We examine models of fermions with infinite-range interactions that realize non-Fermi liquids with a continuously variable U(1) charge density $\mathcal{Q}$ and a nonzero entropy density $\mathcal{S}$ at vanishing temperature. Real-time correlators of operators carrying U(1) charge $q$ at a low temperature $T$ are characterized by a $\mathcal{Q}$-dependent frequency ${\omega }_{\mathcal{S}}=(qT/\hslash )(\partial \mathcal{S}/\partial \mathcal{Q})$, which determines a spectral asymmetry. We show that the correlators match precisely with those of the two-dimensional anti–de Sitter (${\mathrm{AdS}}_2$) horizons of extremal charged black holes. On the black hole side, the matching employs $\mathcal{S}$ as the Bekenstein-Hawking entropy density and the laws of black hole thermodynamics that relate $(\partial \mathcal{S}/\partial \mathcal{Q})/(2\pi )$ to the electric field strength in ${\mathrm{AdS}}_2$. The fermion model entropy is computed using the microscopic degrees of freedom of a UV complete theory without supersymmetry.

In 1933, Meissner and Ochsenfeld reported the expulsion of magnetic flux—the diamagnetic Meissner effect—from the interior of superconducting lead. This discovery was crucial in formulating the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. In exotic superconducting systems BCS theory does not strictly apply. A classical example is a superconductor-magnet hybrid system where magnetic ordering breaks time-reversal symmetry of the superconducting condensate and results in the stabilization of an odd-frequency superconducting state. It has been predicted that under appropriate conditions, odd-frequency superconductivity should manifest in the Meissner state as fluctuations in the sign of the magnetic susceptibility, meaning that the superconductivity can either repel (diamagnetic) or attract (paramagnetic) external magnetic flux. Here, we report local probe measurements of faint magnetic fields in a $\mathrm{Au}/\mathrm{Ho}/\mathrm{Nb}$ trilayer system using low-energy muons, where antiferromagnetic Ho (4.5 nm) breaks time-reversal symmetry of the proximity-induced pair correlations in Au. From depth-resolved measurements below the superconducting transition of Nb, we observe a local enhancement of the magnetic field in Au that exceeds the externally applied field, thus proving the existence of an intrinsic paramagnetic Meissner effect arising from an odd-frequency superconducting state.

In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological (SET) phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain “anomalous” SETs can only occur on the surface of a 3D symmetry-protected topological (SPT) phase. In this paper, we describe a procedure for determining whether a SET of a discrete, on-site, unitary symmetry group $G$ is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions is captured by the fourth cohomology group $H^4(G,\mathrm{U}(1))$, which also precisely labels the set of 3D SPT phases, with symmetry group $G$. An explicit procedure for calculating the cohomology data from a SET is given, with the corresponding physical intuition explained. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3D bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid [$\mathrm{U}(1{)}_2$] topological order with a reduced symmetry ${\mathbb{Z}}_2\times {\mathbb{Z}}_2\subset \mathrm{SO}(3)$, which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3D SPT models realizing the anomalous surface terminations and demonstrate that they are nontrivial by computing three-loop braiding statistics. Possible extensions to antiunitary symmetries are also discussed.

Cuprates and iron-based superconductors are two classes of unconventional high-$T_c$ superconductors based on $3d$ transition elements. Recently, two principles, the correspondence principle and the magnetic selective pairing rule, have emerged to unify their high-$T_c$ superconducting mechanisms. These principles strongly regulate electronic structures that can host high-$T_c$ superconductivity. Guided by these principles, here, we propose high-$T_c$ superconducting candidates that are formed by cation-anion trigonal bipyramidal complexes with a $d^7$ filling configuration on the cation ions. Their superconducting states are expected to be dominated by the $d_{xy}\pm i{d}_{x^2-y^2}$ pairing symmetry.

