Valence bond ground states in a frustrated two-dimensional spin-1/2 Heisenberg antiferromagnet

Chayes, Jennifer; Chayes, Lincoln; Kivelson, Steven

doi:10.1007/bf01244017

Cited by 62 publications

(76 citation statements)

References 60 publications

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“…For VBS consisted of isolated bonds, the energies are easily calculated as summation of the binding energy for each bond. We found the two-spin bond VBS to be the lowestenergy states [28], with − 1 4 J 1 η (VBS 1 in Fig.2) and − 1 4 J 2 η (VBS 2 in Fig.2) per site. For hexagonal VBS, triangular VBS (see Fig.3) and the unitary VBS, the energies are calculated to be − all higher than the two-spin VBS.…”

Section: Heisenberg Model In Slave-fermion Representationmentioning

confidence: 99%

Phase diagram of the Kondo-Heisenberg model on honeycomb lattice with geometrical frustration

Song

Liu

2016

EPL

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We calculated the phase diagram of the Kondo-Heisenberg model on two-dimensional honeycomb lattice with both nearest-neighbor and next-nearest-neighbor antiferromagnetic spin exchanges, to investigate the interplay between RKKY and Kondo interactions at presence of magnetic frustration. Within a mean-field decoupling technology in slave-fermion representation, we derived the zero-temperature phase diagram as a function of Kondo coupling J k and frustration strength Q. The geometrical frustration can destroy the magnetic order, driving the original antiferromagnetic (AF) phase to non-magnetic valence bond state (VBS). In addition, we found two distinct VBS. As J k is increased, a phase transition from AF to Kondo paramagnetic (KP) phase occurs, without the intermediate phase coexisting AF order with Kondo screening found in square lattice systems. In the KP phase, the enhancement of frustration weakens the Kondo screening effect, resulting in a phase transition from KP to VBS. We also found a process to recover the AF order from VBS by increasing J k in a wide range of frustration strength. Our work may provide deeper understanding for the phase transitions in heavy-fermion materials, particularly for those exhibiting triangular frustration.

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Section: Heisenberg Model In Slave-fermion Representationmentioning

confidence: 99%

Phase diagram of the Kondo-Heisenberg model on honeycomb lattice with geometrical frustration

Song

Liu

2016

EPL

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“…4)(in color on line only).K is still necessarily 3-body but at least it now has the form of the Klein Hamiltonian, see e.g. [8] C. The idea here is to take adjacent pairs of site spins from B and encrypt them as the state of a spin = 3/2 particle living on the bond b joining the two sites. We orient b from L to L. Let us set up an indeterminate bijection (Fig.…”

Section: How To Construct a Net Hilbert Space Hmentioning

confidence: 99%

From String Nets to Nonabelions

Fidkowski

Freedman

Nayak

et al. 2009

Commun. Math. Phys.

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Abstract:We discuss Hilbert spaces spanned by the set of string nets, i.e. trivalent graphs, on a lattice. We suggest some routes by which such a Hilbert space could be the low-energy subspace of a model of quantum spins on a lattice with short-ranged interactions. We then explain conditions which a Hamiltonian acting on this string net Hilbert space must satisfy in order for the system to be in the DFib (Doubled Fibonacci) topological phase, that is, be described at low energy by an SO(3) 3 × SO(3) 3 doubled Chern-Simons theory, with the appropriate non-abelian statistics governing the braiding of the low-lying quasiparticle excitations (nonabelions). Using the string net wavefunction, we describe the properties of this phase. Our discussion is informed by mappings of string net wavefunctions to the chromatic polynomial and the Potts model.

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“…We can equally describe in this basis the Valence Bond Crystals, which are characterized by dominant amplitudes associated to the simple symmetry breaking configurations. Many properties of these wavefunctions have been studied theoretically ( [91,92,93,80,81] and references therein), we will see some of them in the following.…”

Section: Introduction: Short Range Versus Long Range Resonating Valenmentioning

confidence: 99%

Frustrated Quantum Magnets

Lhuillier

Misguich

2002

High Magnetic Fields

140

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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 Néel phases. Order by disorder selection is illustrated. All these phases break SU (2) symmetry and are gapless phases with ∆S z = 1 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, or1 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.

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Valence bond ground states in a frustrated two-dimensional spin-1/2 Heisenberg antiferromagnet

Cited by 62 publications

References 60 publications

Phase diagram of the Kondo-Heisenberg model on honeycomb lattice with geometrical frustration

Phase diagram of the Kondo-Heisenberg model on honeycomb lattice with geometrical frustration

From String Nets to Nonabelions

Frustrated Quantum Magnets

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