Field-induced bound-state condensation and spin-nematic phase in SrCu2(BO3)2 revealed by neutron scattering up to 25.9 T.

In quantum magnetic materials, ordered phases induced by an applied magnetic field can be described as the Bose-Einstein condensation (BEC) of magnon excitations. In the strongly frustrated system SrCu2(BO3)2, no clear magnon BEC could be observed, pointing to an alternative mechanism, but the high fields required to probe this physics have remained a barrier to detailed investigation. Here we exploit the first purpose-built high-field neutron scattering facility to measure the spin excitations of SrCu2(BO3)2 up to 25.9 T and use cylinder matrix-product-states (MPS) calculations to reproduce the experimental spectra with high accuracy. Multiple unconventional features point to a condensation of S = 2 bound states into a spin-nematic phase, including the gradients of the one-magnon branches and the persistence of a one-magnon spin gap. This gap reflects a direct analogy with superconductivity, suggesting that the spin-nematic phase in SrCu2(BO3)2 is best understood as a condensate of bosonic Cooper pairs.

Understanding unconventional magnetic order in a candidate axion insulator by resonant elastic x-ray scattering.

Magnetic topological insulators and semimetals are a class of crystalline solids whose properties are strongly influenced by the coupling between non-trivial electronic topology and magnetic spin configurations. Such materials can host exotic electromagnetic responses. Among these are topological insulators with certain types of antiferromagnetic order which are predicted to realize axion electrodynamics. Here we investigate the highly unusual helimagnetic phases recently reported in EuIn2As2, which has been identified as a candidate for an axion insulator. Using resonant elastic x-ray scattering we show that the two types of magnetic order observed in EuIn2As2 are spatially uniform phases with commensurate chiral magnetic structures, ruling out a possible phase-separation scenario, and we propose that entropy associated with low energy spin fluctuations plays a significant role in driving the phase transition between them. Our results establish that the magnetic order in EuIn2As2 satisfies the symmetry requirements for an axion insulator.

Critical line of the triangular Ising antiferromagnet in a field from a C_{3}-symmetric corner transfer matrix algorithm.

The corner transfer matrix renormalization group (CTMRG) algorithm has been extensively used to investigate both classical and quantum two-dimensional (2D) lattice models. The convergence of the algorithm can strongly vary from model to model depending on the underlying geometry and symmetries, and the presence of algebraic correlations. An important factor in the convergence of the algorithm is the lattice symmetry, which can be broken due to the necessity of mapping the problem onto the square lattice. We propose a variant of the CTMRG algorithm, designed for models with C_{3}-symmetry, which we apply to the conceptually simple yet numerically challenging problem of the triangular lattice Ising antiferromagnet in a field, at zero and low temperatures. We study how the finite-temperature three-state Potts critical line in this model approaches the ground-state Kosterlitz-Thouless transition driven by a reduced field (h/T). In this particular instance, we show that the C_{3}-symmetric CTMRG leads to much more precise results than both existing results from exact diagonalization of transfer matrices and Monte Carlo.

Thermal Ising Transition in the Spin-1/2 J_{1}-J_{2} Heisenberg Model.

Using an SU(2) invariant finite-temperature tensor network algorithm, we provide strong numerical evidence in favor of an Ising transition in the collinear phase of the spin-1/2 J_{1}-J_{2} Heisenberg model on the square lattice. In units of J_{2}, the critical temperature reaches a maximal value of T_{c}/J_{2}≃0.18 around J_{2}/J_{1}≃1.0. It is strongly suppressed upon approaching the zero-temperature boundary of the collinear phase J_{2}/J_{1}≃0.6, and it vanishes as 1/log(J_{2}/J_{1}) in the large J_{2}/J_{1} limit, as predicted by Chandra et al., [Phys. Rev. Lett. 64, 88 (1990)PRLTAO0031-900710.1103/PhysRevLett.64.88]. Enforcing the SU(2) symmetry is crucial to avoid the artifact of finite-temperature SU(2) symmetry breaking of U(1) algorithms, opening new perspectives in the investigation of the thermal properties of quantum Heisenberg antiferromagnets.