We study theoretically the far-from-equilibrium relaxation dynamics of spin spiral states in the three-dimensional isotropic Heisenberg model. The investigated problem serves as an archetype for understanding quantum dynamics of isolated many-body systems in the vicinity of a spontaneously broken continuous symmetry. We present a field-theoretical formalism that systematically improves on the mean field for describing the real-time quantum dynamics of generic spin-$1/2$ systems. This is achieved by mapping spins to Majorana fermions followed by a $1/N$ expansion of the resulting two-particle-irreducible effective action. Our analysis reveals rich fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral states. In particular, we find the sudden appearance of long-lived prethermalized plateaus with diverging lifetimes as the spiral winding is tuned toward the thermodynamically stable ferro- or antiferromagnetic phases. The emerging prethermalized states are characterized by different bosonic modes being thermally populated at different effective temperatures and by a hierarchical relaxation process reminiscent of glassy systems. Spin-spin correlators found by solving the nonequilibrium Bethe-Salpeter equation provide further insight into the dynamic formation of correlations, the fate of unstable collective modes, and the emergence of fluctuation-dissipation relations. Our predictions can be verified experimentally using recent realizations of spin spiral states with ultracold atoms in a quantum gas microscope [ et al., Phys. Rev. Lett. 113, 147205 (2014)].

Transition metal compounds often undergo spin-charge-orbital ordering due to strong electron-electron correlations. In contrast, low-dimensional materials can exhibit a Peierls transition arising from low-energy electron-phonon-coupling-induced structural instabilities. We study the electronic structure of the tunnel framework compound ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$, which exhibits a temperature-dependent ($T$-dependent) paramagnetic-to-ferromagnetic-metal transition at $T_C=180\mathrm{K}$ and transforms into a ferromagnetic insulator below $T_{\mathrm{MI}}=95\mathrm{K}$. We observe clear $T$-dependent dynamic valence (charge) fluctuations from above $T_C$ to $T_{\mathrm{MI}}$, which effectively get pinned to an average nominal valence of ${\mathrm{Cr}}^{+3.75}$ (${\mathrm{Cr}}^{4+}:{\mathrm{Cr}}^{3+}$ states in a $3:1$ ratio) in the ferromagnetic-insulating phase. High-resolution laser photoemission shows a $T$-dependent BCS-type energy gap, with $2G(0)\sim 3.5(k_B{T}_{\mathrm{MI}})\sim 35\mathrm{meV}$. First-principles band-structure calculations, using the experimentally estimated on-site Coulomb energy of $U\sim 4\mathrm{eV}$, establish the necessity of strong correlations and finite structural distortions for driving the metal-insulator transition. In spite of the strong correlations, the nonintegral occupancy (2.25 $d\text{−}\text{electrons}/\mathrm{Cr}$) and the half-metallic ferromagnetism in the $t_{2g}$ up-spin band favor a low-energy Peierls metal-insulator transition.

Many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain “pseudopotential” Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi ${\mathbb{Z}}_3$ states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent $\mathrm{SU}(n)$ cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.

Many NP-hard problems can be seen as the task of finding a ground state of a disordered highly connected Ising spin glass. If solutions are sought by means of quantum annealing, it is often necessary to represent those graphs in the annealer’s hardware by means of the graph-minor embedding technique, generating a final Hamiltonian consisting of coupled chains of ferromagnetically bound spins, whose binding energy is a free parameter. In order to investigate the effect of embedding on problems of interest, the fully connected Sherrington-Kirkpatrick model with random $\pm 1$ couplings is programmed on the D-Wave ${\mathrm{Two}}^{\mathrm{TM}}$ annealer using up to 270 qubits interacting on a Chimera-type graph. We present the best embedding prescriptions for encoding the Sherrington-Kirkpatrick problem in the Chimera graph. The results indicate that the optimal choice of embedding parameters could be associated with the emergence of the spin-glass phase of the embedded problem, whose presence was previously uncertain. This optimal parameter setting allows the performance of the quantum annealer to compete with (and potentially outperform, in the absence of analog control errors) optimized simulated annealing algorithms.

