher than that calculated by the harmonic theory developed by Allen and Feldman. The use of anharmonic vibrational frequencies also leads to a higher thermal conductivity compared with that calculated using harmonic vibrational frequencies. The anharmonicity-induced frequency shift is a mechanism for the positive temperature dependence of the thermal conductivity of $a\text{−}{\mathrm{SiO}}_2$ at higher temperatures. Further investigation on the mode diffusivity suggests that although anharmonicity has a larger influence on locons than diffusons, the increase in thermal conductivity due to anharmonicity is mainly contributed by the anharmonicity-induced increase of the diffusivity of diffusons. Finally, it is found that the cross-correlations between diffusons and diffusons contribute most to the thermal conductivity of $a\text{−}{\mathrm{SiO}}_2$, and the locons contribute to the thermal conductivity mainly through collaboration with diffusons. These results offer new insights into the nature of the thermal conduction in $a\text{−}{\mathrm{SiO}}_2$.

Entanglement is a central feature of many-body quantum systems and plays a unique role in quantum phase transitions. In many cases, the entanglement spectrum, which represents the spectrum of the density matrix of a bipartite system, contains valuable information beyond the sole entanglement entropy. Here we investigate the entanglement spectrum of the long-range XXZ model. We show that within the critical phase it exhibits a remarkable self-similarity. The breakdown of self-similarity and the transition away from a Luttinger liquid is consistent with renormalization group theory. Combining the two, we are able to determine the quantum phase diagram of the model and locate the corresponding phase transitions. Our results are confirmed by numerically-exact calculations using tensor-network techniques. Moreover, we show that the self-similar rescaling extends to the geometrical entanglement as well as the Luttinger parameter in the critical phase. Our results pave the way to further studies of entanglement properties in long-range quantum models.

Detecting weak magnetic fields is paramount in areas such as scanning magnetometers and manipulation of magnetic nanoparticles, thus rendering it crucial to increase the weak-field sensitivity for developing next-generation magnetic sensors. The current approaches for high-sensitivity sensors, such as superconducting quantum interference devices, are complex and expensive. By contrast, magnetoresistive sensors and particularly extraordinary magnetoresistive sensors offer a simple operation at room temperature but, to date, at inferior sensitivity. To overcome these challenges, we induce device symmetry breaking to enhance the weak magnetic field sensitivity in semiconductor-metal hybrid structures exhibiting extraordinary magnetoresistance. Retaining the device mirror symmetry yields symmetric magnetoresistance curves with $R\left(B\right)=R(-B)$, which results in inferior detection of weak magnetic fields as ${[dR/dB]}_{B\to 0}=0$. Using finite element modeling, we study the change in device behavior as the symmetry is broken by varying the device geometry by spatially varying the constituent material properties or both. We show that symmetry breaking has three important implications: First, breaking the mirror symmetry causes an asymmetric sensor response with $R\left(B\right)\ne R(-B)$, benefiting from a largely enhanced sensitivity to weak magnetic fields and detection of the magnetic field direction. Second, an interplay with the Hall effect causes a large negative magnetoresistance exceeding 79% at $B=1$ T and room temperature without magnetic constituents or explicit optimization of this property. Third, the asymmetric geometries can be used as a key ingredient toward designing on-demand magnetoresistive characteristics such as linearity at low magnetic fields, step functions, and magnetic switchlike behavior. These implications pave the way for asymmetric topology optimization of magnetoresistive devices with unparalleled performance.

We show that finite current in superconductors can induce topological phase transitions, as a result of the deformation of the quasiparticle spectrum by a finite center-of-mass (COM) momentum of the Cooper pairs. To show the wide applicability of this mechanism, we examine the topological properties of three prototypical systems: the Kitaev chain, $s$-wave superconductors, and $d$-wave superconductors. We introduce a finite COM momentum as an external field corresponding to the supercurrent and show that all the models exhibit current-induced topological phase transitions. We also discuss the possibility of observing the phase transitions in experiments and the relation to the other finite COM momentum pairing states.

