Continuously varying critical exponents in long-range quantum spin ladders - Adelhardt, Patrick; Schmidt, Kai Phillip (SciPost Physics, 2023)
We investigate the quantum-critical behavior between the rung-singlet phase with hidden string order and the Néel phase with broken SU(2)-symmetry in quantum spin ladders with algebraically decaying unfrustrated long-range Heisenberg interactions. To this end, we determine high-order series expansions of energies and observables in the thermodynamic limit about the isolated rung-dimer limit. This is achieved by extending the method of perturbative continuous unitary transformations (pCUT) to long-range Heisenberg interactions and to the calculation of generic observables. The quantumcritical breakdown of the rung-singlet phase then allows us to determine the critical phase transition line and the entire set of critical exponents as a function of the decay exponent of the long-range interaction. We demonstrate long-range mean-field behavior as well as a non-trivial regime of continuously varying critical exponents implying the absence of deconfined criticality contrary to a recent suggestion in the literature.
CRIS-Team Scopus Importer:2023-10-20

Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin - Jahromi, Saeed S.; Hörmann, Max; Adelhardt, Patrick; Fey, Sebastian; Karamnejad, Hooman; Orús, Román; Schmidt, Kai Phillip (Communications Physics, 2024)
We use tensor-network methods and high-order linked-cluster expansions to explore the quantum phase diagram of the antiferromagnetic Kitaev honeycomb model in a magnetic field for general spin S values. Tensor network calculations for the pure Kitaev model confirm the absence of fluxes and spin-spin correlations beyond nearest neighbors, while revealing discrete orientational symmetry breaking for S ∈ 1, 3/2, 2, consistent with the semiclassical limit. An intermediate region between Kitaev phases and the high-field polarized phase is identified for all considered spin values, showing a sequence of potential phases characterized by distinct local magnetization patterns while the total magnetization increases smoothly as a function of the field. Linked-cluster expansions for the high-field zero-momentum gap and spectral weight indicate a quantum critical breakdown of the polarized phase, suggesting exotic physics at intermediate Kitaev couplings.
CRIS-Team Scopus Importer:2024-10-18

Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions - Adelhardt, Patrick; Koziol, Jan; Langheld, Anja; Schmidt, Kai Phillip (Entropy, 2024)
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.<br
Keywords: quantum spin systems; long-range interactions; Ising interactions; XY interactions; Heisenberg interactions; Monte Carlo; series expansion; perturbative continuous unitary transformation; stochastic series expansion; quantum phase transitions; critical exponents; quantum simulation

Order-by-disorder in the antiferromagnetic J1-J2-J3 transverse-field Ising model on the ruby lattice - Duft, Antonia; Koziol, Jan; Adelhardt, Patrick; Mühlhauser, Matthias; Schmidt, Kai Phillip (Physical Review Research, 2024)
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.
CRIS-Team Scopus Importer:2024-10-25

Quantum-critical and dynamical properties of the XXZ bilayer with long-range interactions - Adelhardt, Patrick; Duft, Antonia; Schmidt, Kai Phillip (Physical Review B, 2025)
We study the XXZ square lattice bilayer model with antiferromagnetic nonfrustrating long-range interactions that decay as a power law with the distance. Employing large-scale high-order series expansions with classical Monte Carlo integration (pCUT+MC) about the limit of isolated Heisenberg dimers in the rung-singlet phase, we investigate the one-triplon dispersion and the corresponding spectral weight along the parameter axes of the long-range decay exponent and the XXZ anisotropy. By tuning the latter, we observe two extended regions of 3D XY and Ising universality as well as 3D Heisenberg critical exponents at the isotropic point. Along the decay exponent axis, we demonstrate mean-field behavior for strong long-range couplings, the aforementioned three universality classes for sufficiently weak interactions, and continuously varying critical exponents in between. Using extrapolations, we are able to determine the one-triplon dispersion in a quantitative fashion up to the quantum-critical breakdown of the rung-singlet phase. This allows us to extract the dynamical critical exponent 𝑧 as a function of the decay exponent, displaying a universal behavior. The detected 𝑧<1 for small decay exponents is in agreement with the expected properties of the anomalous Goldstone modes in the ordered phases with broken continuous symmetr
Keywords: Antiferromagnetism; Critical exponents; Goldstone bosons; Hard-core bosons; Long-range interactions; Magnons; Phase diagrams; Quantum criticality; Quantum phase transitions; Triplon; XY model; Quantum many-body systems; Square lattice; Heisenberg model; Linear spin wave theory; Monte Carlo methods; Perturbative methods; Series expansions & exact enumeration

