Raman scattering signatures of spinons and triplons in frustrated antiferromagnets

Physical Review Letters, 1993

The ground state properties of the two dimensional spatially anisotropic Heisenberg model are investigated by use of field theory mappings, spin-wave expansion and Lanczos technique. Evidence for a disorder transition induced by anisotropy at about J y /J x < 0.1 is shown. We argue that the disordered phase is gapless and its long wavelength properties can be interpreted in terms of decoupled one dimensional chains.

Physical Review Letters

We describe electron spin resonance in a quantum spin liquid with significant spin-orbit coupling. We find that the resonance directly probes spinon continuum which makes it an efficient and informative probe of exotic excitations of the spin liquid. Specifically, we consider spinon resonance of three different spinon mean-field Hamiltonians, obtained with the help of projective symmetry group analysis, which model a putative quantum spin liquid state of the triangular rare-earth antiferromagnet YbMgGaO4. The band of absorption is found to be very broad and exhibit strong van Hove singularities of single spinon spectrum as well as pronounced polarization dependence.

Physical Review B, 2009

We study excitations in weakly interacting pairs of quantum spin ladders coupled through geometrically frustrated bonds. The ground state is a disordered spin liquid that at high fields is replaced by an ordered chiral helimagnetic phase. The spectra observed by high-field inelastic neutron scattering experiments on the prototype compound Sul-Cu 2 Cl 4 are qualitatively different from those in the previously studied frustration-free spin liquids. Beyond the critical field H c = 3.7 T, the soft mode that drives the quantum phase transition spawns two separate excitations: a gapless Goldstone mode and a massive magnon. Additional massive quasiparticles are clearly visible below H c , but are destroyed in the ordered phase. In their place one observes a sharply bound excitation continuum.

Journal of Physics: Condensed Matter, 2020

We have formulated a twist operator argument for the geometrically frustrated quantum spin systems on the kagome and triangular lattices, thereby extending the application of the Lieb-Schultz-Mattis (LSM) and Oshikawa-Yamanaka-Affleck (OYA) theorems to these systems. The equivalent large gauge transformation for the geometrically frustrated lattice differs from that for non-frustrated systems due to the existence of multiple sublattices in the unit cell and non-orthogonal basis vectors. Our study for the S = 1/2 kagome Heisenberg antiferromagnet at zero external magnetic field gives a criterion for the existence of a twofold degenerate ground state with a finite excitation gap and fractionalized excitations. At finite field, we predict various plateaux at fractional magnetisation, in analogy with integer and fractional quantum Hall states of the primary sequence. These plateaux correspond to gapped quantum liquid ground states with a fixed number of singlets and spinons in the unit cell. A similar analysis for the triangular lattice predicts a single fractional magnetization plateau at 1/3. Our results are in broad agreement with numerical and experimental studies.

Journal of Applied Physics, 1994

The Raman spectrum of two-dimensional spin-$ Heisenberg antiferromagnets is calculated by exactly diagonalizing clusters of up to 26 sites. The obtained spectra are compared to experimental results for various high-T, precursors, such as La,CuO, and YBa,Cu,O,,. In spite of good agreement in the position of the main excitation in the B rg channel, i.e, the two-magnon peak around 0.4 eV, an additional mechanism has to be invoked to account for the broad and asymmetric shape of the overall spectrum. Here, we consider the phonon-magnon interaction which, in a quasistatic approximation, renormalizes the Heisenberg exchange integral. This mechanism is motivated in part by recent experimental observations that the Raman linewidth broadens with increasing temperature. Our results are in good agreement with Raman scattering experiments performed by various groups; in particular, the calculations reproduce the broad line shape of the two-magnon peak, the asymmetry about its maximum, the existence of spectral weight at high energies, and the observation of nominally forbidden A rg scattering.

Physical Review Letters, 2019

We study the spin liquid candidate of the spin-1/2 J1-J2 Heisenberg antiferromagnet on the triangular lattice by means of density matrix renormalization group (DMRG) simulations. By applying an external Aharonov-Bohm flux insertion in an infinitely long cylinder, we find unambiguous evidence for gapless U (1) Dirac spin liquid behavior. The flux insertion overcomes the finite size restriction for energy gaps and clearly shows gapless behavior at the expected wave-vectors. Using the DMRG transfer matrix, the low-lying excitation spectrum can be extracted, which shows characteristic Dirac cone structures of both spinon-bilinear and monopole excitations. Finally, we confirm that the entanglement entropy follows the predicted universal response under the flux insertion.

arXiv: Strongly Correlated Electrons, 2018

Abelian and non-Abelian topological phases exhibiting protected chiral edge modes are ubiquitous in the realm of the Fractional Quantum Hall (FQH) effect. Here, we investigate a spin-1 Hamiltonian on the square lattice which could, potentially, host the spin liquid analog of the (bosonic) non-Abelian Moore-Read FQH state, as suggested by Exact Diagonalisation of small clusters. Using families of fully SU(2)-spin symmetric and translationally invariant chiral Projected Entangled Pair States (PEPS), variational energy optimization is performed using infinite-PEPS methods, providing good agreement with Density Matrix Renormalisation Group (DMRG) results. A careful analysis of the bulk spin-spin and dimer-dimer correlation functions in the optimized spin liquid suggests that they exhibit long-range `gossamer tails&#39;. We argue these tails are finite-$D$ artifacts of the chiral PEPS, which disappear progressively when the PEPS bond dimension is increased, to obtain a more and more fait...

