arXiv subjects

Claire Lhuillier

Publications and source records attributed to Claire Lhuillier.

18 recordsLinked to original sources

arXiv2017

Chiral spin liquid on kagome antiferromagnet induced by Dzyaloshinskii-Moriya interaction

The quantum spin liquid material herbertsmithite is described by an antiferromagnetic Heisenberg model on the kagome lattice with non-negligible Dzyaloshinskii-Moriya interaction~(DMI). A well established phase transition to the $\mathbf q=0$ long-range order occurs in this model when the DMI strength increases, but the precise nature of a small-DMI phase remains controversial. Here, we describe a new phase obtained from Schwinger-boson mean-field theory that is stable at small DMI, and which can explain the dispersionless spectrum seen in inelastic neutron scattering experiment by Han et al (Nature (London) 492, 406 (2012)}). It is a time-reversal symmetry breaking $\mathbb Z_2$ spin liquid, with the unique property of a small and constant spin gap in an extended region of the Brillouin zone. The phase diagram as a function of DMI and spin size is given, and dynamical spin structure factors are presented.

cond-mat.str-el↗

arXiv2016

Projective symmetry group classification of chiral spin liquids

We present a general review of the projective symmetry group classification of fermionic quantum spin liquids for lattice models of spin $S=1/2$. We then introduce a systematic generalization of the approach for symmetric $\mathbb{Z}_2$ quantum spin liquids to the one of chiral phases (i.e., singlet states that break time reversal and lattice reflection, but conserve their product). We apply this framework to classify and discuss possible chiral spin liquids on triangular and kagome lattices. We give a detailed prescription on how to construct quadratic spinon Hamiltonians and microscopic wave functions for each representation class on these lattices. Among the chiral $\mathbb{Z}_2$ states, we study the subset of U(1) phases variationally in the antiferromagnetic $J_1$-$J_2$-$J_d$ Heisenberg model on the kagome lattice. We discuss static spin structure factors and symmetry constraints on the bulk spectra of these phases.

cond-mat.str-el↗

arXiv2015

Gapless chiral spin liquid in a kagome Heisenberg model

Motivated by recent experiments on the Heisenberg S=1/2 quantum spin liquid candidate material kapellasite, we classify all possible chiral (time-reversal symmetry breaking) spin liquids with fermionic spinons on the kagome lattice. We obtain the phase diagram for the physically relevant extended Heisenberg model, comparing the energies of a wide range of microscopic variational wave functions. We propose that, at low temperature, kapellasite exhibits a gapless chiral spin liquid phase with spinon Fermi surfaces. This two-dimensional state inherits many properties of the nearby one-dimensional phase of decoupled anti-ferromagnetic spin chains, but also shows some remarkable differences. We discuss the spin structure factors and other physical properties.

cond-mat.str-el↗

arXiv2013

Time-reversal-symmetry-breaking chiral spin liquids: a projective symmetry group approach of bosonic mean-field theories

Projective symmetry groups (PSG) are the mathematical tools which allow to list and classify mean-field spin liquids (SL) based on a parton construction. The seminal work of Wen and its subsequent extension to bosons by Wang and Vishwanath concerned the so-called symmetric SL: i.e. states that break neither lattice symmetries nor time reversal invariance. Here we generalize this approach to chiral (time reversal symmetry breaking) SL described in a Schwinger boson mean-field approach. A special emphasis is put on frustrated lattices (triangular and kagome lattices), where the possibility of a chiral SL ground state has recently been discussed. The PSG approach is detailed for the triangular lattice case. Results for other lattices are given in the appendices. The physical significance of gauge invariant quantities called fluxes is discussed both in the classical limit and in the quantum SL and their expressions in terms of spin observables are given.

cond-mat.str-el↗

arXiv2012

Two-dimensional quantum antiferromagnets

This review presents some theoretical advances in the field of quantum magnetism in two-dimensional systems, and quantum spin liquids in particular. It is to be published as a chapter in the second edition of the book "Frustrated spin systems", edited by H. T. Diep (World-Scientific). The section (Sec. 7) devoted to the kagome antiferromagnet has been completely rewritten/updated, as well as the concluding section (Sec. 8). The other sections (Secs. 1-6) are unchanged from the first edition of the book (published in 2005)

cond-mat.str-el↗

arXiv2011

The kagome antiferromagnet: a chiral topological spin liquid ?

