We explain how gapped quantum spin liquids, both conventional and “fractonic,” may be unambiguously diagnosed experimentally using the technique of multidimensional coherent spectroscopy. “Conventional” nonchiral gapped quantum spin liquids (e.g., $Z_2$ spin liquid) do not have sharp signatures in linear response, but they $\mathit{do}$ have clear fingerprints in nonlinear response, accessible through the already existing experimental technique of two-dimensional coherent spectroscopy. Type I fracton phases (e.g., X-cube) are (surprisingly) even easier to distinguish, with strongly suggestive features even in linear response, and unambiguous signatures in nonlinear response. Type II fracton systems, like Haah's code, are most subtle, and they may require consideration of high-order nonlinear response for unambiguous diagnosis.

Optical control of chirality in chiral superconductors bears potential for future topological quantum computing applications. When a chiral domain is written and erased by a laser spot, the Majorana modes around the domain can be manipulated on ultrafast timescales. Here we study topological superconductors with two chiral order parameters coupled via light fields by a time-dependent real-space Ginzburg-Landau approach. Continuous optical driving, or the application of supercurrent, hybridizes the two chiral order parameters, allowing one to induce and control the superconducting state beyond what is possible in equilibrium. We show that superconductivity can even be enhanced if the mutual coupling between two order parameters is sufficiently strong. Furthermore, we demonstrate that short optical pulses with spot size larger than a critical one can overcome a counteracting diffusion effect and write, erase, or move chiral domains. Surprisingly, these domains are found to be stable, which might enable optically programmable quantum computers in the future.

Non-Fermi liquids (NFLs) are a class of strongly interacting gapless fermionic systems without long-lived quasiparticle excitations. An important group of NFL models feature itinerant fermions coupled to soft bosonic fluctuations near a quantum-critical point and are widely believed to capture the essential physics of many unconventional superconductors. However, numerically, the direct observation of a canonical NFL behavior in such systems, characterized by a power-law form in the Green's function, has been elusive. Here, we consider a Sachdev-Ye-Kitaev (SYK)-like model with random Yukawa interaction between critical bosons and fermions (dubbed the Yukawa-SYK model). We show that it is immune from the minus-sign problem and hence can be solved exactly via large-scale quantum Monte Carlo simulation beyond the large-$N$ limit accessible to analytical approaches. Our simulation demonstrates that the Yukawa-SYK model features “self-tuned quantum criticality”; namely, the system is critical independent of the bosonic bare mass. We put these results to the test at finite $N$, and our unbiased numerics reveal clear evidence of these exotic quantum-critical NFL properties—the power-law behavior in the Green's function of fermions and bosons—which propels the theoretical understanding of critical Planckian metals and unconventional superconductors.

Magnetic skyrmions are topological spin textures that can be used as information carriers for the next-generation information storage and processing. The electric-field controlling of skyrmions in such devices is essential but remains technologically challenging. Here, using the first-principle calculation and the Ginzburg-Landau theory, we propose a reliable process for writing and deleting skyrmions by electric fields, on the platform of a multiferroic heterostructure, particularly the ${\text{Cr}}_2{\text{Ge}}_2{\text{Te}}_6/{\text{In}}_2{\text{Se}}_3$ heterostructure. We show that the electric field controls the electric polarization and indirectly influences the antisymmetric Dzyaloshinskii-Moriya interaction (DMI) between the magnetic moments. The latter is responsible for the generation and removal of the skyrmion spin textures, and we study this mechanism by the Ginzburg-Landau analysis. We discuss the real-space Berry curvature, topological Hall effects, possible quantum anomalous Hall effect, and other competing magnetic structures. These results represent examples of quantum technology and may have potential applications in future skyrmionics and the device fabrication.

The full transient dielectric-function (DF) tensor of ZnO after UV-laser excitation in the spectral range 1.4–3.6 eV is obtained by measuring an $m$-plane-oriented ZnO thin film with femtosecond (fs)-time-resolved spectroscopic ellipsometry. From the merits of the method, we can distinguish between changes in the real and the imaginary part of the DF as well as changes in birefringence and dichroism, respectively. We find pump-induced switching from positive to negative birefringence in almost the entire measured spectral range for about 1 ps. Simultaneously, weak dichroism in the spectral range below 3.0 eV hints at contributions of inter-valence-band transitions. Line-shape analysis of the DF above the band gap based on discrete exciton, exciton-continuum, and exciton-phonon-complex contributions shows a maximal dynamic increase in the transient exciton energy by 80 meV. The absorption coefficient below the band gap reveals an exponential line shape attributed to Urbach-rule absorption mediated by exciton–longitudinal-optic-phonon interaction. The transient DF is supported by first-principles calculations for ${10}^{20}{\mathrm{cm}}^{-3}$ excited electron-hole pairs in ideal bulk ZnO.

