arXiv subjects

P. Adelhardt

Publications and source records attributed to P. Adelhardt.

6 recordsLinked to original sources

arXiv2024

Monte Carlo based techniques for quantum magnets with long-range interactions

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 in 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 to extract high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo which enables calculations on large finite systems. Finite-size scaling can then be used to determine 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.

cond-mat.str-el↗

arXiv2023

Order-by-disorder in the antiferromagnetic $J_1$-$J_2$-$J_3$ transverse-field Ising model on the ruby lattice

We investigate the quantum phase diagram of the $J_1$-$J_2$-$J_3$ 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 $J_2>J_3$, 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 3d-XY quantum phase transition to the polarized high-field phase. For $J_3>J_2$, 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.

cond-mat.str-el↗

arXiv2022

Continuously varying critical exponents in long-range quantum spin ladders

We investigate the quantum-critical behavior between the rung-singlet phase with hidden string order and the N\'eel phase with broken $SU(2)$-symmetry on quantum spin ladders with algebraically decaying unfrustrated long-range Heisenberg interactions. Combining perturbative continuous unitary transformations (pCUT) with a white-graph expansion and Monte Carlo simulations yields high-order series expansions of energies and observables in the thermodynamic limit about the isolated rung-dimer limit. The breakdown of the rung-singlet phase allows to determine the critical line and the entire set of critical exponents as a function of the decay exponent of the long-range interaction. A non-trivial regime of continuously varying critical exponents as well as long-range mean-field behavior is demonstrated reminiscent of the long-range transverse-field Ising model.

cond-mat.str-el↗

arXiv2022

Scaling at quantum phase transitions above the upper critical dimension

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.

cond-mat.str-el↗

arXiv2020

Quantum criticality and excitations of a long-range anisotropic $XY$-chain in a transverse field

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 ferro- and antiferromagnetic case. While for the limiting case of the isotropic long-range XY model we can extract the elementary one quasi-particle dispersion analytically and calculate two quasi-particle 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 $\nu$ analytically by a bosonic quantum-field theory.

cond-mat.str-el↗

arXiv2017

Quantum phase transitions to topological Haldane phases in spin-one chains studied by linked-cluster expansions

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 non-topological 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 unsatisfactory 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.

cond-mat.str-el↗