There is a counterintuitive expectation proposed by Huse et al. [Phys. Rev. B 88, 014206 (2013)] and Chandran et al. [Phys. Rev. B 89, 144201 (2014)]: Localization protects the quantum order of the ground state, even in highly excited eigenstates. In this Rapid Communication, we numerically investigate the localization protection for symmetry-protected topological (SPT) order by considering a modified XXZ spin model, related to an interacting Su-Schrieffer-Heeger (SSH) model. We systematically study how many-body localization (MBL) protects SPT for different disorder types and different forms of interactions. A certain disorder leads to the clear degeneracy of the low-lying entanglement spectrum of each excited many-body eigenstate. This fact indicates that the existence of edge modes, which is a hallmark of SPT order, is protected by the MBL in excited many-body eigenstates. In addition, we also report how the MBL-protected edge modes in excited many-body eigenstates fade away for a diagonal-type disorder.

We introduce a Floquet spinor Bose-Einstein condensate induced by a periodically driven quadratic Zeeman coupling whose frequency is larger than any other energy scales. By examining a spin-1 system available in ultracold atomic gases, we demonstrate that such an external driving field has great effect on the condensate through emergence of a unique spin-exchange interaction. We uncover that the ferromagnetic condensate has several unconventional stationary states and thus exhibits rich continuous phase transitions. On the other hand, the antiferromagnetic condensate is found to possess a nontrivial metastable region, which supports unusual elementary excitations and hysteresis phenomena.

The Jahn-Teller distortion that can remove electronic degeneracies in partially occupied states and results in systematic atomic displacements is a common underlying feature to many of the intriguing phenomena observed in $3d$ perovskites, encompassing magnetism, superconductivity, orbital ordering, and colossal magnetoresistance. Although the seminal Jahn and Teller theorem was postulated almost a century ago, the origins of this effect in perovskite materials are still debated, including propositions such as superexchange, spin-phonon coupling, sterically induced lattice distortions, and strong dynamical correlation effects. Although the end result of Jahn-Teller distortions often includes a mix of such various contributions, due to coupling of various lattice, spin, and electronic modes with the distortions (“fingerprints” or “consequences” of Jahn-Teller), it is not clear what the primary cause is, i.e., which cases are caused by a pure electronic instability associated with degeneracy removal, as implied in the Jahn-Teller theorem, and which cases originate from other causes, such as semiclassical size effects. We propose a way to distinguish the materials with an electronic instability associated with degeneracy removal being the primary cause of the Jahn-Teller distortions, from others with octahedral rotation or tilts from a steric effect playing the primary role in electron-lattice coupling. This work provides a unified and quantitative density functional theory explanation of the experimentally observed trends of octahedral deformations in $AB{X}_3$ perovskites, without recourse to the dynamically correlated vision of electron interactions codified by the Mott-Hubbard mechanism. We inquire about the origin and predictability of different types of octahedral deformation by using a Landau-esque approach, where the orbital occupation pattern of a symmetric structure is perturbed, finding whether it is prone to total energy lowering the electronic instability or not. This is done for a systematic series of $AB{X}_3$ perovskite compounds having $3d$-orbital degeneracies, using the density functional approach. We identify (i) systems prone to an electronic instability (a true Jahn-Teller effect), such as $\mathrm{KCr}{\mathrm{F}}_3, \mathrm{KCu}{\mathrm{F}}_3, \mathrm{LaV}{\mathrm{O}}_3, \mathrm{KFe}{\mathrm{F}}_3$, and $\mathrm{KCo}{\mathrm{F}}_3$, where the instability is independent of magnetic order, and forces a specific orbital arrangement that is accommodated by a $B{X}_6$ octahedral deformation with a specific symmetry. On the other hand, (ii) compounds such as $\mathrm{LaTi}{\mathrm{O}}_3$ and $\mathrm{LaMn}{\mathrm{O}}_3$ with delocalized $d$ states do not show any electronically driven instability. Here, the alternate orbital ordering, which is an energy-lowering event irrespective of the presence of electronic instabilities, simply results from the coupling of lattice modes induced by semiclassical size effects (sterically induced), such as $B{X}_6$ octahedra rotations. (iii) Although $R\mathrm{V}{\mathrm{O}}_3$ ($R=\mathrm{Lu}-\mathrm{La}$, Y) perovskites exhibit hybridizations similarly to $\mathrm{LaTi}{\mathrm{O}}_3$, their $t_{2g}^2$ electronic structure is highly unstable and preserves the Jahn-Teller effect. However, here coexisting steric deformations and Jahn-Teller distortions result in strongly entangled spin-orbital properties.