Topological crystalline superconductors have attracted rapidly rising attention due to the possibility of higher-order phases, which support Majorana modes on boundaries in $d-2$ or lower dimensions. However, although the classification and bulk topological invariants in such systems have been well studied, it is generally difficult to faithfully predict the boundary Majoranas from the band-structure information due to the lack of well-established bulk-boundary correspondence. Here we propose a protocol for deriving symmetry indicators that depend on a minimal set of necessary symmetry data of the bulk bands and can diagnose boundary features. Specifically, to obtain indicators manifesting clear bulk-boundary correspondence, we combine the topological crystal classification scheme in real space and a twisted equivariant K-group analysis in momentum space. The key step is to disentangle the generally mixed strong and weak indicators through a systematic basis-matching procedure between our real-space and momentum-space approaches. We demonstrate our protocol using an example of two-dimensional time-reversal odd-parity superconductors, where the inversion symmetry is known to protect a higher-order phase with corner Majoranas. Symmetry indicators derived from our protocol can be readily applied to an ab initio database and could fuel material predictions for strong and weak topological crystalline superconductors with various boundary features.

We propose a method for studying the strong interaction regimes in twisted bilayer graphene using hybrid Wannier functions that are Wannier-like in one direction and Bloch-like in the other. We focus on the active bands as given by the continuum model proposed by Bistritzer and MacDonald, [Proc. Natl. Acad. Sci. 108, 12233 (2011)] and discuss the properties of corresponding hybrid Wannier functions. We then employ the method for a study of the fillings of $\pm 3$ electrons per moiré cell using the Hartree-Fock method. We discuss at length different regimes under which a quantized anomalous Hall effect is seen in these two fillings.

We show that magnetic fluctuations can destroy the Hebel-Slichter peak in conventional superconductors. The Hebel-Slichter peak has previously been expected to survive even in the presence of strong electronic interactions. However, we show that antiferromagnetic fluctuations suppress the peak at $\mathit{q}=0$ in the imaginary part of the magnetic susceptibility ${\chi }_{+-}^{″}\left(\mathit{q},\omega \right)$, which causes the Hebel-Slichter peak. This is of general interest as in many materials superconductivity is found near a magnetically ordered phase, and the absence of a Hebel-Slichter peak is taken as evidence of unconventional superconductivity in these systems. For example, no Hebel-Slichter peak is observed in the $\kappa \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_{2}X$ organic superconductors but heat capacity measurements have been taken to indicate $s$-wave superconductivity. Similarly, experiments indicate nodeless superconductivity in many iron pnictide superconductors which exhibit no peak in the relaxation rate. If antiferromagnetic fluctuations destroy the putative Hebel-Slichter peak in organic superconductors, then the peak should be restored by applying a pressure, which is known to suppress antiferromagnetic correlations in these materials.

Symmetry-protected topological (SPT) phases are gapped phases of matter that cannot be deformed to a trivial phase without breaking the symmetry or closing the bulk gap. Here we introduce a notion of a topological obstruction that is not captured by bulk energy gap closings in periodic boundary conditions. More specifically, given a symmetric boundary termination we say two bulk Hamiltonians belong to distinct boundary obstructed topological phases (BOTPs) if they can be deformed to each other on a system with periodic boundaries, but cannot be deformed to each other in the open system without closing the gap at at least one high-symmetry surface. BOTPs are not topological phases of matter in the standard sense since they are adiabatically deformable to each other on a torus, but, similar to SPTs, they are associated with boundary signatures in open systems such as surface states or fractional corner charges. In contrast to SPTs, these boundary signatures are not anomalous and can be removed by symmetrically adding lower-dimensional SPTs on the boundary, but they are stable as long as the spectral gap at high-symmetry edges/surfaces remains open. We show that the double-mirror quadrupole model of [W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Science 357, 61 (2017)] is a prototypical example of such phases, and present a detailed analysis of several aspects of boundary obstructions in this model. In addition, we introduce several three-dimensional models having boundary obstructions, which are characterized either by surface states or fractional corner charges. Furthermore, we provide a complete characterization of boundary obstructed phases in terms of symmetry representations. Namely, two distinct BOTP phases correspond to equivalent band representations in the periodic system which become inequivalent upon restricting the symmetry group to that of the open system. This is used to shown that for a given open boundary, there is only one class of BOTPs which corresponds to a local representation of the symmetry of the open system and thus can be designated as the trivial phase. All other BOTP classes do not correspond to local representation of the open system and as a result necessarily exhibit a filling anomaly or gapless surface states.

