Entanglement in Quantum Field Theory
A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".
Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 791
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,
Recently, interest has grown considerably in formulating measures of quantum entanglement and applying them to extended quantum systems with many degrees of freedom, such as quantum spin chains. One of these measures is entanglement entropy. Suppose that the whole system is in a pure quantum state |Ψ>, with density matrix ρ = |Ψ><Ψ|, and an observer A measures only a subset, A, of a complete set of commuting observables, while another observer, B, measures the remainder. The reduced density matrix of A is ρA = TrB ρ. The entanglement entropy is the von Neumann entropy, SA = −TrA ρA log ρA, associated with this reduced density matrix. It is easy to see that SA = SB. For an unentangled product state, SA = 0. Conversely, SA should be a maximum for a maximally entangled state.
On the other hand, It is well known that close to a quantum critical point, where the correlation length, ξ, is much larger than the lattice spacing, a, the low-lying excitations and the long-distance behavior of the correlations in the ground state of a quantum spin chain are believed to be described by quantum field theory in 1+1 dimensions. If the dispersion relationship of low-lying excitations is linear for k wave numbers, such that ξ −1 ≪ |k| ≪ a −1, the field theory is relativistic. In general, for 1+1-dimensional theory at a critical point, one can derive analogous formulas for the entanglement entropy in cases when subsystem A consists of an arbitrary number of disjointed intervals of the real line and when the whole system itself has a finite length L.
Prof. Dr. Leonardo dos Santos Lima
Guest Editor
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Keywords
- spin transport
- electrical transport
- Heisenberg model
- quantum phase transition
- quantum entanglement
- quantum correlation
- price dynamics
- nonlinear stochastic differential equations
- econophysics
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