Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum

Strongly correlated analogues of topological insulators have been explored in systems with purely on-site symmetries, such as time-reversal or charge conservation. Here, we use recently developed tensor network tools to study a quantum state of interacting bosons which is featureless in the bulk, but distinguished from an atomic insulator in that it exhibits entanglement which is protected by its spatial symmetries. These properties are encoded in a model many-body wavefunction that describes a fully symmetric insulator of bosons on the honeycomb lattice at half filling per site. While the resulting integer unit cell filling allows the state to bypass `no-go' theorems that trigger fractionalization at fractional filling, it nevertheless has nontrivial entanglement, protected by symmetry. We demonstrate this by computing the boundary entanglement spectra, finding a gapless entanglement edge described by a conformal field theory as well as degeneracies protected by the non-trivial action of combined charge-conservation and spatial symmetries on the edge. Here, the tight-binding representation of the space group symmetries plays a particular role in allowing certain entanglement cuts that are not allowed on other lattices of the same symmetry, suggesting that the lattice representation can serve as an additional symmetry ingredient in protecting an interacting topological phase. Our results extend to a related insulating state of electrons, with short-ranged entanglement and no band insulator analogue.Comment: 18 pages, 13 figures Added additional reference

Scaling and data collapse from local moments in frustrated disordered quantum spin systems

Recently measurements on various spin-1/2 quantum magnets such as H$_3$LiIr$_2$O$_6$, LiZn$_2$Mo$_3$O$_8$, ZnCu$_3$(OH)$_6$Cl$_2$ and 1T-TaS$_2$ -- all described by magnetic frustration and quenched disorder but with no other common relation -- nevertheless showed apparently universal scaling features at low temperature. In particular the heat capacity C[H,T] in temperature T and magnetic field H exhibits T/H data collapse reminiscent of scaling near a critical point. Here we propose a theory for this scaling collapse based on an emergent random-singlet regime extended to include spin-orbit coupling and antisymmetric Dzyaloshinskii-Moriya (DM) interactions. We derive the scaling $C[H,T]/T \sim H^{-\gamma} F_q[T/H]$ with $F_q[x] = x^{q}$ at small $x$, with $q \in$ (0,1,2) an integer exponent whose value depends on spatial symmetries. The agreement with experiments indicates that a fraction of spins form random valence bonds and that these are surrounded by a quantum paramagnetic phase. We also discuss distinct scaling for magnetization with a $q$-dependent subdominant term enforced by Maxwell's relations.Comment: v2. Expanded argument in Appendix 2 and revised for clarity. v3. Fixed typo in Fig 3 caption. Main text 4 pages 4 figures, Appendix 6 pages 1 figur

Impact of disorder on dynamics and ordering in the honeycomb-lattice iridate Na2IrO3

Kitaev's honeycomb spin-liquid model and its proposed realization in materials such as α-RuCl3, Li2IrO3, and Na2IrO3 continue to present open questions about how the dynamics of a spin liquid are modified in the presence of non-Kitaev interactions as well as the presence of inhomogeneities. Here we use Na23 nuclear magnetic resonance to probe both static and dynamical magnetic properties in single-crystal Na2IrO3. We find that the NMR shift follows the bulk susceptibility above 30 K but deviates from it below; moreover below TN the spectra show a broad distribution of internal magnetic fields. Both of these results provide evidence for inequivalent magnetic sites at low temperature, suggesting inhomogeneities are important for the magnetism. The spin-lattice relaxation rate is isotropic and diverges at TN, suggesting that the Kitaev cubic axes may control the critical quantum spin fluctuations. In the ordered state, we observe gapless excitations, which may arise from site substitution, emergent defects from milder disorder, or possibly be associated with nearby quantum paramagnetic states distinct from the Kitaev spin liquid

High-temperature magnetic anomaly in the Kitaev hyperhoneycomb compound β-Li2IrO3

We report the existence of a high-temperature magnetic anomaly in the three-dimensional Kitaev candidate material, β-Li2IrO3. Signatures of the anomaly appear in magnetization, heat capacity, and muon spin relaxation measurements. The onset coincides with a reordering of the principal axes of magnetization, which is thought to be connected to the onset of Kitaev-like correlations in the system. The anomaly also shows magnetic hysteresis with a spatially anisotropic magnitude that follows the spin-anisotropic exchange anisotropy of the underlying Kitaev Hamiltonian. We discuss possible scenarios for a bulk and impurity origin

Composite fermion duality for half-filled multicomponent Landau levels

We study the interplay of particle-hole symmetry and fermion-vortex duality in multicomponent half-filled Landau levels, such as quantum Hall gallium arsenide bilayers and graphene. For the ν=1/2+1/2 bilayer, we show that particle-hole-symmetric interlayer Cooper pairing of composite fermions leads to precisely the same phase as the electron exciton condensate realized in experiments. This equivalence is easily understood by applying the recent Dirac fermion formulation of ν=1/2 to two components. It can also be described by Halperin-Lee-Read composite fermions undergoing interlayer p[subscript x]+ip[subscript y] pairing. A renormalization group analysis showing strong instability to interlayer pairing at large separation d→∞ demonstrates that two initially decoupled composite Fermi liquids can be smoothly tuned into the conventional bilayer exciton condensate without encountering a phase transition. We also discuss multicomponent systems relevant to graphene, derive related phases including a Z[subscript 2] gauge theory with spin-half visons, and argue for symmetry-enforced gaplessness under full SU(N[subscript f]) flavor symmetry when the number of components N[subscript f] is even.MIT Department of Physics Pappalardo ProgramUnited States. Dept. of Energy (Grant DE-SC0008739)Simons Foundation (Simons Investigator Award