Discovery of quantum phases in the Shastry-Sutherland compound SrCu2(BO3)2 under extreme conditions of field and pressure.

The 2-dimensional layered oxide material SrCu2(BO3)2, long studied as a realization of the Shastry-Sutherland spin topology, exhibits a range of intriguing physics as a function of both hydrostatic pressure and magnetic field, with a still debated intermediate plaquette phase appearing at approximately 20 kbar and a possible deconfined critical point at higher pressure. Here, we employ a tunnel diode oscillator (TDO) technique to probe the behavior in the combined extreme conditions of high pressure, high magnetic field, and low temperature. We reveal an extensive phase space consisting of multiple magnetic analogs of the elusive supersolid phase and a magnetization plateau. In particular, a 10 × 2 supersolid and a 1/5 plateau, identified by infinite Projected Entangled Pair States (iPEPS) calculations, are found to rely on the presence of both magnetic and non-magnetic particles in the sea of dimer singlets. These states are best understood as descendants of the full-plaquette phase, the leading candidate for the intermediate phase of SrCu2(BO3)2.

Direct observation of spin correlations in an artificial triangular lattice Ising spin system with grazing-incidence small-angle neutron scattering.

The triangular lattice with Ising magnetic moments is an archetypical example of geometric frustration. In the case of dipolar-coupled out-of-plane moments, the geometric frustration results in a disordered classical spin-liquid state at higher temperatures while the system is predicted to transition to an anti-ferromagnetic stripe ground state at low temperatures. In this work we fabricate artificial triangular Ising spin systems without and with uniaxial in-plane compression to tune the nature and temperature of the correlations. We probe the energy scale and nature of magnetic correlations by grazing-incidence small-angle neutron scattering. In particular, we apply a newly-developed empirical structure-factor model to describe the measured short-range correlated spin-liquid state, and find good agreement with theoretical predictions. We demonstrate that grazing-incidence neutron scattering on our high-quality samples, in conjunction with detailed modeling of the scattering using the Distorted Wave Born Approximation, can be used to experimentally quantify the spin-liquid-like correlations in highly-frustrated artificial spin systems.

Kibble-Zurek exponent and chiral transition of the period-4 phase of Rydberg chains.

Chains of Rydberg atoms have emerged as an amazing playground to study quantum physics in 1D. Playing with inter-atomic distances and laser detuning, one can in particular explore the commensurate-incommensurate transition out of density waves through the Kibble-Zurek mechanism, and the possible presence of a chiral transition with dynamical exponent z > 1. Here, we address this problem theoretically with effective blockade models where the short-distance repulsions are replaced by a constraint of no double occupancy. For the period-4 phase, we show that there is an Ashkin-Teller transition point with exponent ν = 0.78 surrounded by a direct chiral transition with a dynamical exponent z = 1.11 and a Kibble-Zurek exponent µ = 0.41. For Rydberg atoms with a van der Waals potential, we suggest that the experimental value µ = 0.25 is due to a chiral transition with z ≃ 1.9 and ν ≃ 0.47 surrounding an Ashkin-Teller transition close to the 4-state Potts universality.

Haldane Gap of the Three-Box Symmetric SU(3) Chain.

Motivated by the recent generalization of the Haldane conjecture to SU(3) chains [Lajkó et al., Nucl. Phys. B924, 508 (2017)NUPBBO0550-321310.1016/j.nuclphysb.2017.09.015] according to which a Haldane gap should be present for symmetric representations if the number of boxes in the Young diagram is a multiple of three, we develop a density matrix renormalization group algorithm based on standard Young tableaus to study the model with three boxes directly in the representations of the global SU(3) symmetry. We show that there is a finite gap between the singlet and the symmetric [3 0 0] sector Δ_{[3 0 0]}/J=0.040±0.006 where J is the antiferromagnetic Heisenberg coupling, and we argue on the basis of the structure of the low energy states that this is sufficient to conclude that the spectrum is gapped.

Magnetic-Field-Induced Bound States in Spin-1/2 Ladders.

