Condensed Matter

We aim to provide a concise review on theoretical background on emergent quantum electrodynamics in pyrochlore quantum spin ice. We first introduce elementary excitations in quantum spin ice using a simple model and then extend the discussion to more realistic systems. Implications to experiments are also discussed.

In this tutorial, we will review the microscopic aspects of rare-earth magnets relevant for quantum spin ice. We first discuss the single-ion properties of the variety of rare-earth atoms that appear in quantum spin ice candidate materials. Second, we consider the origin of the two-ion exchange interactions, including electric and magnetic multipolar interactions, super-exchange and virtual crystal field mediated interactions. We provide a detailed microscopic basis for the super-exchange interaction and discuss the implications of its multipolar structure for models of rare-earth materials. Finally, we introduce the generic symmetry allowed anisotropic exchange model for rare-earth pyrochlore magnets.

In this talk we present a study of the “breathing” pyrochlore compound Ba3Yb2Zn5O11. Due to the nearly decoupled nature of its tetrahedral units, this compound serves as an ideal testbed for exploring the nature of anisotropic exchange in a theoretically and experimentally tractable rare-earth system. The relevant low-energy model of the Yb3+ tetrahedra is parametrized by four anisotropic exchange constants and is capable of reproducing the inelastic neutron scattering data, specific heat, and magnetic susceptibility with high fidelity. Using this model, we predict the appearance of an unusual non-Kramers octupolar paramagnet at low temperatures. We further speculate on possible collective, inter-tetrahedron physics of these non-Kramers doublets and discuss applications to about anisotropic exchange in other rare-earth magnets.

The XY pyrochlore Er2Ti2O7 has garnered much attention due to the possibility that its ground state selection could originate from an order-by-disorder mechanism [1,2]. However, recently, theoretical work has exploited the fact that the symmetry breaking in this system is a rare case of high discrete symmetry (Z6) [3]. This work studied the effect of a magnetic field on the Z6 symmetry breaking and predicted rich and controllable magnetothermodynamic properties. Indeed, the authors predict numerous domains transitions in the low field regime that strongly depends on the field direction. In this talk, I will present neutron scattering data on Er2Ti2O7 with a magnetic field applied along different high symmetry directions which provides the first experimental evidence for this rich Z6 domain phase behavior [4].

In recent years, there has been a resurgence of interest in the study of chiral spin liquids (CSLs), topologically ordered states of matter that are closely related to the celebrated fractional quantum Hall states. This resurgence has been driven by the introduction of exact parent Hamiltonians and a number of numerical studies that have identified CSLs in local spin models. However, our understanding of how and why these states emerge is still lacking. I will discuss evidence supporting one particularly intuitive mechanism in which they arise as "quantum-disordered" descendants of certain non-coplanar magnetic parent states, uniting many of the CSLs found so far under a common framework.

Many-body quantum systems are often hard to simulate on a computer, due to the computational complexity generated by non-classical correlations or entanglement between parts of these systems. An alternate platform is to experimentally simulate non-trivial quantum models on synthetic quantum matter composed of cold atomic systems. These systems exhibit excellent quantum coherence properties due to their isolation from environment, and hence faithfully evolve in time under the prescribed quantum Hamiltonian. In this talk, I will focus on simulating models of quantum magnetism with laser-cooled trapped atomic ions. Two internal states of each ion represent a spin-1/2 system that can be initialized, manipulated, and detected with near perfection by laser beams. Precisely tuned optical dipole forces couple individual spins to the collective vibrational (phonon) states of the ions, which mediate effective spin-spin interactions. By suitably tailoring these couplings, the interactions can be tuned dynamically in magnitude, sign, and range, allowing for the investigation of a large class of problems in quantum many-body physics.

The topological Haldane model (THM) on a honeycomb lattice is a prototype of systems hosting topological phases of matter without external fields. It is the simplest model exhibiting the quantum Hall effect without Landau levels, which motivated theoretical and experimental explorations of topological insulators and superconductors. Despite its simplicity, its realization in condensed matter systems has been elusive due to a seemingly difficult condition of spinless fermions with sublattice-dependent magnetic flux terms. While there have been theoretical proposals including elaborate atomic-scale engineering, identifying candidate THM materials has not been successful, and the first experimental realization was recently made in ultracold atoms. Here we suggest that a series of Fe-based honeycomb ferromagnetic insulators, AFe2(PO4)2 (A=Ba,Cs,K,La) possess Chern bands described by the THM.

