There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Annual review of condensed matter physics

Kamihara and coworkers' report of superconductivity at ${T}_{c}=26\text{ }\text{ }\mathrm{K}$ in fluorine-doped LaFeAsO inspired a worldwide effort to understand the nature of the superconductivity in this new class of compounds. These iron pnictide and chalcogenide (FePn/Ch) superconductors have Fe electrons at the Fermi surface, plus an unusual Fermiology that can change rapidly with doping, which lead to normal and superconducting state properties very different from those in standard electron-phonon coupled ``conventional'' superconductors. Clearly, superconductivity and magnetism or magnetic fluctuations are intimately related in the FePn/Ch, and even coexist in some. Open questions, including the superconducting nodal structure in a number of compounds, abound and are often dependent on improved sample quality for their solution. With ${T}_{c}$ values up to 56 K, the six distinct Fe-containing superconducting structures exhibit complex but often comparable behaviors. The search for correlations and explanations in this fascinating field of research would benefit from an organization of the large, seemingly disparate data set. This review provides an overview, using numerous references, with a focus on the materials and their superconductivity.

Superconductivity in iron compounds

Thermalizing quantum systems are conventionallydescribed by statistical mechanics at equilib-rium. However, not all systems fall into this category, with many-body localization providinga generic mechanism for thermalization to fail in strongly disordered systems. Many-bodylocalized (MBL) systems remain perfect insulators at nonzero temperature, which do notthermalize and therefore cannot be describedusing statistical mechanics. This Colloquiumreviews recent theoretical and experimental advances in studies of MBL systems, focusing onthe new perspective provided by entanglement and nonequilibrium experimental probes suchas quantum quenches. Theoretically, MBL systems exhibit a new kind of robust integrability: anextensive set of quasilocal integrals of motion emerges, which provides an intuitive explanationof the breakdown of thermalization. A description based on quasilocal integrals of motion isused to predict dynamical properties of MBL systems, such as the spreading of quantumentanglement, the behavior of local observables, and the response to external dissipativeprocesses. Furthermore, MBL systems can exhibit eigenstate transitions and quantum ordersforbidden in thermodynamic equilibrium. An outline isgiven of the current theoretical under-standing of the quantum-to-classical transitionbetween many-body localized and ergodic phasesand anomalous transport in the vicinity of that transition. Experimentally, synthetic quantumsystems, which are well isolated from an external thermal reservoir, provide natural platforms forrealizing the MBL phase. Recent experiments with ultracold atoms, trapped ions, superconductingqubits, and quantum materials, in which different signatures of many-body localization have beenobserved, are reviewed. This Colloquium concludes by listing outstanding challenges andpromising future research directions.

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Colloquium: Many-body localization, thermalization, and entanglement

Interacting quantum systems are expected to thermalize, but in some situations in the presence of disorder they can exist in localized states instead. This many-body localization is studied experimentally in a small system with programmable disorder. When a system thermalizes it loses all memory of its initial conditions. Even within a closed quantum system, subsystems usually thermalize using the rest of the system as a heat bath. Exceptions to quantum thermalization have been observed, but typically require inherent symmetries1,2 or noninteracting particles in the presence of static disorder3,4,5,6. However, for strong interactions and high excitation energy there are cases, known as many-body localization (MBL), where disordered quantum systems can fail to thermalize7,8,9,10. We experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmable random disorder to ten spins initialized far from equilibrium. Using experimental and numerical methods we observe the essential signatures of MBL: initial-state memory retention, Poissonian distributed energy level spacings, and evidence of long-time entanglement growth. Our platform can be scaled to more spins, where a detailed modelling of MBL becomes impossible.