We study the unitary time evolution of antiferromagnetic order in the Hubbard model after a quench starting from the perfect Néel state. In this setup, which is well suited for experiments with cold atoms, one can distinguish fundamentally different pathways for melting of long-range order at weak and strong interaction. In the Mott insulating regime, melting of long-range order occurs due to the ultrafast transfer of energy from charge excitations to the spin background, while local magnetic moments and their exchange coupling persist during the process. The latter can be demonstrated by a local spin-precession experiment. At weak interaction, local moments decay along with the long-range order. The dynamics is governed by residual quasiparticles, which are reflected in oscillations of the off-diagonal components of the momentum distribution. Such oscillations provide an alternative route to study the prethermalization phenomenon and its influence on the dynamics away from the integrable (noninteracting) limit. The Hubbard model is solved within nonequilibrium dynamical mean-field theory, using the density-matrix renormalization group as an impurity solver.

Three-dimensional topological Dirac semimetals have a linear dispersion in 3D momentum space and are viewed as the 3D analogues of graphene. Here, we report angle-dependent magnetotransport on the newly revealed ${\mathrm{Cd}}_3{\mathrm{As}}_2$ single crystals and clearly show how the Fermi surface evolves with crystallographic orientations. Remarkably, when the magnetic field lies in the [112] or $[44\overline{1}]$ axis, magnetoresistance oscillations with only single period are present. However, the oscillation shows double periods when the field is applied along the $[1\overline{\mathbf{1}}0]$ direction. Moreover, aligning the magnetic field at certain directions also gives rise to double period oscillations. We attribute the observed anomalous oscillation behavior to the sophisticated geometry of Fermi surface and illustrate a complete 3D Fermi surface with two nested anisotropic ellipsoids around the Dirac points. Additionally, a submillimeter mean-free path at 6 K is found in ${\mathrm{Cd}}_3{\mathrm{As}}_2$ crystals, indicating ballistic transport in this material. By measuring the magnetoresistance up to 60 T, we reach the quantum limit ($n=1$ Landau level) at about 43 T. These results improve the knowledge of the Dirac semimetal material ${\mathrm{Cd}}_3{\mathrm{As}}_2$ and also pave the way for proposing new electronic applications based on 3D Dirac materials.

We study a series of ${\mathrm{LiFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ compounds with different Co concentrations by transport, optical spectroscopy, angle-resolved photoemission spectroscopy, and nuclear magnetic resonance. We observe a Fermi-liquid to non-Fermi-liquid to Fermi-liquid (FL-NFL-FL) crossover alongside a monotonic suppression of the superconductivity with increasing Co content. In parallel to the FL-NFL-FL crossover, we find that both the low-energy spin fluctuations and Fermi surface nesting are enhanced and then diminished, strongly suggesting that the NFL behavior in ${\mathrm{LiFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ is induced by low-energy spin fluctuations that are very likely tuned by Fermi surface nesting. Our study reveals a unique phase diagram of ${\mathrm{LiFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ where the region of NFL is moved to the boundary of the superconducting phase, implying that they are probably governed by different mechanisms.

The magnetoelectric (ME) effect, i.e., cross control of magnetization (electric polarization) by an external electric (magnetic) field, may introduce a new design principle for novel spin devices. To enhance the ME signal, control of a phase competition has recently been revealed as a promising approach. Here, we report the successful chemical-doping control of the distinct ME phases in a polar magnet ${\mathrm{Fe}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$, in which an antiferromagnetic state is competing with a ferrimagnetic state. We demonstrate that Zn doping stabilizes the metamagnetic state to realize the spontaneous ferrimagnetic state and varies the ME coefficients from large negative to large positive values; for instance, the diagonal component of the ME coefficients under the magnetic field perpendicular to the polar axis varies from $\text{−}142\mathrm{ps}/\mathrm{m}$ to $107\mathrm{ps}/\mathrm{m}$ by doping Zn from 12.5% to 50%. This remarkable doping control of the ME property originates from coexisting distinct ME mechanisms, which are selectively tunable by substituting one of the two distinct magnetic sites in the unit cell with nonmagnetic Zn.