A recent experiment reported a large anomalous Hall effect in magic angle twisted bilayer graphene (TBG) aligned with a hexagonal boron nitride (h-BN) substrate at 3/4 filling of the conduction band. In this paper we study this system theoretically and propose explanations of this observation. We emphasize that the physics for this system is qualitatively different from the pure TBG system. The aligned h-BN breaks in-plane twofold rotation symmetry and gaps out the Dirac crossings of ordinary TBG. The resulting valence and conduction bands of each valley carry equal and opposite Chern numbers $C=\pm 1$. A useful framework is provided by a lattice extended Hubbard model for this system, which we derive. An obvious possible explanation of the anomalous Hall effect is that at $3/4$ filling the system is a spin-valley polarized ferromagnetic insulator where the electrons completely fill a Chern band. We also examine an alternate, more radical proposal of a compressible valley-polarized but spin-unpolarized composite Fermi-liquid metallic state. We argue that either state is compatible with current experiments and propose ways to distinguish between them in the future. We also briefly discuss the physics at $1/2$ filling.

We show how a superconducting circuit consisting of three identical nonlinear oscillators in series considered in terms of its electrical modes can implement a strong, native three-body interaction among qubits. Because of strong interactions, part of the qubit subspace is coupled to higher levels. The remaining qubit states can be used to implement a restricted Fredkin gate, which in turn implements a controlled-not gate or a spin transistor. Including nonsymmetric contributions from couplings to ground and external control, we alter the circuit slightly to compensate and find average fidelities for our implementation of the above gates above $99.5\%$ with operation times on the order of a nanosecond. Additionally, we show how to analytically include all orders of the cosine contributions from Josephson junctions to the Hamiltonian of a superconducting circuit.

We investigate the microscopic description of exciton-polaritons that involves electrons, holes and photons within a two-dimensional microcavity. We show that in order to recover the simplified exciton-photon model that is typically used to describe polaritons, one must correctly define the exciton-photon detuning and exciton-photon (Rabi) coupling in terms of the bare microscopic parameters. For the case of unscreened Coulomb interactions, we find that the exciton-photon detuning is strongly shifted from its bare value in a manner akin to renormalization in quantum electrodynamics. Within the renormalized theory, we exactly solve the problem of a single exciton-polariton for the first time and obtain the full spectral response of the microcavity. In particular, we find that the electron-hole wave function of the polariton can be significantly modified by the very strong Rabi couplings achieved in current experiments. Our microscopic approach furthermore allows us to obtain the effective interaction between identical polaritons for any light-matter coupling. Crucially, we show that the standard treatment of polariton-polariton interactions in the very strong coupling regime is incorrect, since it neglects the light-induced modification of the exciton size and thus greatly overestimates the effect of Pauli exclusion on the Rabi coupling, i.e., the saturation of exciton oscillator strength. Our findings thus provide the foundations for understanding and characterizing exciton-polariton systems across the whole range of polariton densities.

Collective magnetic excitation modes, magnons, can be coherently coupled to microwave photons in the single excitation limit. This allows for access to quantum properties of magnons and opens up a range of applications in quantum information processing, with the intrinsic magnon linewidth representing the coherence time of a quantum resonator. Our measurement system consists of a yttrium iron garnet sphere and a three-dimensional microwave cavity at temperatures and excitation powers typical for superconducting quantum circuit experiments. We perform spectroscopic measurements to determine the limiting factor of magnon coherence at these experimental conditions. Using the input-output formalism, we extract the magnon linewidth ${\kappa }_{\mathrm{m}}$. We attribute the limitations of the coherence time at lowest temperatures and excitation powers to incoherent losses into a bath of near-resonance two-level systems (TLSs), a generic loss mechanism known from superconducting circuits under these experimental conditions. We find that the TLSs saturate when increasing the excitation power from quantum excitation to multiphoton excitation and their contribution to the linewidth vanishes. At higher temperatures, the TLSs saturate thermally and the magnon linewidth decreases as well.

We report on low-temperature heat-transport properties of the spin-1/2 triangular-lattice antiferromagnet ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$. Broad maxima in the thermal conductivity along the three principal axes, observed at about 5 K, are interpreted in terms of the Debye model, including the phonon umklapp scattering. For thermal transport along the $b$ axis, we found a pronounced field-dependent anomaly, close to the transition into the three-dimensional long-range-ordered state. No such anomalies were found for the transport along the $a$ and $c$ directions. We argue that this anisotropic behavior is related to an additional heat-transport channel through magnetic excitations, that can best propagate along the direction of the largest exchange interaction. In addition, peculiarities of the heat transport of ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ in magnetic fields up to the saturation field and above are discussed.

