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Quantum Criticality of Two-Dimensional Quantum Magnets with Long-Range Interactions
Sebastian Fey1, Sebastian C Kapfer1, Kai Phillip Schmidt1
1Lehrstuhl für Theoretische Physik I, Staudtstraße 7, Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany.
Physical Review Letters
|April 24, 2019
Summary
We investigated quantum magnets with long-range interactions, finding that unfrustrated systems transition from mean-field to nearest-neighbor universality. Frustrated systems on a square lattice maintain nearest-neighbor universality, while triangular lattices may exhibit first-order transitions.
Area of Science:
- Condensed Matter Physics
- Quantum Magnetism
- Statistical Mechanics
Background:
- Quantum magnets exhibit critical phenomena governed by interactions.
- Long-range interactions can significantly alter magnetic phase transitions.
- Understanding universality classes is key to classifying critical behavior.
Purpose of the Study:
- To study the critical breakdown of two-dimensional quantum magnets.
- To investigate the effects of algebraically decaying long-range interactions.
- To analyze the transverse-field Ising model on square and triangular lattices.
Main Methods:
- Combining perturbative continuous unitary transformations with classical Monte Carlo simulations.
- Extracting high-order series for one-particle excitations.
- Analyzing the high-field quantum paramagnet phase.
Main Results:
- Unfrustrated systems transition from mean-field to nearest-neighbor universality with continuously varying critical exponents.
- Frustrated systems on the square lattice remain in the nearest-neighbor universality class, irrespective of interaction range.
- Quantum criticality on the triangular lattice appears to be terminated by a first-order phase transition line.
Conclusions:
- Long-range interactions can drive significant changes in universality classes for quantum magnets.
- Lattice frustration plays a crucial role in determining the impact of long-range interactions.
- The study provides insights into the complex phase diagrams of frustrated quantum magnetic systems.
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