We investigate two different types of relativistic Kondo effects, distinguished by heavy-impurity degrees of freedom, by focusing on the energy-momentum dispersion relations of the ground state with condensates composed of a light Dirac fermion and a nonrelativistic impurity fermion. Heavy-fermion degrees of freedom are introduced in terms of two types of heavy-fermion effective theories, in other words, two heavy-fermion limits for the heavy Dirac fermion, which are known as the heavy-quark effective theories (HQETs) in high-energy physics. While the first one includes only the heavy-particle component, the second one contains both the heavy-particle and heavy-antiparticle components, which are opposite in their parity. From these theories, we obtain two types of Kondo effects, in which the dispersions near the Fermi surface are very similar, but they differ in the structure at low momentum. We also classify the possible forms of condensates in the two limits. The two Kondo effects will be examined by experiments with Dirac/Weyl semimetals or quark matter, lattice simulations, and cold-atom simulations.

We theoretically investigate the optical activity of three-dimensional Dirac semimetals (DSMs) using circular dichroism (CD). We show that DSMs in the presence of a magnetic field in any one of the mirror-symmetric planes of the materials exhibit a notable dichroic behavior. In particular, for different orientations of the light field with respect to the mirror-symmetric plane, the CD in type-II DSMs can detect the presence of mirror anomaly by showing sharply distinct patterns at the mirror-symmetric angle. Interestingly, we find that the CD can also distinguish type-II DSMs having only one Dirac point at a time-reversal invariant momentum from type-I DSMs with a pair of Dirac points on the rotation axis of the crystals.

We introduce a two-parameter approximate counter-diabatic term into the Hamiltonian of the transverse-field Ising model for quantum annealing to accelerate convergence to the solution, generalizing an existing single-parameter approach. The protocol is equivalent to unconventional diabatic control of the longitudinal and transverse fields in the transverse-field Ising model and thus makes it more feasible for experimental realization than an introduction of new terms such as nonstoquastic catalysts toward the same goal of performance enhancement. We test the idea for the $p$-spin model with $p=3$, which has a first-order quantum phase transition, and show that our two-parameter approach leads to significantly larger ground-state fidelity and lower residual energy than those by traditional quantum annealing and by the single-parameter method. We also find a scaling advantage in terms of the time-to-solution as a function of the system size in a certain range of parameters as compared to the traditional methods in the sense that an exponential time complexity is reduced to another exponential complexity with a smaller coefficient. Although the present method may not always lead to a drastic exponential speedup in difficult optimization problems, it is useful because of its versatility and applicability for any problem after a simple algebraic manipulation, in contrast to some other powerful prescriptions for acceleration such as nonstoquastic catalysts in which one should carefully study in advance if it works in a given problem and should identify a proper way to meticulously control the system parameters to achieve the goal, which is generally highly nontrivial.

As a series of work about “fractonic superfluids,” in this paper, we develop an exotic fractonic superfluid phase in $d$-dimensional space where subdimensional particles—their mobility is partially restricted—are condensed. The off-diagonal long range order (ODLRO) is investigated. To demonstrate, we consider “lineons”—a subdimensional particle whose mobility is free only in certain one-dimensional directions. We start with a $d$-component microscopic Hamiltonian model. The model respects a higher-rank symmetry such that both particle numbers of each component and angular charge moments are conserved quantities. By performing the Hartree-Fock-Bogoliubov approximation, we derive a set of Gross-Pitaevskii equations and a Bogoliubov–de Gennes (BdG) Hamiltonian, which leads to a description of both condensed components and unification of gapless phonons and gapped rotons. With the coherent-path-integral representation, we also derive the long-wavelength effective field theory of gapless Goldstone modes and analyze quantum fluctuations around classical ground states. The Euler-Lagrange equations and Noether charges/currents are also studied. In two spatial dimensions and higher, such an ODLRO stays stable against quantum fluctuations. Finally, we study vortex configurations. The higher-rank symmetry enforces a hierarchy of thermal vortex excitations whose structures are dominated by two guiding statements. Specially, we construct two types of vortex excitations, the conventional and dipole vortices. The latter carries a charge with dimension as a momentum. The two statements can be more generally applicable. Further perspectives are discussed.

We investigate the nature of the magnetic excitations of a bilayer single-orbital Hubbard model in the intermediate-coupling regime. This model exhibits a quantum phase transition (QPT) between a paramagnetic (PM) and an insulating antiferromagnetic (AFM) phase at a critical value of the coupling strength. By using the random phase approximation, we show that the QPT is continuous when the PM state is a band insulator and that the corresponding quantum critical point (QCP) arises from the condensation of preformed excitons. These low-energy excitons re-emerge on the other side of the QCP as the transverse and longitudinal modes of the AFM state. In particular, the longitudinal mode remains sharp for the model parameters relevant to ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ because of the strong easy-axis anisotropy of this material.