Physical Review B, 2017

Confinement is a process by which particles with fractional quantum numbers bind together to form quasiparticles with integer quantum numbers. The constituent particles are confined by an attractive interaction whose strength increases with increasing particle separation and as a consequence, individual particles are not found in isolation. This phenomenon is well known in particle physics where quarks are confined in baryons and mesons. An analogous phenomenon occurs in certain spatially anisotropic magnetic insulators. These can be thought of in terms of weakly coupled chains of spins S=1/2, and a spin flip thus carries integer spin S=1. Interestingly the collective excitations in these systems, called spinons, turn out to carry fractional spin quantum number S=1/2. Interestingly, at sufficiently low temperatures the weak coupling between chains can induce an attractive interaction between pairs of spinons that increases with their separation and thus leads to confinement. In this paper, we employ inelastic neutron scattering to investigate the spinonconfinement process in the quasi-one dimensional, spin-1/2, antiferromagnet with Heisenberg-Ising (XXZ) anisotropy SrCo2V2O8. A wide temperature range both above and below the long-range ordering temperature TN =5.2 K is explored. Spinon excitations are observed above TN in quantitative agreement with established theory. Below TN the pairs of spinons are confined and two sequences of meson-like bound states with longitudinal and transverse polarizations are observed. Several theoretical approaches are used to explain the data. These are based on a description in terms of a one-dimensional, S=1/2 XXZ antiferromagnetic spin chain, where the interchain couplings are modelled by an effective staggered magnetic mean-field. A wide range of exchange anisotropies are investigated and the parameters specific to SrCo2V2O8 are identified. A new theoretical technique based on Tangent-space Matrix Product States gives a very complete description of the data and provides good agreement not only with the energies of the bound modes but also with their intensities. We also successfully explained the effect of temperature on the excitations including the experimentally observed thermally induced resonance between longitudinal modes below TN , and the transitions between thermally excited spinon states above TN. In summary, our work establishes SrCo2V2O8 as a beautiful paradigm for spinon confinement in a quasi-one dimensional quantum magnet and provides a comprehensive picture of this process.

Physical Review Letters, 1997

It is shown that a sufficiently strong four-spin interaction in the spin-1/2 spin ladder can cause dimerization. Such interaction can be generated either by phonons or (in the doped state) by the conventional Coulomb repulsion between the holes. The dimerized phases are thermodynamically undistinguishable from the Haldane phase, but have dramatically different correlation functions: the dynamical magnetic susceptibility, instead of displaying a sharp single magnon peak near q = π, shows only a two-particle threshold separated from the ground state by a gap.

Physical Review B, 2014

We explore the effect of the third-nearest neighbors on the magnetic properties of the Heisenberg model on an anisotropic triangular lattice. We obtain the phase diagram of the model using Schwinger boson mean-field theory. Competition between Néel, spiral, and collinear magnetically ordered phases is found as we vary the ratios of the nearest J 1 , next-nearest J 2 , and third-nearest J 3 neighbor exchange couplings. A spin-liquid phase is stabilized between the spiral and collinear ordered states when J 2 /J 1 1.8, for rather small J 3 /J 1 0.1. The lowest-energy two-spinon dispersions relevant to neutron scattering experiments are analyzed and compared to semiclassical magnon dispersions finding significant differences in the spiral and collinear phases between the two approaches. The results are discussed in the context of the anisotropic triangular materials: Cs 2 CuCl 4 and Cs 2 CuBr 4 and layered organic materials, κ-(BEDT-TTF) 2 X, and Y [Pd(dmit) 2 ] 2 .

Physical Review Letters, 2002

Using Random Phase Approximation, we show that a crossed-chains model of a spin-1/2 Heisenberg spins, with frustrated interchain couplings, has a non-dimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations. The results are confirmed by a bosonization study, which shows that the system is an example of a 'sliding Luttinger liquid'. In an external field, the system develops an incommensurate field-induced long range order with a finite transition temperature.

Journal of the Physical Society of Japan, 2013

The spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with ferromagnetic nextnearest-neighbour (NNN) interaction is investigated. The ground state is the Haldane phase for weak NNN interaction, and is the ferromagnetic phase for weak antiferromagnetic interaction. We find a series of topologically distinct spin-gap phases with various magnitudes of edge spins for strong NNN interaction. The phase boundaries between these phases are determined on the basis of the DMRG calculation with additional spins that compensate the edge spins. It is found that each of the exact solutions with short-range antiferromagnetic correlation on the ferromagnetic-nonmagnetic phase boundary is representative of each spin gap phase.

Physical Review Letters, 2005

Physical Review B, 2012

We present the theory of a three dimensional fractionalized topological insulator in the form of a U (1) spin liquid with gapped fermionic spinons in the bulk and topologically protected gapless spinon surface states. Starting from a spin-rotation invariant spin-1/2 model on a pyrochlore lattice with frustrated antiferromagnetic and ferromagnetic exchange interactions, we show that decomposition of the latter interactions, within slave-fermion representation of the spins, can naturally give rise to an emergent spin-orbit coupling for the spinons by spontaneously breaking the spin rotation symmetry. The time reversal symmetry, however, is preserved. This stabilizes a fractionalized topological insulator which also has bulk bond spin-nematic order. We describe the low energy properties of this state.

Physical Review B