/pdf/many-body-localization-in-a-quantum-simulator-with-5b3eiez36m.pdf

Many-body localization in a quantum simulator with programmable random disorder

We study four different models of Chern insulators in the presence of strong electronic repulsion at partial fillings. We observe that all cases exhibit a Laughlin-like phase at filling fraction $1/3$. We provide evidence of such a strongly correlated topological phase by studying both the energy and the entanglement spectra. In order to identify the key ingredients of the emergence of Laughlin physics in these systems, we show how they are affected when tuning the band structure. We also address the question of the relevance of the Berry curvature flatness in this problem. Using three-body interactions, we show that some models can also host a topological phase reminiscent of the $\ensuremath{\nu}=1/2$ Pfaffian Moore-Read state. Additionally, we identify the structures indicating cluster correlations in the entanglement spectra.

Zoology of fractional Chern insulators

We introduce a Bloch-like basis in a $C$-component lowest Landau level fractional quantum Hall (FQH) effect, which entangles the real and internal degrees of freedom and preserves an ${N}_{x}\ifmmode\times\else\texttimes\fi{}{N}_{y}$ full lattice translational symmetry. We implement the Haldane pseudopotential Hamiltonians in this new basis. Their ground states are the model FQH wave functions, and our Bloch basis allows for a mutatis mutandis transcription of these model wave functions to the fractional Chern insulator of arbitrary Chern number $C$, obtaining wave functions different from all previous proposals. For $Cg1$, our wave functions are related to color-dependent magnetic-flux inserted versions of Halperin and non-Abelian color-singlet states. We then provide large-size numerical results for both the $C=1$ and $C=3$ cases. This new approach leads to improved overlaps compared to previous proposals. We also discuss the adiabatic continuation from the fractional Chern insulator to the FQH in our Bloch basis, both from the energy and the entanglement spectrum perspectives.

BLOCH model wave functions and pseudopotentials for all fractional Chern insulators.

What mechanisms underlie the electron pairing responsible for the high-temperature superconductivity of iron-based superconductors? A group of theorists from Purdue, Princeton and China explore one proposed mechanism that is gaining traction and elucidate its concrete consequences for the superconducting order parameter.

https://link.aps.org/pdf/10.1103/PhysRevX.1.011009

Robustness of s-Wave Pairing in Electron-Overdoped A(1-y)Fe(2-x)Se(2) (A = K, Cs)

Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the Z_{3} Read-Rezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the Z_{3} Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the nonunitary Gaffnian wave function.

Braiding non-Abelian quasiholes in fractional quantum Hall states.

Using self consistent mean field and functional renormalization group approaches we show that s-wave pairing symmetry is robust in the heavily electron-doped iron chalcogenides $(\text{K, Cs}) \text{Fe}_{2-x}\text{Se}_2 $. This is because in these materials the leading antiferromagnetic (AFM) exchange coupling is between next-nearest-neighbor (NNN) sites while the nearest neighbor (NN) magnetic exchange coupling is ferromagnetic (FM). This is different from the iron pnictides, where the NN magnetic exchange coupling is AFM and leads to strong competition between s-wave and d-wave pairing in the electron overdoped region. Our finding of a robust s-wave pairing in $(\text{K, Cs}) \text{Fe}_{2-x}\text{Se}_2$ differs from the d-wave pairing result obtained by other theories where non-local bare interaction terms and the NNN $J_2$ term are underestimated. Detecting the pairing symmetry in $(\text{K, Cs}) \text{Fe}_{2-x}\text{Se}_2 $ may hence provide important insights regarding the mechanism of superconducting pairing in iron based superconductors.

Yang-Le Wu

Papers

Zoology of fractional Chern insulators

BLOCH model wave functions and pseudopotentials for all fractional Chern insulators.

Robustness of s-Wave Pairing in Electron-Overdoped A(1-y)Fe(2-x)Se(2) (A = K, Cs)

Braiding non-Abelian quasiholes in fractional quantum Hall states.

Robustness of s-wave Pairing in Electron-Overdoped $\text{A}_{1-y}\text{Fe}_{2-x}\text{Se}_2$