Two-particle bound states and one-particle structure factor in a Heisenberg bilayer system

Collins, Andrew M.; Hamer, C. J.

doi:10.1103/physrevb.78.054419

Cited by 16 publications

(19 citation statements)

References 49 publications

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“…Φ 44 are given in Appendix C. For d = 2 our expressions (33-40) agree with those given in Ref. 25. Finally, the cubic term, present only in the asymmetric case κ = 0, reads:…”

Section: Normal-ordered Hamiltoniansupporting

confidence: 80%

Nonlinear bond-operator theory and1/dexpansion for coupled-dimer magnets. I. Paramagnetic phase

et al. 2015

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For coupled-dimer Heisenberg magnets, a paradigm of magnetic quantum phase transitions, we develop a systematic expansion in 1/d, the inverse number of space dimensions. The expansion employs a formulation of the bond-operator technique and is based on the observation that a suitably chosen product-state wavefunction yields exact zero-temperature expectation values of local observables in the d → ∞ limit, with corrections vanishing as 1/d. We demonstrate the approach for a model of dimers on a hypercubic lattice, which generalizes the square-lattice bilayer Heisenberg model to arbitrary d. In this paper, we use the 1/d expansion to calculate static and dynamic observables at zero temperature in the paramagnetic singlet phase, up to the quantum phase transition, and compare the results with numerical data available for d = 2. Contact is also made with previously proposed refinements of bond-operator theory as well as with a perturbative expansion in the inter-dimer coupling. In a companion paper, the present 1/d expansion will be extended to the ordered phase, where it is shown to consistently describe the entire phase diagram including the quantum critical point.

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“…Φ 44 are given in Appendix C. For d = 2 our expressions (33-40) agree with those given in Ref. 25. Finally, the cubic term, present only in the asymmetric case κ = 0, reads:…”

Section: Normal-ordered Hamiltoniansupporting

confidence: 80%

Nonlinear bond-operator theory and1/dexpansion for coupled-dimer magnets. I. Paramagnetic phase

et al. 2015

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“…This model Hamiltonian has been studied extensively for the S = 1/2 square lattice bilayer. 11,[14][15][16][17][18] The effects of disorder, induced by site dilution, have also been explored. 19 However, there has been relatively little work on understanding the higher spin generalizations of the Hamiltonian in Eq.…”

Section: Introductionmentioning

confidence: 99%

Néel to dimer transition in spin-Santiferromagnets: Comparing bond operator theory with quantum Monte Carlo simulations for bilayer Heisenberg models

2011

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We study the Néel to dimer transition driven by interlayer exchange coupling in spin-S Heisenberg antiferromagnets on bilayer square and honeycomb lattices for S = 1/2, 1, and 3/2. Using exact stochastic series expansion quantum Monte Carlo (QMC) calculations, we find that the critical value of the interlayer coupling, J ⊥c [S], increases with increasing S, with clear evidence that the transition is in the O(3) universality class for all S. Using bond operator mean-field theory restricted to singlet and triplet states, we find J ⊥c [S] ∝ S(S + 1), in qualitative accord with QMC, but the resulting J ⊥c [S] is significantly smaller than the QMC value. For S = 1/2, incorporating triplet-triplet interactions within a variational approach yields a critical interlayer coupling, which agrees well with QMC. For higher spin, we argue that it is crucial to account for the high-energy quintet modes, and we show that including these within a perturbative scheme leads to reasonable agreement with QMC results for S = 1 and 3/2. We discuss the broad implications of our results for systems such as the triangular lattice S = 1 dimer compound Ba 3 Mn 2 O 8 and the S = 3/2 bilayer honeycomb material Bi 3 Mn 4 O 12 (NO 3 ).

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“…Our dispersion agrees at least qualitatively with known excitation spectra for this model. [24][25][26]28 Interestingly, our approach also allows us to estimate quasiparticle lifetimes which are inaccessible within many more conventional methods. Above g ≈ 0.2, we find small but finite spectral broadenings near the point.…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…15,[20][21][22] From there, many approaches have used the QMC results on the BHM as a benchmark for their applicability, such as Schwinger-boson Gutzwiller projection, 23 dimer expansions, 24 high-temperature and Ising expansions, 25 Guttwiller-projected Bose gas, 26 bondoperator mean field, 27 and triplet-wave expansions. 28 We likewise intend to benchmark our cluster FRG for the BHM against the established numerical evidence. Note that the BHM is a challenging problem for PFFRG being the precursor of our cluster FRG: While the PFFRG is insensitive to the sign problem and hence can conveniently treat magnetically frustrated scenarios in general, the quantitative analysis of a transition from a zero-dimensional dimer product state to a two-dimensional magnetically ordered state is rather involved and usually necessitates full self-consistent resummation and minimal violation of Ward identities in the diagrammatic summation.…”

Section: Introductionmentioning

confidence: 99%

Cluster functional renormalization group

Reuther

Thomale

2014

Phys. Rev. B

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Functional renormalization group (FRG) has become a diverse and powerful tool to derive effective low-energy scattering vertices of interacting many-body systems. Starting from a free expansion point of the action, the flow of the RG parameter allows us to trace the evolution of the effective one-and two-particle vertices towards low energies by taking into account the vertex corrections between all parquet channels in an unbiased fashion. In this work, we generalize the expansion point at which the diagrammatic resummation procedure is initiated from a free UV limit to a cluster product state. We formulate a cluster FRG scheme where the noninteracting building blocks (i.e., decoupled spin clusters) are treated exactly, and the intercluster couplings are addressed via RG. As a benchmark study, we apply our cluster FRG scheme to the spin-1 2 bilayer Heisenberg model (BHM) on a square lattice where the neighboring sites in the two layers form the individual two-site clusters. Comparing with existing numerical evidence for the BHM, we obtain reasonable findings for the spin susceptibility, the spin-triplet excitation energy, and quasiparticle weight even in coupling regimes close to antiferromagnetic order. The concept of cluster FRG promises applications to a large class of interacting electron systems.

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Two-particle bound states and one-particle structure factor in a Heisenberg bilayer system

Cited by 16 publications

References 49 publications

Nonlinear bond-operator theory and1/dexpansion for coupled-dimer magnets. I. Paramagnetic phase

Nonlinear bond-operator theory and1/dexpansion for coupled-dimer magnets. I. Paramagnetic phase

Néel to dimer transition in spin-Santiferromagnets: Comparing bond operator theory with quantum Monte Carlo simulations for bilayer Heisenberg models

Cluster functional renormalization group

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