We investigate the second quantization form of the entanglement Hamiltonian (EH) of various subregions for the ground state of several interacting lattice fermions and spin models. The relation between the EH and the model Hamiltonian itself is an unsolved problem for the ground state of generic local Hamiltonians. In this paper, we demonstrate that the EH is practically local and its dominant components are related to the terms present in the model Hamiltonian up to a smooth spatially varying temperature even for (a) discrete lattice systems, (b) systems with no emergent conformal or Lorentz symmetry, and (c) subsystems with nonflat boundaries, up to relatively strong interactions. We show that the mentioned local temperature at a given point decays in a manner inversely proportional to its distance from the boundary between the subsystem and the environment. We find the subdominant terms in the EH as well and show that they are severely suppressed away from the boundaries of subsystem and are relatively small near them.

Ferromagnetism in two-dimensional ${\mathrm{CrI}}_3$ has generated a lot of excitement, and it was recently proposed that the spin-orbit coupling (SOC) in iodine may generate bond-dependent spin interactions leading to magnetic anisotropy. Here, we derive a microscopic spin model of $S=3/2$ on transition metals surrounded by heavy ligands in honeycomb Mott insulators using a strong-coupling perturbation theory. For ideal octahedra we find Heisenberg and Kitaev interactions, which favor the magnetic moment along the cubic axis via quantum fluctuations. When a slight trigonal distortion of the octahedra is present together with the SOC, three additional interactions arise, composed of the off-diagonal symmetric $\mathrm{\Gamma }$ and ${\mathrm{\Gamma }}^{\prime }$ and single-ion anisotropy. The resulting magnetic anisotropy pins the moment perpendicular to the honeycomb plane as observed in a single layer of ${\mathrm{CrI}}_3$, suggesting the significance of SOC and trigonal distortion in understanding magnetism of two-dimensional Mott insulators. A comparison with the spin-orbit coupled $J_{\mathrm{eff}}=1/2$ and $S=1$ models is also presented.

We study the phase-ordering dynamics of a uniform Bose gas in two dimensions following a quench into the ordered phase. We explore the crossover between dissipative and conservative evolution by performing numerical simulations within the classical field methodology. Regardless of the dissipation strength, we find clear evidence for universal scaling, with dynamical critical exponent $z$ characterizing the growth of the correlation length. In the dissipative limit we find growth consistent with the logarithmically corrected law ${[t/log(t/t_0)]}^{1/z}$, and exponent $z=2$, in agreement with previous studies. Decreasing the dissipation towards the conservative limit, we find strong numerical evidence for the expected growth law $t^{1/z}$. However, we observe a smooth crossover in $z$ that converges to an anomalous value distinctly lower than 2 at a small finite dissipation strength. We show that this lower exponent may be attributable to a power-law vortex mobility arising from vortex-sound interactions.

We observe a structural phase transition between two configurations of a superradiant crystal by coupling a Bose-Einstein condensate to an optical cavity and applying imbalanced transverse pump fields. The transition can be interpreted as a transition between two nonpolar, centro-symmetric structures involving a change in polarization. We find that this first order phase transition is accompanied by transient dynamics of the order parameter which we measure in real time. The phase transition and the excitation spectrum can be derived from a microscopic Hamiltonian, in quantitative agreement with our experimental data.

We predict that junctions between an antiferromagnetic insulator and a superconductor provide a robust platform to create a one-dimensional topological superconducting state. Its emergence does not require the presence of intrinsic spin-orbit coupling nor noncollinear magnetism, but arises solely from repulsive electronic interactions on interfacial solitonic states. We demonstrate that a topological superconducting state is generated by repulsive interactions at arbitrarily small coupling strength, and that the size of the topological gap rapidly saturates to one of the parent trivial superconductor. Our results put forward antiferromagnetic insulators as a new platform for interaction-driven topological superconductivity.

We report on the fate of the quantum Hall effect in graphene under intense laser illumination. By using Floquet theory combined with both a low energy description and full tight-binding models, we clarify the selection rules, the quasienergy band structure, as well as their connection with the two-terminal and multiterminal conductance in a device setup as relevant for experiments. We show that the well-known dynamical gaps that appear in the Floquet spectrum at $\pm \hslash \mathrm{\Omega }/2$ lead to a switch-off of the quantum Hall edge transport for different edge terminations except for the armchair one, where two terms cancel out exactly. More interestingly, we show that near the Dirac point changing the laser polarization (circular right or circular left) controls the Hall conductance, by allowing to switch it on or off, or even by flipping its sign, thereby reversing the chirality of the edge states. This might lead to new avenues to fully control topologically protected transport.