We present the synthesis and physical properties of a breathing pyrochlore magnet ${\mathrm{CuAlCr}}_4{\mathrm{S}}_8$ via synchrotron x-ray diffraction, magnetization under ambient and applied hydrostatic pressure, heat capacity, and muon spin relaxation/rotation measurements. ${\mathrm{CuAlCr}}_4{\mathrm{S}}_8$ exhibits positive thermal expansion with a concave upward temperature dependence. We observed a sharp antiferromagnetic ordering transition of a purely magnetic nature at 20 K, which shifts by as much as 3.2 K on application of 600 MPa pressure. The breathing factor ($B_f=J^{\prime }/J$) in breathing pyrochlores can be an important parameter to tune the magnetic ground states of the pyrochlore lattice. The breathing factor can be modulated through the breathing ratio, the ratio of the sizes of the two tetrahedra, by using different elements at the $A$ and $A^{\prime }$ sites in the breathing pyrochlore structure. We find that ${\mathrm{CuAlCr}}_4{\mathrm{S}}_8$ has a breathing ratio of 1.0663(8), which is comparable to other sulfur breathing pyrochlores.

Ternary iron nitrides are of considerable interest due to their diverse magnetic properties. We find, based on first principles calculations, that the relatively minor structural distortion from the cubic antiperovskite structure in ${\mathrm{Fe}}_3\mathrm{GeN}$, consisting of octahedral rotations, leads to unusual magnetic behavior. In particular, there is a separation into Fe sites with very different magnetic behaviors, specifically a site with Fe atoms having a stable local moment and a site where the Fe shows characteristics of much more itinerant behavior. This shows a remarkable flexibility of the Fe magnetic behavior in these nitrides and points towards the possibility of systems where minor structural and chemical changes can lead to dramatic changes in magnetic properties. The results suggest that, analogously to oxide perovskite materials, modulation of magnetic properties via chemical or strain control of octahedral rotation may be feasible. This may then lead to approaches for tuning magnetism to realize properties of interest, for example, tuning magnetic transitions to quantum critical regimes or to proximity to metamagnetic transitions of interest for devices.

Strongly correlated systems with the interplay of electronic, charge, spin, and orbital degrees of freedom have, in recent times, received a surge of interest because of their rich physics, novel physical properties, and potential applications. In the present work, we study the structural, magnetic, and electronic properties and orbital ordering in layered perovskite-type $A\mathrm{Mn}{\mathrm{F}}_4 (A=\mathrm{K},\mathrm{Rb})$ from first principles. A detailed analysis of the electronic properties in both compounds reveals an interesting nodal-line-like dispersion at $\sim 0.4$ eV below the Fermi level at the hinges of the Brillouin zone. Magnetic properties reflect the quasi-two-dimensional magnetism in these compounds, with very weak exchange interaction between the layers. Our results report the robust in-plane ferromagnetic spin order in $A\mathrm{Mn}{\mathrm{F}}_4$ ($A$=K, Rb) with the critical temperatures estimated to be around 30–60 K. We also find an anti-ferro-orbital ordering within the $ab$ plane and a ferro-orbital ordering out of plane favoring the $C$-type orbital order in these compounds.

The thermodynamic and dynamical properties of a model of Dirac fermions with a deconfined quantum critical point (DQCP) separating an interaction-generated quantum spin Hall insulator from an $s$-wave superconductor [Liu et al., Nat. Commun. 10, 2658 (2019)] are studied using quantum Monte Carlo simulations. Inside the deconfined quantum critical region bound by the single-particle gap, spinons and spinless charge-$2e$ skyrmions emerge. Since the model conserves total spin and charge, and has a single length scale, these excitations lead to a characteristic linear temperature dependence of the uniform spin and charge susceptibilities. At the DQCP, the order parameter dynamic structure factors show remarkable similarities that support emergent Lorentz symmetry. Above a critical temperature, superconductivity is destroyed by the proliferation of spin-1/2 vortices.

Invertible fermionic topological (IFT) phases are gapped phases of matter with nondegenerate ground states on any closed spatial manifold. When open boundary conditions are imposed, nontrivial IFT phases support gapless boundary degrees of freedom. Distinct IFT phases in one-dimensional space with an internal symmetry group $G_f$ have been characterized by a triplet of indices $\left(\right[(\nu ,\rho )],[\mu \left]\right)$. Our main result is an elementary derivation of the fermionic stacking rules of one-dimensional IFT phases for any given internal symmetry group $G_f$ from the perspective of the boundary, i.e., we give an explicit operational definition for the boundary representation $(\left[({\nu }_{\wedge },{\rho }_{\wedge })\right],\left[{\mu }_{\wedge }\right])$ obtained from stacking two IFT phases characterized by the triplets of boundary indices $(\left[({\nu }_1,{\rho }_1)\right],\left[{\mu }_1\right])$ and $(\left[({\nu }_2,{\rho }_2)\right],\left[{\mu }_2\right])$, respectively.