Motivated by the recently observed intriguing mode splittings in a magnetic field with inelastic neutron scattering in the spin ladder compound (C_{5}H_{12}N)_{2}CuBr_{4} (BPCB), we investigate the nature of the spin ladder excitations using a density matrix renormalization group and analytical arguments. Starting from the fully frustrated ladder, for which we derive the low-energy spectrum, we show that bound states are generically present close to k=0 in the dynamical structure factor of spin ladders above H_{c1}, and that they are characterized by a field-independent binding energy and an intensity that grows with H-H_{c1}. These predictions are shown to explain quantitatively the split modes observed in BPCB.

Exploring the Kondo Effect of an Extended Impurity with Chains of Co Adatoms in a Magnetic Field.

Motivated by recent STM experiments, we explore the magnetic field induced Kondo effect that takes place at symmetry protected level crossings in finite Co adatom chains. We argue that the effective two-level system realized at a level crossing acts as an extended impurity coupled to the conduction electrons of the substrate by a distribution of Kondo couplings at the sites of the chain. Using auxiliary-field quantum Monte Carlo simulations, which quantitatively reproduce the field dependence of the zero-bias signal, we show that a proper Kondo resonance is present at the sites where the effective Kondo coupling dominates. Our modeling and numerical simulations provide a theoretical basis for the interpretation of the STM spectrum in terms of level crossings of the Co adatom chains.

Asymptotic Freedom and Large Spin Antiferromagnetic Chains.

Building on the mapping of large-S spin chains onto the O(3) nonlinear σ model with coupling constant 2/S, and on general properties of that model (asymptotic freedom, implying that perturbation theory is valid at high energy, and Elitzur's conjecture that rotationally invariant quantities are infrared finite in perturbation theory), we use the Holstein-Primakoff representation to derive analytic expressions for the equal-time and dynamical spin-spin correlations valid at distances smaller than S^{-1}exp(πS) or at energies larger than JS^{2}exp(-πS), where J is the Heisenberg exchange coupling. This is supported by comparing the static correlations with quantum Monte Carlo simulations for S=5/2.

Emergent bound states and impurity pairs in chemically doped Shastry-Sutherland system.

Impurities often play a defining role in the ground states of frustrated quantum magnets. Studies of their effects are crucial in understanding of the phase diagram in these materials. SrCu2(BO3)2, an experimental realization of the Shastry-Sutherland (SS) lattice, provides a unique model system for such studies using both experimental and numerical approaches. Here we report effects of impurities on the crystals of bound states, and doping-induced emergent ground states in Mg-doped SrCu2(BO3)2, which remain stable in high magnetic fields. Using four complementary magnetometry techniques and theoretical simulations, a rich impurity-induced phenomenology at high fields is discovered. The results demonstrate a rare example in which even a small doping concentration interacts strongly with both triplets and bound states of triplets, and thus plays a significant role in the magnetization process even at high magnetic fields. Our findings provide insights into the study of impurity effects in geometrically frustrated quantum magnets.

Floating Phase versus Chiral Transition in a 1D Hard-Boson Model.

We investigate the nature of the phase transition between the period-three charge-density wave and the disordered phase of a hard-boson model proposed in the context of cold-atom experiments. Building on a density-matrix renormalization group algorithm that takes full advantage of the hard-boson constraints, we study systems with up to 9000 sites and calculate the correlation length and the wave vector of the incommensurate short-range correlations with unprecedented accuracy. We provide strong numerical evidence that there is an intermediate floating phase far enough from the integrable Potts point, while in its vicinity, our numerical data are consistent with a unique transition in the Huse-Fisher chiral universality class.

Chiral Spin Liquids in Triangular-Lattice SU(N) Fermionic Mott Insulators with Artificial Gauge Fields.

We show that, in the presence of a π/2 artificial gauge field per plaquette, Mott insulating phases of ultracold fermions with SU(N) symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by an approximate ground space of N low-lying singlets for periodic boundary conditions, and by chiral edge states described by the SU(N)_{1} Wess-Zumino-Novikov-Witten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for N between 3 and 9, and by a parton construction based on a set of N Gutzwiller projected fermionic wave functions with flux π/N per triangular plaquette. Experimental implications are briefly discussed.

Topological Aspects of Symmetry Breaking in Triangular-Lattice Ising Antiferromagnets.

