Entanglement in Quantum Spin Systems
A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".
Deadline for manuscript submissions: 30 November 2024 | Viewed by 898
Special Issue Editor
Interests: quantum correlation; magnon bands; topological phase transition; spin and thermal Hall effect; frustrated magnetism
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
In recent years, there has been an large interest in understanding entanglement properties in quantum spin systems, such as the XXZ model of integer and half-integer spin, the Hubbard model, Bose–Hubbard, and so on, as well as in non-equilibrium quantum spin systems. In general, for spin systems, like the quantum one-dimensional XXZ model, their properties may depend on spin value, the geometry of the lattice and different types of interactions within the system: Dzyaloshinskii–Moriya interaction, single-ion anisotropy, spin–phonon coupling, and so on. For instance, it is well known that in the quantum one-dimensional Heisenberg model (XXZ model in the isotropic point), there is a gap in the spectrum (Haldane’s gap). The same model, of half-integer spin, is gapless due to the Lieb, Schultz and Mattis theorem. Moreover, elementary excitations are different in each case (integer and half-integer spin). While in the former (integer spin), the excitations are magnons, in the second (half-integer spin), the excitations are spinons. In addition, many models may present different types of quantum and topological phase transitions, induced by the different types of couplings present in the system.
Recently, there has been an interest in understanding the interplay between quantum entanglement and quantum phase transition in quantum spin systems both in equilibrium and in non-equilibrium. The analysis of the bipartite entanglement between two partitions of the system is not well understood yet. In general, close to the critical point, there are large effects of quantum fluctuations on quantum entanglement, where, in general, the correlation length, ξ, is much larger than the lattice spacing, a, and the low-lying excitations and the long-distance behavior of the correlations in the ground state are believed to be described by a quantum field theory in 1+1 dimensions. For a 1+1-dimensional theory at the critical point, one can derive analogous expressions for reduced density matrix entropy and other measures of entanglement such as entanglement negativity, quantum discord, and so on.
Prof. Dr. Leonardo dos Santos Lima
Guest Editor
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Keywords
- thermal and spin Hall transport
- spin Hall effect
- spintronics
- longitudinal spin transport
- quantum spin one-half and integer spin Heisenberg model
- topological phase transition
- quantum entanglement
- magnon bands
- stochastic differential equations and Fokker–Planck equations