Inspired by the recent discovery of a new instability towards a chiral phase of the classical Heisenberg model on the kagome lattice, we propose a specific chiral spin liquid that reconciles different, well-established results concerning both the classical and quantum models. This proposal is analyzed in an extended mean-field Schwinger boson framework encompassing time reversal symmetry breaking phases which allows both a classical and a quantum phase description. At low temperatures, we find quantum fluctuations favor this chiral phase, which is stable against small perturbations of second and third neighbor interactions. For spin-1/2 this phase may be, beyond mean-field, a chiral gapped spin liquid. Such a phase is consistent with Density Matrix Renormalization Group results of Yan et al. (Science 322, 1173 (2011)). Mysterious features of the low lying excitations of exact diagonalization spectra also find an explanation in this framework. Moreover, thermal fluctuations compete with quantum ones and induce a transition from this flux phase to a planar zero flux phase at a non zero value of the renormalized temperature (T/S^2), reconciling these results with those obtained for the classical system.

cond-mat.str-el↗

arXiv2011

Lattice symmetries and regular states in classical frustrated antiferromagnets

We consider some classical and frustrated lattice spin models with global O(3) spin symmetry. There is no general analytical method to find a ground-state if the spin dependence of the Hamiltonian is more than quadratic (i.e. beyond the Heisenberg model) and/or if the lattice has more than one site per unit cell. To deal with these situations, we introduce a family of variational spin configurations, dubbed "regular states", which respect all the lattice symmetries modulo global O(3) spin transformations (rotations and/or spin flips). The construction of these states is explicited through a group theoretical approach, and all the regular states on the square, triangular, honeycomb and kagome lattices are listed. Their equal time structure factors and powder-averages are shown for comparison with experiments. All the well known Néel states with 2 or 3 sublattices appear amongst regular states on various lattices, but the regular states also encompass exotic non-planar states with cubic, tetrahedral or cuboctahedral geometry of the T=0 order parameter. Whatever the details of the Hamiltonian (with the same symmetry group), a large fraction of these regular states are energetically stationary with respect to small deviations of the spins. In fact these regular states appear as exact ground-states in a very large range of parameter space of the simplest models that we have been looking at. As examples, we display the variational phase diagrams of the J1-J2-J3 Heisenberg model on all the previous lattices as well as that of the J1-J2-K ring-exchange model on square and triangular lattices.

cond-mat.str-el↗

arXiv2009

Low energy excitations of the kagome antiferromagnet and the spin gap issue

In this paper we report the latest results of exact diagonalizations of SU(2) invariant models on various lattices (square, triangular, hexagonal, checkerboard and kagome lattices). We focus on the low lying levels in each S sector. The differences in behavior between gapless systems and gapped ones are exhibited. The plausibility of a gapless spin liquid in the Heisenberg model on the kagome lattice is discussed. A rough estimate of the spin susceptibility in such an hypothesis is given.The evolution of the intra-S channel spectra under the effect of a small perturbation is consistent with the proximity of a quantum critical point. We emphasize that the very small intra-S channel energy scale observed in exact spectra is a very interesting information to understand the low T dynamics of this model.

cond-mat.str-el↗

arXiv2009

Dynamical Correlations of the Kagome S=1/2 Heisenberg Quantum Antiferromagnet

We determine dynamical response functions of the S=1/2 Heisenberg quantum antiferromagnet on the kagome lattice based on large-scale exact diagonalizations combined with a continued fraction technique. The dynamical spin structure factor has important spectral weight predominantly along the boundary of the extended Brillouin zone and energy scans reveal broad response extending over a range of 2 \sim 3J concomitant with pronounced intensity at lowest available energies. Dispersive features are largely absent. Dynamical singlet correlations -- which are relevant for inelastic light probes -- reveal a similar broad response, with a high intensity at low frequencies omega/J \lesssim 0.2J. These low energy singlet excitations do however not seem to favor a specific valence bond crystal, but instead spread over many symmetry allowed eigenstates.

