Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin

Jahromi, Saeed S.; Hörmann, Max; Adelhardt, Patrick; Fey, Sebastian; Orús, Román; Schmidt, K. P.

doi:10.48550/arxiv.2111.06132

Cited by 2 publications

(2 citation statements)

References 53 publications

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“…High-field expansions of models where the ground state is coupled with the first excited states can also be computationally very demanding. An example is the Kitaev model in a field [64,65]. The proposed transformation could help to reach higher orders for that system.…”

Section: Discussionmentioning

confidence: 99%

Projective cluster-additive transformation for quantum lattice models

Hörmann,

Schmidt

2023

SciPost Phys.

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We construct a projection-based cluster-additive transformation that block-diagonalizes wide classes of lattice Hamiltonians \mathcal{H}=\mathcal{H}_0 +Vℋ=ℋ0+V. Its cluster additivity is an essential ingredient to set up perturbative or non-perturbative linked-cluster expansions for degenerate excitation subspaces of \mathcal{H}_0ℋ0. Our transformation generalizes the minimal transformation known amongst others under the names Takahashi’s transformation, Schrieffer-Wolff transformation, des Cloiseaux effective Hamiltonian, canonical van Vleck effective Hamiltonian or two-block orthogonalization method. The effective cluster-additive Hamiltonian and the transformation for a given subspace of \mathcal{H}ℋ, that is adiabatically connected to the eigenspace of \mathcal{H}_0ℋ0 with eigenvalue e_0^ne0n, solely depends on the eigenspaces of \mathcal{H}ℋ connected to e_0^me0m with e_0^m\leq e_0^ne0m≤e0n. In contrast, other cluster-additive transformations like the multi-block orthogonalization method or perturbative continuous unitary transformations need a larger basis. This can be exploited to implement the transformation efficiently both perturbatively and non-perturbatively. As a benchmark, we perform perturbative and non-perturbative linked-cluster expansions in the low-field ordered phase of the transverse-field Ising model on the square lattice for single spin-flips and two spin-flip bound-states.

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Section: Discussionmentioning

confidence: 99%

Projective cluster-additive transformation for quantum lattice models

Hörmann,

Schmidt

2023

SciPost Phys.

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“…which is essentially the form of the Hamiltonian when performing a high-field series expansion [204] for Kitaev's honeycomb model [205], where each site has one x-, y-, and z-type Ising interaction bond to one of its neighbours on the honeycomb lattice, respectively.…”

Section: White Graphs For Long-range Interactionsmentioning

confidence: 99%

Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions

Adelhardt,

Koziol,

Langheld

et al. 2024

Entropy

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Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum–optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

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Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin

Cited by 2 publications

References 53 publications

Projective cluster-additive transformation for quantum lattice models

Projective cluster-additive transformation for quantum lattice models

Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions

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