The charge density wave (CDW) in solids is a collective ground state combining lattice distortions and charge ordering. It is defined by a complex order parameter with an amplitude and a phase. The amplitude and wavelength of the charge modulation are readily accessible to experiment. However, accurate measurements of the corresponding phase are significantly more challenging. Here we combine reciprocal and real space information to map the full complex order parameter based on topographic scanning tunneling microscopy (STM) images. Our technique overcomes limitations of Fourier space based techniques to achieve distinct amplitude and phase images with high spatial resolution. Applying this analysis to transition metal dichalcogenides provides striking evidence that their CDWs consist of three individual unidirectional charge modulations whose ordering vectors are connected by the fundamental rotational symmetry of the crystalline lattice. Spatial variations in the relative phases of these three modulations account for the different CDW contrasts often observed in STM topographic images. Phase images further reveal topological defects and discommensurations, a singularity predicted by theory for a nearly commensurate CDW. Such precise real space mapping of the complex order parameter provides a powerful tool for a deeper understanding of the CDW ground state whose formation mechanisms remain largely unclear.

We identify theoretically the geometric phases of the electrons' spinor that can be detected in measurements of charge and spin transport through Aharonov-Bohm interferometers threaded by a magnetic flux $\mathrm{\Phi }$ (in units of the flux quantum) where Rashba spin-orbit and Zeeman interactions are active. We show that the combined effect of these two interactions produces a $sin\left(\mathrm{\Phi }\right)$ [in addition to the usual $cos\left(\mathrm{\Phi }\right)$] dependence of the magnetoconductance, whose amplitude is proportional to the Zeeman field. Therefore, although the magnetoconductance is an even function of the magnetic field, it is not a periodic function of it, and the widely used concept of a phase shift in the Aharonov-Bohm oscillations, as indicated in previous work, is not applicable. We find the directions of the spin polarizations in the system and show that in general (even without the Zeeman term) the spin currents are not conserved, implying the generation of magnetization in the terminals attached to the interferometer.

We present an exactly solvable $p$-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the $p+ip$ Richardson-Gaudin fermionic model, such as a third-order quantum phase transition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair Bose superfluid, and the exact eigenstate at the quantum critical point is a pair condensate analogous to the fermionic Moore-Read state.

We find closed-form solution of the Euler equation for a chiral magnet in terms of a skyrmion or a meron depending on the relative strengths of magnetic anisotropy and magnetic field. We show that the relevant length scales for these solutions primarily depend on the strengths of Dzyaloshinskii-Moriya interaction through its ratios, respectively, with magnetic field and magnetic anisotropy. We thus unambiguously determine the parameter dependencies on the radius of the topological structures particularly of the skyrmions, showing an excellent agreement with experiments and first-principles studies. An anisotropic Dzyaloshinskii-Moriya interaction suitable for thin films made with $C_{nv}$ symmetric materials is found to stabilize antiskyrmion and antimeron, which are prototypical for $D_{2d}$ symmetric systems, depending on the degree of anisotropy. Based on these solutions, we obtain a phase diagram by comparing the energies of various collinear and noncollinear competing phases.

We compute and compare even- and odd-parity superconducting order parameters of strontium ruthenate (${\mathrm{Sr}}_2{\mathrm{RuO}}_4$) in the limit of weak interactions, resulting from a fully microscopic three-dimensional model including spin-orbit coupling. We find that odd-parity helical and even-parity $d$-wave order are favored for smaller and larger values of the Hund's coupling parameter $J$, respectively. Both orders are found compatible with specific heat data and the recently reported nuclear magnetic resonance (NMR) Knight shift drop [A. Pustogow et al., Nature 574, 72 (2019)]. The chiral $p$-wave order, numerically very competitive with helical order, sharply conflicts with the NMR experiment.

Determining the symmetry of the order parameter of unconventional superconductors remains a recurrent topic and nontrivial task in the field of strongly correlated electron systems. Here we show that the behavior of Dirac points away from the Fermi energy is a potential tool to unveil the orbital structure of a superconducting state. In particular, we show that gap openings in such Dirac crossings are a signature of nonunitary multiorbital superconducting order. Consequently, also spectral features at higher energy can help us to identify broken symmetries of superconducting phases and the orbital structure of nonunitary states. Our results show how angle-resolved photoemission spectroscopy measurements can be used to detect nonunitary multiorbital superconductivity.

The existence of quasi-long-range order is demonstrated in nonequilibrium steady states in isotropic $XY$ spin chains including two types of additional terms that each generate a gap in the energy spectrum. The system is driven out of equilibrium by initializing a domain-wall magnetization profile through application of an external magnetic field and switching off the magnetic field at the same time the energy gap is activated. An energy gap is produced by either applying a staggered magnetic field in the $z$ direction or introducing a modulation to the $XY$ coupling. The magnetization, spin current, and spin-spin correlation functions are computed analytically in the thermodynamic limit at long times after the quench. For both types of systems, we find the persistence of power-law correlations despite the ground-state correlation functions exhibiting exponential decay.