We study the dynamical melting of “hot” one-dimensional many-body localized systems. As disorder is weakened below a critical value, these nonthermal quantum glasses melt via a continuous dynamical phase transition into classical thermal liquids. By accounting for collective resonant tunneling processes, we derive and numerically solve an effective model for such quantum-to-classical transitions and compute their universal critical properties. Notably, the classical thermal liquid exhibits a broad regime of anomalously slow subdiffusive equilibration dynamics and energy transport. The subdiffusive regime is characterized by a continuously evolving dynamical critical exponent that diverges with a universal power at the transition. Our approach elucidates the universal long-distance, low-energy scaling structure of many-body delocalization transitions in one dimension, in a way that is transparently connected to the underlying microscopic physics. We discuss experimentally testable signatures of the predicted scaling properties.

We formulate a theory of the many-body localization transition based on a novel real-space renormalization group (RG) approach. The results of this theory are corroborated and intuitively explained with a phenomenological effective description of the critical point and of the “badly conducting” state found near the critical point on the delocalized side. The theory leads to the following sharp predictions: (i) The delocalized state established near the transition is a Griffiths phase, which exhibits subdiffusive transport of conserved quantities and sub-ballistic spreading of entanglement. The anomalous diffusion exponent $\alpha <1/2$ vanishes continuously at the critical point. The system does thermalize in this Griffiths phase. (ii) The many-body localization transition is controlled by a new kind of infinite-randomness RG fixed point, where the broadly distributed scaling variable is closely related to the eigenstate entanglement entropy. Dynamically, the entanglement grows as $\sim \log t$ at the critical point, as it does in the localized phase. (iii) In the vicinity of the critical point, the ratio of the entanglement entropy to the thermal entropy and its variance (and, in fact, all moments) are scaling functions of $L/\xi$, where $L$ is the length of the system and $\xi$ is the correlation length, which has a power-law divergence at the critical point.

We propose a universal, on-chip quantum transducer based on surface acoustic waves in piezoactive materials. Because of the intrinsic piezoelectric (and/or magnetostrictive) properties of the material, our approach provides a universal platform capable of coherently linking a broad array of qubits, including quantum dots, trapped ions, nitrogen-vacancy centers, or superconducting qubits. The quantized modes of surface acoustic waves lie in the gigahertz range and can be strongly confined close to the surface in phononic cavities and guided in acoustic waveguides. We show that this type of surface acoustic excitation can be utilized efficiently as a quantum bus, serving as an on-chip, mechanical cavity-QED equivalent of microwave photons and enabling long-range coupling of a wide range of qubits.

Plasmonic gratings that support both localized and propagating plasmons have wide applications in solar cells and optical biosensing. In this paper, we report on a most unusual grating designed to capture light efficiently into surface plasmons and concentrate their energy at hot spots where the field is resonantly enhanced. The dispersion of the surface plasmons shows degeneracy points at $k=0$, where, despite a strongly modulated grating, hidden symmetries forbid hybridization of plasmons traveling in opposite directions.

