Exact spectra, spin susceptibilities, and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice

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

doi:10.1103/physrevb.50.10048

Cited by 391 publications

(512 citation statements)

References 55 publications

(105 reference statements)

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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%

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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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Section: Excitations: Low-energy Towers Of Statesmentioning

confidence: 99%

Section: Excitations: Low-energy Towers Of Statesmentioning

confidence: 99%

Quantum magnetism on the Cairo pentagonal lattice

2012

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“…In the triangular case, the ground state of such n.n. model is known to be the standard AF longrange order (LRO), the 120-degrees structure [18,19]. Hence, to explain the QSL behavior observed in these organic salts, some ingredient not taken into account in the simplest Heisenberg model is required.…”

mentioning

confidence: 99%

Quantum Spin-Liquid Behavior in the Spin-1/2 Random-Bond Heisenberg Antiferromagnet on the Kagome Lattice

2014

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The effect of the quenched bond-randomness on the ordering of the S = 1/2 antiferromagnetic Heisenberg model on the kagome lattice is investigated by means of an exact-diagonalization method. When the randomness exceeds a critical value, the ground state of the model exhibits a transition within the non-magnetic state into the randomness-relevant gapless spin-liquid state. Implications to the S = 1/2 kagome-lattice antiferromagnet herbertsmithite is discussed.Since the proposal by P.W. Anderson of the resonating valence bond state [1], the quantum spin-liquid (QSL) state possibly realized in certain S = 1/2 frustrated magnets has attracted interest of researchers [2]. After a long experimental quest, several candidate materials were recently reported in geometrically frustrated magnets, including both the triangular-lattice and the kagome-lattice antiferromagnets (AFs).Examples of the triangular-lattice AF might be S = 1/2 organic salts such as κ-(ET) 2 Cu 2 (CN) 3 [3][4][5][6] and [7][8][9][10], which exhibit no magnetic ordering, neither regular nor random, down to a very low temperature. The QSL state of these compounds exhibits gapless behaviors characterized by, e.g., the lowtemperature specific heat [4,9] or the thermal conductivity [5,8] linear in the absolute temperature T . An example of the second category, the kagome-lattice AF, might be herbertsmithite CuZn 3 (OH) 6 Cl 2 [11][12][13][14][15][16][17]. No magnetic order is observed down to 20mK in spite of the exchange coupling of 180K, while gapless behaviors are observed in various physical quantities.The origin of the QSL behavior observed in these triangular-lattice organic salts and the kagome-lattice herbertsmithite has attracted tremendous interest, and various theoretical proposals have been made. The simplest possible reference model might be the S = 1/2 AF Heisenberg model with the nearest-neighbor (n.n.) bilinear coupling. In the triangular case, the ground state of such n.n. model is known to be the standard AF longrange order (LRO), the 120-degrees structure [18,19]. Hence, to explain the QSL behavior observed in these organic salts, some ingredient not taken into account in the simplest Heisenberg model is required. In the kagome case, by contrast, the ground state of the n.n. model is believed to be some sort of QSL state without the magnetic LRO, although its nature is still under hot debate. Various scenarios, including the Z 2 spin liquid [20][21][22][23][24], the algebraic U(1) spin liquid [25][26][27][28], the chiral spin liquid [29] and the valence bond crystal (VBC) [30][31][32] etc. have been proposed. It is not entirely clear at the present stage, however, which of these, or any of these, applies to the experimentally observed QSL state of herbertsmithite.Most of the recent theories pre-assumes that the system is clean enough that the quenched randomness plays a negligible role. Meanwhile, it was recently suggested in ref. [33] that the QSL of the triangular-lattice organic salts might be the randomness-induced one, the randomsi...

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“…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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Exact spectra, spin susceptibilities, and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice

Cited by 391 publications

References 55 publications

Quantum magnetism on the Cairo pentagonal lattice

Quantum magnetism on the Cairo pentagonal lattice

Quantum Spin-Liquid Behavior in the Spin-1/2 Random-Bond Heisenberg Antiferromagnet on the Kagome Lattice

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

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