cond-mat.str-el↗

arXiv2008

Thermal destruction of chiral order in a two-dimensional model of coupled trihedra

We introduce a minimal model describing the physics of classical two-dimensional (2D) frustrated Heisenberg systems, where spins order in a non-planar way at T=0. This model, consisting of coupled trihedra (or Ising-$\mathbb{R}P^3$ model), encompasses Ising (chiral) degrees of freedom, spin-wave excitations and $\Z_2$ vortices. Extensive Monte Carlo simulations show that the T=0 chiral order disappears at finite temperature in a continuous phase transition in the 2D Ising universality class, despite misleading intermediate-size effects observed at the transition. The analysis of configurations reveals that short-range spin fluctuations and $\Z_2$ vortices proliferate near the chiral domain walls explaining the strong renormalization of the transition temperature. Chiral domain walls can themselves carry an unlocalized $\Z_2$ topological charge, and vortices are then preferentially paired with charged walls. Further, we conjecture that the anomalous size-effects suggest the proximity of the present model to a tricritical point. A body of results is presented, that all support this claim: (i) First-order transitions obtained by Monte Carlo simulations on several related models (ii) Approximate mapping between the Ising-$\mathbb{R}P^3$ model and a dilute Ising model (exhibiting a tricritical point) and, finally, (iii) Mean-field results obtained for Ising-multispin Hamiltonians, derived from the high-temperature expansion for the vector spins of the Ising-$\mathbb{R}P^3$ model.

cond-mat.stat-mech↗

arXiv2005

Twelve sublattice ordered phase in the J1-J2 model on the kagome lattice

Motivated by recent experiments on an S=1/2 antiferromagnet on the kagome lattice, we investigate the Heisenberg J1-J2 model with ferromagnetic J1 and antiferromagnetic J2. Classically the ground state displays Neel long range order with 12 non-coplanar sublattices. The order parameter has the symmetry of a cuboctahedron so that it fully breaks SO(3) as well as the spin-flip symmetry, and we expect from the latter a Z2 symmetry breaking pattern. As might be expected from the Mermin-Wagner theorem in two dimensions, the SO(3) symmetry is restored by thermal fluctuations while the Z2 symmetry breaking persists up to a finite temperature. A complete study of S=1/2 exact spectra reveals that the classical order subsists for quantum spins in a finite range of parameters. First order spin wave calculations give the range of existence of this phase and the renormalisations at T=0 of the order parameters associated to both symmetry breakings. This phase is destroyed by quantum fluctuations for a small but finite J2/|J1|\simeq3 consistently with exact spectra studies which indicate a gapped phase.

cond-mat.str-el↗

arXiv2005

Quantum dimer model with Z_2 liquid ground-state: interpolation between cylinder and disk topologies and toy model for a topological quantum-bit

We consider a quantum dimer model (QDM) on the kagome lattice which was introduced recently [Phys. Rev. Lett. 89, 137202 (2002)]. It realizes a Z_2 liquid phase and its spectrum was obtained exactly. It displays a topological degeneracy when the lattice has a non-trivial geometry (cylinder, torus, etc). We discuss and solve two extensions of the model where perturbations along lines are introduced: first the introduction of a potential energy term repelling (or attracting) the dimers along a line is added, second a perturbation allowing to create, move or destroy monomers. For each of these perturbations we show that there exists a critical value above which, in the thermodynamic limit, the degeneracy of the ground-state is lifted from 2 (on a cylinder) to 1. In both cases the exact value of the gap between the first two levels is obtained by a mapping to an Ising chain in transverse field. This model provides an example of solvable Hamiltonian for a topological quantum bit where the two perturbations act as a diagonal and a transverse operator in the two-dimensional subspace. We discuss how crossing the transitions may be used in the manipulation of the quantum bit to optimize simultaneously the frequency of operation and the losses due to decoherence.