The spatial localization of quantum states plays a central role in condensed-matter phenomena, ranging from many-body localization to topological matter. Building on the dissipation-fluctuation theorem, we propose that the localization properties of a quantum-engineered system can be probed by spectroscopy, namely, by measuring its excitation rate upon a periodic drive. We apply this method to various examples that are of direct experimental relevance in ultracold atomic gases, including Anderson localization, topological edge modes, and interacting particles in a harmonic trap. Moreover, inspired by a relation between quantum fluctuations and the quantum metric, we describe how our scheme can be generalized in view of extracting the full quantum-geometric tensor of many-body systems. Our approach opens an avenue for probing localization, as well as quantum fluctuations, geometry and entanglement, in synthetic quantum matter.

Recently, ${\mathrm{Cd}}_3{\mathrm{As}}_2$ has attracted intensive research interest as an archetypical Dirac semimetal, hosting three-dimensional linear-dispersive electronic bands near the Fermi level. Previous studies have shown that single-crystalline ${\mathrm{Cd}}_3{\mathrm{As}}_2$ has an anomalously low lattice thermal conductivity, ranging from 0.3 to 0.7 W/mK at 300 K, which has been attributed to point defects. In this work, we combine first-principles lattice dynamics calculations and temperature-dependent high-resolution Raman spectroscopy of high-quality single-crystal thin films grown by molecular-beam epitaxy to reveal the existence of a group of soft optical phonon modes at the Brillouin-zone center of ${\mathrm{Cd}}_3{\mathrm{As}}_2$. These soft phonon modes significantly increase the scattering phase space of heat-carrying acoustic phonons and are the origin of the low lattice thermal conductivity of ${\mathrm{Cd}}_3{\mathrm{As}}_2$. Furthermore, we show that the interplay between the phonon-phonon Umklapp scattering rates and the soft optical phonon frequency explains the unusual nonmonotonic temperature dependence of the lattice thermal conductivity of ${\mathrm{Cd}}_3{\mathrm{As}}_2$. Our results further suggest that the soft phonon modes are potentially induced by a Kohn anomaly associated with the Dirac nodes, in analogy to similar, nonetheless weaker, effects in graphene and Weyl semimetals.

We show that the exact ground state of the Lieb-Mattis Hamiltonian is an equal-weight superposition of all possible classical Néel states, and provide an exact formulation of this superposition in the $z$-spin basis for both $S=1/2$ and general $S$ using Schwinger bosons. In general, a superposition of possible rotations on a general initial state is symmetric if and only if the initial state has a nonzero overlap with a singlet state and is otherwise made up of states that vanish due to the symmetrization. Most notably, $|s,m=0\rangle$ states will vanish if symmetrized, which explains how a superposition of Néel states projects onto its singlet component.

Polarized neutron diffraction allows one to determine the local susceptibility tensor on the magnetic site both in single crystals and powders. It is widely used in the studies of single crystals, but it is still hardly applicable to a number of highly interesting powder materials, such as molecular magnets or nanoscale systems because of the low luminosity of existing instruments and the absence of appropriate data analysis software. We show that these difficulties can be overcome by using a large area detector in combination with the two-dimensional Rietveld method and powder samples with a magnetically induced preferred crystallite orientation. This is demonstrated by revisiting two test powder compounds, namely, the low anisotropy (soft) ferrimagnetic compound ${\mathrm{Fe}}_3{\mathrm{O}}_4$ and the spin-ice compound ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ with high local anisotropy. The values of the magnetic moments in ${\mathrm{Fe}}_3{\mathrm{O}}_4$ and the susceptibility tensors of ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at various temperatures and fields were found in perfect agreement with these found earlier in single-crystal experiments. The magnetically induced preferred crystallite orientation was used to study the local susceptibility of a single-molecule magnet $\mathrm{Co}{\left({\left[{\left({\mathrm{CH}}_3\right)}_2\mathrm{N}\right]}_2\mathrm{CS}\right)}_2{\mathrm{Cl}}_2$. Hence, the studies of local magnetic anisotropy in powder systems might now become accessible.

Hybrid quantum dot-oscillator systems have become attractive platforms to inspect quantum coherence effects at the nanoscale. Here, we investigate a Cooper-pair splitter setup consisting of two quantum dots, each linearly coupled to a local resonator. The latter can be realized either by a microwave cavity or a nanomechanical resonator. Focusing on the subgap regime, we demonstrate that cross-Andreev reflection, through which Cooper pairs are split into both dots, can induce nonlocal correlations between the two resonators. Harnessing these correlations allows to establish and control a nonlocal photon transfer between them. The proposed scheme can act as a photonic valve with single-photon accuracy, with potential applications for quantum heat engines and refrigerators involving mesoscopic resonators.