The 2D S = 1/2 square-lattice Heisenberg model is a keystone of theoretical studies of quantum magnetism. It also has very good realizations in several classes of layered insulators with localized electronic spins. While spin-wave theory provides a good understanding of the antiferromagnetic ground state and low-lying excitations of the Heisenberg model, an anomaly in the excitations at higher energy around wave-number q = (\pi, 0) has been diffi_cult to explain. At first sight, the anomaly is just a suppression of the excitation energy by a few percent, but it also represents a more dramatic shift of spectral weight in the dynamic spin structure factor from the single- magnon (spin wave) pole to a continuum. Recent neutron scattering experiments on the quasi-2D material Cu(DCOO)2_.4D2O (the best realization so far of the 2D Heisenberg model) were even interpreted as a complete lack of magnon pole at the anomaly; instead it was suggested that the excitations there are fractional (spinons) [1]. I will discuss recent quantum Monte Carlo and stochastic analytic continuation results pointing to the existence of fragile q~(\pi,0) magnon excitations in the Heisenberg model [2], which can be fractionalized by interactions competing with the nearest-neighbor exchange coupling. This phenomenon can be understood phenomenologically within a simple theory of magnon-spinon mixing.

Area laws were first discovered by Bekenstein and Hawking, who found that the entropy of a black hole grows proportional to its surface area, and not its volume. Entropy area laws have since become a fundamental part of modern physics, from the holographic principle in quantum gravity to ground state wavefunctions of quantum matter, where entanglement entropy is generically found to obey area law scaling. As no experiments are currently capable of directly probing the entanglement area law in naturally occurring many-body systems, evidence of its existence is based on studies of simplified theories. Using new exact microscopic numerical simulations of superfluid 4He, we demonstrate for the first time an area law scaling of entanglement entropy in a real quantum liquid in three dimensions. We validate the fundamental principles underlying its physical origin, and present an "entanglement equation of state" showing how it depends on the density of the superfluid.

In 1999, A. W. Hunt et al. discovered that all the NMR anomalies detected at the charge density wave (CDW) order transition Tcharge ~ 60 K of nearly non-superconducting La1.48Nd0.4Sr0.12CuO4 are shared by superconducting La1.88Sr0.12CuO4 (Tc ~ 30K) [1]. The unexpected finding inevitably led us to conclude that charge order must exist even in the superconducting La2-xSrxCuO4, sending a shockwave in the high-Tc community [2]. Subsequent search of charge order peaks based on scattering techniques, however, failed to detect additional evidence for charge order until very recently. In view of the recent confirmation of charge order in many superconducting cuprates by X-ray diffraction techniques, we revisit the old problem of charge order using newer NMR techniques that have become available in recent years.

In this talk I will introduce a relatively little-studied but intriguing family of metals, the delafossite series of layered oxides ABO2 in which the A site is occupied by Pd or Pt, and the B site by a transition metal. For reasons that are not perfectly understood, these materials have amazingly high electrical conductivity, with mean free paths of hundreds of angstroms (longer than even elemental copper or silver) at room temperature, growing to tens of microns at low temperatures. The electronic structure that yields these properties is in one way very simple, with a single half filled conduction band, but in another sense very rich, because the nearly free electrons originate mainly from the (Pt,Pd) layers in the crystal structure, while the adjacent transition metal oxide layers host Mott insulating states to which the conduction electrons also have some coupling. My group is interested in the delafossites for a number of reasons. Firstly, they are possible hosts for electronic transport at the crossover between ballistic and hydrodynamic regimes, which we investigate by fabricating size-restricted microstructures using focused ion beam techniques. As layered materials that can be cleaved at low temperatures, they are also well suited to study by angle resolved photoemission spectroscopy, and host a variety of interesting surface states in addition to a simple single-band bulk electronic structure. I will discuss our findings on non-magnetic PdCoO2, PtCoO2 and PdRhO2 and magnetic PdCrO2.