Order versus disorder in the quantum Heisenberg antiferromagnet on the<b><i>kagomé</i></b>lattice using exact spectra analysis

Lecheminant, P.; Bernu, B.; Lhuillier, C.; Pierre, Laurent; Sindzingre, Philippe

doi:10.1103/physrevb.56.2521

Cited by 395 publications

(469 citation statements)

References 44 publications

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“…1. The magnetic order survives in the quantum model, at least for large enough J 2 , as it has been established by exact diagonalization studies [49]. However, the precise phase boundary between the magnetically ordered phases and the disordered spin-liquid region at J 2 ≈ 0 has not been determined yet (see Ref.…”

Section: Introductionmentioning

confidence: 95%

Phase diagram of theJ1−J2Heisenberg model on the kagome lattice

et al. 2015

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We perform an extensive density-matrix renormalization-group study of the ground-state phase diagram of the spin-1/2 J 1 -J 2 Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at J 2 = 0. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around J 2 ≈ 0, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic J 2 , the ground state displays signatures of the magnetic order of the √ 3 × √ 3 and the q = 0 type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the q = 0 ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.

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Section: Introductionmentioning

confidence: 95%

Phase diagram of theJ1−J2Heisenberg model on the kagome lattice

et al. 2015

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“…One should mention that, while it is well established that the √ 3 × √ 3 order survives at smaller J 2 (i.e., at J 2 > −1), 19 it is still a challenging task to determine the phase diagram of the J 1 -J 2 KHA in the limit J 2 ≈ 0. In particular, the nature of the ground state of the pure kagome Heisenberg antiferromagnet (i.e., at J 2 = 0,J 1 > 0) is still debated.…”

Section: Models and Methodsmentioning

confidence: 99%

“…In combination with exact diagonalization techniques, tower of states spectroscopy is routinely used to detect symmetry broken phases. [16][17][18][19][20][21][22][23] So far, tower of states structures in ES have only been observed numerically in the superfluid phase of the 2D BoseHubbard model, 15 where the formation of a Bose condensate is associated with the breaking of a U(1) gauge symmetry (reflecting conservation of the total number of particles in finite systems). The resulting TOS spectrum, however, (and the lower part of the ES thereof) is "trivial" with one level (excitation) per particle number sector.…”

Section: Introductionmentioning

confidence: 99%

Entanglement spectroscopy of SU(2)-broken phases in two dimensions

et al. 2013

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In magnetically ordered systems, the breaking of SU(2) symmetry in the thermodynamic limit is associated with the appearance of a special type of low-lying excitations in finite-size energy spectra, the so-called tower of states (TOS). In the present work, we numerically demonstrate that there is a correspondence between the SU(2) tower of states and the lower part of the ground-state entanglement spectrum (ES). Using state-of-the-art density matrix renormalization group (DMRG) calculations, we examine the ES of the 2D antiferromagnetic J 1 -J 2 Heisenberg model on both the triangular and kagome lattice. At large ferromagnetic J 2 , the model exhibits a magnetically ordered ground state. Correspondingly, its ES contains a family of low-lying levels that are reminiscent of the energy tower of states. Their behavior (level counting, finite-size scaling in the thermodynamic limit) sharply reflects TOS features, and is characterized in terms of an effective entanglement Hamiltonian that we provide. At large system sizes, TOS levels are divided from the rest by an entanglement gap. Our analysis suggests that (TOS) entanglement spectroscopy provides an alternative tool for detecting and characterizing SU(2)-broken phases using DMRG.

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“…This is done by looking at the symmetry structure of the so-called Anderson towers of states. 38 It is by now established, following the seminal work by Bernu et al 39,40 and Lecheminant et al 41,42 , that a given magnetic phase in the thermodynamic limit shows up in finite-size spectra through the clear formation of a tower of states which scale as S(S + 1)/N and is well separated from higher excitations. A wavepacket out of this infinite tower would be stationary in the thermodynamic limit and would correspond to the given classical state.…”

Section: Excitations: Low-energy Towers Of Statesmentioning

confidence: 99%

“…Not surprisingly then, the multiplicities and symmetry properties of this set of states are intimately connected to the symmetries that are broken in the classical phase and can actually be derived by group theory alone. [39][40][41][42][43][44] Now, the collinear and the orthogonal phase break the full symmetry group of the Hamiltonian in a different way, so the structure of the corresponding tower of states should be very different from each other. In App.…”

Section: Excitations: Low-energy Towers Of Statesmentioning

confidence: 99%

Quantum magnetism on the Cairo pentagonal lattice

2012

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We present an extensive analytical and numerical study of the antiferromagnetic Heisenberg model on the Cairo pentagonal lattice, the dual of the Shastry-Sutherland lattice with a close realization in the S = 5/2 compound Bi2Fe4O9. We consider a model with two exchange couplings suggested by the symmetry of the lattice, and investigate the nature of the ground state as a function of their ratio x and the spin S. After establishing the classical phase diagram we switch on quantum mechanics in a gradual way that highlights the different role of quantum fluctuations on the two inequivalent sites of the lattice. The most important findings for S = 1/2 include: (i) a surprising interplay between a collinear and a four-sublattice orthogonal phase due to an underlying order-by-disorder mechanism at small x (related to an emergent J1-J2 effective model with J2 ≫ J1), and (ii) a non-magnetic and possibly spin-nematic phase with d-wave symmetry at intermediate x.

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Order versus disorder in the quantum Heisenberg antiferromagnet on thekagomélattice using exact spectra analysis

Cited by 395 publications

References 44 publications

Phase diagram of theJ1−J2Heisenberg model on the kagome lattice

Phase diagram of theJ1−J2Heisenberg model on the kagome lattice

Entanglement spectroscopy of SU(2)-broken phases in two dimensions

Quantum magnetism on the Cairo pentagonal lattice

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