Order-by-disorder and long-range interactions in the antiferromagnetic transverse-field Ising model on the triangular lattice—A perturbative point of view

Koziol, Jan Alexander; Mühlhauser, Matthias; Schmidt, Kai Phillip

doi:10.1016/j.rinp.2024.107794

Results in Physics

2024

DOI: 10.1016/j.rinp.2024.107794

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Order-by-disorder and long-range interactions in the antiferromagnetic transverse-field Ising model on the triangular lattice—A perturbative point of view

Jan Alexander Koziol,

Matthias Mühlhauser,

Kai Phillip Schmidt

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Cited by 3 publications

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Order-by-disorder in the antiferromagnetic J1−J2−J3 transverse-field Ising model on the ruby lattice

Duft,

Koziol,

Adelhardt

et al. 2024

Phys. Rev. Research

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We investigate the quantum phase diagram of the J1−J2−J3 antiferromagnetic transverse-field Ising model on the ruby lattice. In the low-field limit we derive an effective quantum dimer model, analyzing how the extensive ground-state degeneracy at zero field is lifted by an order-by-disorder scenario. We support our analysis by studying the gap closing of the high-field phase using series expansions. For J2>J3, we find a columnar phase at low fields, followed by a clock-ordered phase stabilized by resonating plaquettes at intermediate field values, and an emergent three-dimensional (3D)-XY quantum phase transition to the polarized high-field phase. For J3>J2, an order-by-disorder mechanism stabilizes a distinct k=(0,0) order and a quantum phase transition in the 3D-Ising universality class is observed. Further, we discuss the possible implementation of the columnar- and clock-ordered phase in existing Rydberg atom quantum simulators. When taking into account the full algebraically decaying long-range interactions on the ruby lattice, we find that long-range interactions favor the same ground state as the quantum fluctuations induced by a transverse field, which could make the ruby lattice a promising candidate for the realization of a clock-ordered phase. Published by the American Physical Society 2024

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Order-by-disorder in the antiferromagnetic J1−J2−J3 transverse-field Ising model on the ruby lattice

Duft,

Koziol,

Adelhardt

et al. 2024

Phys. Rev. Research

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Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices

Koziol,

Morigi,

Schmidt

2024

SciPost Phys.

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We analyse the ground-state quantum phase diagram of hardcore Bosons interacting with repulsive dipolar potentials. The bosons dynamics is described by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The ground state results from the interplay between the lattice geometry and the long-range interactions, which we account for by means of a classical spin mean-field approach limited by the size of the considered unit cells. This extended classical spin mean-field theory accounts for the long-range density-density interaction without truncation. We consider three different lattice geometries: square, honeycomb, and triangular. In the limit of zero hopping the ground state is always a devil’s staircase of solid (gapped) phases. Such crystalline phases with broken translational symmetry are robust with respect to finite hopping amplitudes. At intermediate hopping amplitudes, these gapped phases melt, giving rise to various lattice supersolid phases, which can have exotic features with multiple sublattice densities. At sufficiently large hoppings the ground state is a superfluid. The stability of phases predicted by our approach is gauged by comparison to the known quantum phase diagrams of the Bose-Hubbard model with nearest-neighbour interactions as well as quantum Monte Carlo simulations for the dipolar case on the square and triangular lattice. Our results are of immediate relevance for experimental realisations of self-organised crystalline ordering patterns in analogue quantum simulators, e.g., with ultracold dipolar atoms in an optical lattice.

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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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Order-by-disorder and long-range interactions in the antiferromagnetic transverse-field Ising model on the triangular lattice—A perturbative point of view

Cited by 3 publications

References 16 publications

Order-by-disorder in the antiferromagnetic J1−J2−J3 transverse-field Ising model on the ruby lattice

Order-by-disorder in the antiferromagnetic J1−J2−J3 transverse-field Ising model on the ruby lattice

Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices

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

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