Quantum criticality and excitations of a long-range anisotropic XY chain in a transverse field - Adelhardt, Patrick; Koziol, Jan; Schellenberger, Andreas; Schmidt, Kai Phillip (Physical Review B, 2020)
The critical breakdown of a one-dimensional quantum magnet with long-range interactions is studied by investigating the high-field polarized phase of the anisotropic XY model in a transverse field for the ferromagnetic and antiferromagnetic cases. While for the limiting case of the isotropic long-range XY model we can extract the elementary one-quasiparticle dispersion analytically and calculate two-quasiparticle excitation energies quantitatively in a numerical fashion, for the long-range Ising limit as well as in the intermediate regime we use perturbative continuous unitary transformations on white graphs in combination with classical Monte Carlo simulations for the graph embedding to extract high-order series expansions in the thermodynamic limit. This enables us to determine the quantum-critical breakdown of the high-field polarized phase by analyzing the gap closing including associated critical exponents and multiplicative logarithmic corrections. In addition, for the ferromagnetic isotropic XY model we determined the critical exponents z and v analytically by a bosonic quantum-field theory.
CRIS-Team WoS Importer:2020-11-27

Quantum phase transitions to topological Haldane phases in spin-one chains studied by linked-cluster expansions - Adelhardt, Patrick; Gritsch, Julian; Hille, M.; Reiß, David; Schmidt, Kai Phillip (Physical Review B, 2017)
We use linked-cluster expansions to analyze the quantum phase transitions between symmetry-unbroken trivial and topological Haldane phases in two different spin-one chains. The first model is the spin-one Heisenberg chain in the presence of a single-ion anisotropy, while the second one is the dimerized spin-one Heisenberg chain. For both models, we determine the ground-state energy and the one-particle gap inside the nontopological phase as a high-order series using perturbative continuous unitary transformations. Extrapolations of the gap series are applied to locate the quantum critical point and to extract the associated critical exponent. We find that this approach works unsatisfactorily for the anisotropic chain, since the quality of the extrapolation appears insufficient due to the large correlation length exponent. In contrast, extrapolation schemes display very good convergence for the gap closing in the case of the dimerized spin-one Heisenberg chain.

Scaling at quantum phase transitions above the upper critical dimension - Langheld, Anja; Koziol, Jan; Adelhardt, Patrick; Kapfer, Sebastian; Schmidt, Kai Phillip (SciPost Physics, 2022)
The hyperscaling relation and standard finite-size scaling (FSS) are known to break down above the upper critical dimension due to dangerous irrelevant variables. We establish a coherent formalism for FSS at quantum phase transitions above the upper critical dimension following the recently introduced Q-FSS formalism for thermal phase transitions. Contrary to long-standing belief, the correlation sector is affected by dangerous irrelevant variables. The presented formalism recovers a generalized hyperscaling relation and FSS form. Using this new FSS formalism, we determine the full set of critical exponents for the long-range transverse-field Ising chain in all criticality regimes ranging from the nearest-neighbor to the long-range mean-field regime. For the same model, we also explicitly confirm the effect of dangerous irrelevant variables on the characteristic length scale.
CRIS-Team Scopus Importer:2022-12-02