Quantum criticality and excitations of a long-range anisotropic $XY$-chain in a transverse field
| Autor: | Kai Phillip Schmidt, Jan Alexander Koziol, Patrick Adelhardt, Andreas Schellenberger |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Quantum Physics Strongly Correlated Electrons (cond-mat.str-el) Monte Carlo method Isotropy FOS: Physical sciences 02 engineering and technology 021001 nanoscience & nanotechnology Classical XY model 01 natural sciences Condensed Matter - Strongly Correlated Electrons Quantum mechanics 0103 physical sciences Thermodynamic limit Antiferromagnetism Ising model Quantum Physics (quant-ph) 010306 general physics 0210 nano-technology Series expansion Critical exponent |
| Popis: | 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. Comment: 11 pages, 4 figures |
| Databáze: | OpenAIRE |
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