cond-mat.str-el↗

arXiv2005

Frustrated Quantum Magnets

A description of different phases of two dimensional magnetic insulators is given. The first chapters are devoted to the understanding of the symmetry breaking mechanism in the semi-classical Neel phases. Order by disorder selection is illustrated. All these phases break SU(2) symmetry and are gapless phases with magnon excitations. Different gapful quantum phases exist in two dimensions: the Valence Bond Crystal phases (VBC) which have long range order in local S=0 objects (either dimers in the usual Valence Bond acception or quadrumers..), but also Resonating Valence Bond Spin Liquids (RVBSL), which have no long range order in any local order parameter and an absence of susceptibility to any local probe. VBC have gapful S = 0, or 1 excitations, RVBSL on the contrary have deconfined spin-1/2 excitations. Examples of these two kinds of quantum phases are given in chapters 4 and 5. A special class of magnets (on the kagome or pyrochlore lattices) has an infinite local degeneracy in the classical limit: they give birth in the quantum limit to different behaviors which are illustrated and questionned in the last lecture.

cond-mat.str-el↗

arXiv2001

Frustrated quantum magnets

In these lectures we sketch a rapid survey of recent theoretical advances in the study of frustrated quantum magnets with a special emphasis on two dimensional magnets.

cond-mat.str-el↗

arXiv2000

From Neel long-range order to spin-liquids in the multiple-spin exchange model

The phase diagram of the multiple-spin exchange model on the triangular lattice is studied using exact diagonalizations. The two-spin (J_2) and four-spin (J_4) exchanges have been taken into account for 12, 16, 19, 21, 24, and 27 site samples in the parameter region J_4=0 - 0.25 (for a fixed J_2=1). It is found that the three-sublattice Néel ordered state built up by the pure two-spin exchange can be destroyed by the four-spin exchange, forming a spin-liquid state. The different data suggest that the phase diagram in this range of parameters exhibits two phases. The pure J_2 phase is a three-sublattice Neel ordered phase, a small J_4 drives it into a spin-liquid state with a spin gap filled of a large number of singlets. This spin-liquid phase is not of the same generic kind as the phase studied by Misguich et al. [Phys. Rev. B 60, 1064 (1999)]. It is observed on the finite-size samples that the spin liquid phase, as the Neel ordered phase, exhibits a magnetization plateau at m = 1/3, and for J_4 >0.15 a second plateau atm=1/2. These two plateaus are associated respectively to the semi-classical orderings uud and uuud.

cond-mat.str-el↗

arXiv2000

Magneto-thermodynamics of the spin-1/2 Kagome antiferromagnet

In this paper, we use a new hybrid method to compute the thermodynamic behavior of the spin-1/2 Kagome antiferromagnet under the influence of a large external magnetic field. We find a T^2 low-temperature behavior and a very low sensitivity of the specific heat to a strong external magnetic field. We display clear evidence that this low temperature magneto-thermal effect is associated to the existence of low-lying fluctuating singlets, but also that the whole picture (T^2 behavior of Cv and thermally activated spin susceptibility) implies contribution of both non magnetic and magnetic excitations. Comparison with experiments is made.

cond-mat.str-el↗

arXiv2000

Some remarks on the Lieb-Schultz-Mattis theorem and its extension to higher dimensions

The extension of the Lieb-Schultz-Mattis theorem to dimensions larger than one is discussed. It is explained why the variational wave-function built by the previous authors is of no help to prove the theorem in dimension larger than one. The short range R.V.B. picture of Sutherland, Rokhsar and Kivelson, Read and Chakraborty gives a strong support to the assertion that the theorem is indeed valid in any dimension. Some illustrations of the general ideas are displayed on exact spectra.

cond-mat.str-el↗

arXiv1998

Spin-Liquid phase of the Multiple-Spin Exchange Hamiltonian on the Triangular Lattice

We performed an exact diagonalization study of the spin liquid phase of the Multiple-Spin Exchange model on the triangular lattice. It is characterized by no Neel Long Range Order (NLRO), short-ranged magnetic correlations and a spin gap. We found no LRO in any local order parameter we investigated (chiral, dimer,...). The probable asymptotic ground state degeneracy is discussed. We argue that it could be of topological origin and that the system is probably not a chiral spin liquid. A possible relation to the Affleck-Kennedy-Lieb-Tasaki (AKLT) phase is discussed.

cond-mat.str-el↗