Effective Hamiltonians and dilution effects in Kagome and related anti-ferromagnets

Henley, Christopher L.

doi:10.1139/p01-097

Cited by 72 publications

(110 citation statements)

References 31 publications

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“…The first Heisenberg spin liquid to be identified unambiguously, the antiferromagnet on the pyrochlore lattice [7,12] is a U (1) spin liquid exhibiting pinch-points in its structure factor indicating algebraically decaying correlations [7,[12][13][14][15], as well as fractionalisation of its microscopic degrees of freedom: disorder in the form of dilution creates new, weakly-interacting, magnetic degrees of freedom which possess a half of the microscopic magnetic moments of the Heisenberg model [16,17].…”

Section: Pacs Numbersmentioning

confidence: 99%

Fractionalized Z2 Classical Heisenberg Spin Liquids

2017

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Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for classical Heisenberg models, only one kind of fractionalised spin liquid phase, the so-called Coulomb or U (1) spin liquid, has until recently been identified: this exhibits algebraic spin correlations and impurity moments, 'orphan spins', whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalisation in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a Z2 spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavour. PACS numbers:Fractionalisation is one of the several unusual properties generally observed in systems evading low temperature conventional symmetry breaking ordered states in favor of unconventional topological orders. On account of such exotic behavior, much attention has been devoted to the identification of systems exhibiting such new topological physics. Frustrated magnets [1][2][3] have played a prominent role, where several spin liquids (SL) [4,5] starting in the late 90s [6] were identified [7][8][9].While by now a multitude of quantum SL have been discovered [10] and classified [11], the situation with classical Heisenberg SL is comparatively much sparser. The first Heisenberg spin liquid to be identified unambiguously, the antiferromagnet on the pyrochlore lattice [7,12] is a U (1) spin liquid exhibiting pinch-points in its structure factor indicating algebraically decaying correlations [7,[12][13][14][15], as well as fractionalisation of its microscopic degrees of freedom: disorder in the form of dilution creates new, weakly-interacting, magnetic degrees of freedom which possess a half of the microscopic magnetic moments of the Heisenberg model [16,17].Such fractionalisation is perhaps the cleanest signature of spin-liquidity in such a classical setting, as definitions in terms of topological field theory are frustrated by the bulk gapless excitations due to the continuous classical nature of the Heisenberg spins.Given the by now overwhelming variety of known quantum spin liquids (for an example, see Ref. 18), it may therefore come as a surprise that no corresponding richness appears to exist for classical Heisenberg magnets: the U (1) case is the only one studied in detail. It turns up in many settings, such as the checkerboard and pyrochlore lattices (for n = 2 component spins) [7,12], the kagome (for n > 3 component spins) [19,20], or the SCGO 'pyrochlore slab' [21].Here we ask the question whether this absence of evidence of other types of spin liquid is evidence of absence. The answer is that there is indeed more diversity than has been so far recognised: we identify a new SL class which and a kagome (right) lattices. These can be respectively seen as fully connected squares forming a kagome, and fully connected hexagons forming a triangular, la...

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Section: Pacs Numbersmentioning

confidence: 99%

Fractionalized Z2 Classical Heisenberg Spin Liquids

2017

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“…9 This biquadratic interaction represents an effective Hamiltonian that is generated by quantum and/or thermal fluctuations. 43 We have incorporated such a biquadratic spin interaction and optimized its (fielddependent) coupling constant such that we reproduce the leading 1/S energy differences between several important states in the classical ground-state manifold. In this way, we find that quantum zero-point energy can be semiquantitatively described by the following classical biquadratic Hamiltonian with negative coupling constant:…”

Section: E Biquadratic Approximation Of Quantum Fluctuations (Zero-pmentioning

confidence: 99%

Deformed triangular lattice antiferromagnets in a magnetic field: Role of spatial anisotropy and Dzyaloshinskii-Moriya interactions

et al. 2011

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Recent experiments on the anisotropic spin-1/2 triangular antiferromagnet Cs 2 CuBr 4 have revealed a remarkably rich phase diagram in applied magnetic fields, consisting of an unexpectedly large number of ordered phases. Motivated by this finding, we study the role of three ingredients-spatial anisotropy, Dzyaloshinskii-Moriya interactions, and quantum fluctuations-on the magnetization process of a triangular antiferromagnet, coming from the semiclassical limit. The richness of the problem stems from two key facts: (1) the classical isotropic model with a magnetic field exhibits a large accidental ground-state degeneracy and (2) these three ingredients compete with one another and split this degeneracy in opposing ways. Using a variety of complementary approaches, including extensive Monte Carlo numerics, spin-wave theory, and an analysis of Bose-Einstein condensation of magnons at high fields, we find that their interplay gives rise to a complex phase diagram consisting of numerous incommensurate and commensurate phases. Our results shed light on the observed phase diagram for Cs 2 CuBr 4 and suggest a number of future theoretical and experimental directions that will be useful for obtaining a complete understanding of this material's interesting phenomenology.

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“…Instead, our approach is to express E ′ as an effective Hamiltonian H eff [12], for a generic classical ground state, often via crude approximations that have no controlled small parameter, yet result in an elegant form. For any H eff , we seek (i) its (approximate) analytic form (ii) its energy scale, (iii) which spin pattern gives the minimum E harm , and (iv) how large is the remaining degeneracy.…”

Section: Introductionmentioning

confidence: 99%

“…The effective Hamiltonian has value beyond the possibility (as here) that it leads us to unexpected ground states. First, we can model the T > 0 behavior using a Boltzmann ensemble exp(−βH eff ) [12]. Second, starting from H eff , more complete models may be built by the addition of anisotropies, quantum tunneling [13], or dilution [12].…”

Section: Introductionmentioning

confidence: 99%

“…First, we can model the T > 0 behavior using a Boltzmann ensemble exp(−βH eff ) [12]. Second, starting from H eff , more complete models may be built by the addition of anisotropies, quantum tunneling [13], or dilution [12]. Apart from analytics, we also pursued the brute-force approach of fitting H eff to a database of numerically evaluated energies; minimizing the resulting H eff may well lead us to a new ground state not represented in the database.…”

Section: Introductionmentioning

confidence: 99%

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Effective Hamiltonians for large-Spyrochlore antiferromagnets

Hizi

Henley

2007

J. Phys.: Condens. Matter

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Abstract. The pyrochlore lattice Heisenberg antiferromagnet has a massive classical ground state degeneracy. We summarize three approximation schemes, valid for large spin length S, to capture the (partial) lifting of this degeneracy when zero-point quantum fluctuations are taken into account; all three are related to analytic loop expansions. The first is harmonic order spin waves; at this order, there remains an infinite manifold of degenerate collinear ground states, related by a gauge-like symmetry. The second is anharmonic (quartic order) spin waves, using a self-consistent approximation; the harmonic-order degeneracy is split, but (within numerical precision) some degeneracy may remain, with entropy still of order L in a system of L 3 sites. The third is a large-N approximation, a standard and convenient approach for frustrated antiferromagnets; however, the large-N result contradicts the harmonic order at O(S) hence must be wrong (for large S).

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Effective Hamiltonians and dilution effects in Kagome and related anti-ferromagnets

Cited by 72 publications

References 31 publications

Fractionalized Z2 Classical Heisenberg Spin Liquids

Fractionalized Z2 Classical Heisenberg Spin Liquids

Deformed triangular lattice antiferromagnets in a magnetic field: Role of spatial anisotropy and Dzyaloshinskii-Moriya interactions

Effective Hamiltonians for large-Spyrochlore antiferromagnets

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