We propose a particle-hole symmetric theory of the Fermi-liquid ground state of a half-filled Landau level. This theory should be applicable for a Dirac fermion in the magnetic field at charge neutrality, as well as for the $\nu =\frac{1}{2}$ quantum Hall ground state of nonrelativistic fermions in the limit of negligible inter-Landau-level mixing. We argue that when particle-hole symmetry is exact, the composite fermion is a massless Dirac fermion, characterized by a Berry phase of $\pi$ around the Fermi circle. We write down a tentative effective field theory of such a fermion and discuss the discrete symmetries, in particular, $\mathcal{C}\mathcal{P}$. The Dirac composite fermions interact through a gauge, but non-Chern-Simons, interaction. The particle-hole conjugate pair of Jain-sequence states at filling factors $n/(2n+1)$ and $(n+1)/(2n+1)$, which in the conventional composite fermion picture corresponds to integer quantum Hall states with different filling factors, $n$ and $n+1$, is now mapped to the same half-integer filling factor $n+\frac{1}{2}$ of the Dirac composite fermion. The Pfaffian and anti-Pfaffian states are interpreted as $d$-wave Bardeen-Cooper-Schrieffer paired states of the Dirac fermion with orbital angular momentum of opposite signs, while $s$-wave pairing would give rise to a particle-hole symmetric non-Abelian gapped phase. When particle-hole symmetry is not exact, the Dirac fermion has a $\mathcal{C}\mathcal{P}$-breaking mass. The conventional fermionic Chern-Simons theory is shown to emerge in the nonrelativistic limit of the massive theory.

Electron spin qubits in silicon, whether in quantum dots or in donor atoms, have long been considered attractive qubits for the implementation of a quantum computer because of silicon’s “semiconductor vacuum” character and its compatibility with the microelectronics industry. While donor electron spins in silicon provide extremely long coherence times and access to the nuclear spin via the hyperfine interaction, quantum dots have the complementary advantages of fast electrical operations, tunability, and scalability. Here, we present an approach to a novel hybrid double quantum dot by coupling a donor to a lithographically patterned artificial atom. Using gate-based rf reflectometry, we probe the charge stability of this double quantum-dot system and the variation of quantum capacitance at the interdot charge transition. Using microwave spectroscopy, we find a tunnel coupling of 2.7 GHz and characterize the charge dynamics, which reveals a charge $T_2^{*}$ of 200 ps and a relaxation time $T_1$ of 100 ns. Additionally, we demonstrate a spin blockade at the inderdot transition, opening up the possibility to operate this coupled system as a singlet-triplet qubit or to transfer a coherent spin state between the quantum dot and the donor electron and nucleus.

Weyl semimetal is the three-dimensional analog of graphene. According to quantum field theory, the appearance of Weyl points near the Fermi level will cause novel transport phenomena related to chiral anomaly. In the present paper, we report the experimental evidence for the long-anticipated negative magnetoresistance generated by the chiral anomaly in a newly predicted time-reversal-invariant Weyl semimetal material TaAs. Clear Shubnikov de Haas (SdH) oscillations have been detected starting from a very weak magnetic field. Analysis of the SdH peaks gives the Berry phase accumulated along the cyclotron orbits as $\pi$, indicating the existence of Weyl points.

Junctions and interfaces consisting of unconventional superconductors provide an excellent experimental playground to study exotic phenomena related to the phase of the order parameter. Not only does the complex structure of unconventional order parameters have an impact on the Josephson effects, but it also may profoundly alter the quasiparticle excitation spectrum near a junction. Here, by using spectroscopic-imaging scanning tunneling microscopy, we visualize the spatial evolution of the LDOS near twin boundaries (TBs) of the nodal superconductor FeSe. The $\pi /2$ rotation of the crystallographic orientation across the TB twists the structure of the unconventional order parameter, which may, in principle, bring about a zero-energy LDOS peak at the TB. The LDOS at the TB observed in our study, in contrast, does not exhibit any signature of a zero-energy peak, and an apparent gap amplitude remains finite all the way across the TB. The low-energy quasiparticle excitations associated with the gap nodes are affected by the TB over a distance more than an order of magnitude larger than the coherence length ${\xi }_{ab}$. The modification of the low-energy states is even more prominent in the region between two neighboring TBs separated by a distance $\approx 7{\xi }_{ab}$. In this region, the spectral weight near the Fermi level ($\approx \pm 0.2\mathrm{meV}$) due to the nodal quasiparticle spectrum is almost completely removed. These behaviors suggest that the TB induces a fully gapped state, invoking a possible twist of the order parameter structure, which breaks time-reversal symmetry.