Using a specially designed Monte Carlo algorithm with directed loops, we investigate the triangular lattice Ising antiferromagnet with coupling beyond the nearest neighbors. We show that the first-order transition from the stripe state to the paramagnet can be split, giving rise to an intermediate nematic phase in which algebraic correlations coexist with a broken symmetry. Furthermore, we demonstrate the emergence of several properties of a more topological nature such as fractional edge excitations in the stripe state, the proliferation of double domain walls in the nematic phase, and the Kasteleyn transition between them. Experimental implications are briefly discussed.

Disorder-Driven Spin-Orbital Liquid Behavior in the Ba3XSb2O9 Materials.

Recent experiments on the Ba(3)XSb(2)O(9) family have revealed materials that potentially realize spin- and spin-orbital liquid physics. However, the lattice structure of these materials is complicated due to the presence of charged X(2+)-Sb(5+) dumbbells, with two possible orientations. To model the lattice structure, we consider a frustrated model of charged dumbbells on the triangular lattice, with long-range Coulomb interactions. We study this model using Monte Carlo simulation, and find a freezing temperature, T(frz), at which the simulated structure factor matches well to low-temperature x-ray diffraction data for Ba(3)CuSb(2)O(9). At T=T(frz) we find a complicated "branching" structure of superexchange-linked X(2+) clusters, which form a fractal pattern with fractal dimension d(f)=1.90. We show that this gives a natural explanation for the presence of orphan spins. Finally we provide a plausible mechanism by which such dumbbell disorder can promote a spin-orbital resonant state with delocalized orphan spins.

Anderson tower of states and nematic order of spin-1 bosonic atoms on a 2D lattice.

We investigate the structure of the spectrum of antiferromagnetically coupled spin-1 bosons on a square lattice using degenerate perturbation theory and exact diagonalizations of finite clusters. We show that the superfluid phase develops an Anderson tower of states typical of nematic long-range order with broken SU(2) symmetry. We further show that this order persists into the Mott-insulating phase down to zero hopping for one boson per site and down to a critical hopping for two bosons per site, in agreement with mean-field and quantum Monte Carlo results. The connection with the transition between a fragmented condensate and a polar one in a single trap is briefly discussed.

Exact Diagonalization of Heisenberg SU(N) models.

Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labeled by the set of standard Young tableaux in which the matrix of the Heisenberg SU(N) model (the quantum permutation of N-color objects) takes an explicit and extremely simple form. Since the relative dimension of the full Hilbert space to that of the singlet space on n sites increases very fast with N, this formulation allows us to extend exact diagonalizations of finite clusters to much larger values of N than accessible so far. Using this method, we show that, on the square lattice, there is long-range color order for SU(5), spontaneous dimerization for SU(8), and evidence in favor of a quantum liquid for SU(10).

Crystals of bound states in the magnetization plateaus of the Shastry-Sutherland model.

Using infinite projected entangled-pair states, we show that the Shastry-Sutherland model in an external magnetic field has low-magnetization plateaus which, in contrast to previous predictions, correspond to crystals of bound states of triplets, and not to crystals of triplets. The first sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with experiments on the orthogonal-dimer antiferromagnet SrCu2(BO3)2, and they can be naturally understood as regular patterns of bound states, including the intriguing 2/15 one. We also show that, even in a confined geometry, two triplets bind into a localized bound state with Sz=2. Finally, we discuss the role of competing domain-wall and supersolid phases, as well as that of additional anisotropic interactions.

Evidence for columnar order in the fully frustrated transverse field Ising model on the square lattice.

Using extensive classical and quantum Monte Carlo simulations, we investigate the ground-state phase diagram of the fully frustrated transverse field Ising model on the square lattice. We show that pure columnar order develops in the low-field phase above a surprisingly large length scale, below which an effective U(1) symmetry is present. The same conclusion applies to the quantum dimer model with purely kinetic energy, to which the model reduces in the zero-field limit, as well as to the stacked classical version of the model. By contrast, the 2D classical version of the model is shown to develop plaquette order. Semiclassical arguments show that the transition from plaquette to columnar order is a consequence of quantum fluctuations.