Quantum Statistical Complexity Measure as a Signaling of Correlation Transitions
André T. Cesário,
Diego L. B. Ferreira,
Tiago Debarba,
Fernando Iemini,
Thiago O. Maciel,
Reinaldo O. Vianna
Affiliations
André T. Cesário
Departamento de Física, ICEx, Universidade Federal de Minas Gerais (UFMG), Av. Pres. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil
Diego L. B. Ferreira
Departamento de Física, ICEx, Universidade Federal de Minas Gerais (UFMG), Av. Pres. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil
Tiago Debarba
Departamento Acadêmico de Ciências da Natureza, Universidade Tecnológica Federal do Paraná (UTFPR), Campus Cornélio Procópio, Avenida Alberto Carazzai 1640, Cornélio Procópio 86300-000, Brazil
Fernando Iemini
Instituto de Física, Universidade Federal Fluminense (UFF), Niterói 24210-346, Brazil
Thiago O. Maciel
Instituto de Física, Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro 21941-972, Brazil
Reinaldo O. Vianna
Departamento de Física, ICEx, Universidade Federal de Minas Gerais (UFMG), Av. Pres. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signaling function of quantum order–disorder transitions. We discuss the possibility for such transitions to characterize interesting physical phenomena, as quantum phase transitions, or abrupt variations in correlation distributions. We apply our measure on two exactly solvable Hamiltonian models: the 1D-Quantum Ising Model (in the single-particle reduced state), and on Heisenberg XXZ spin-1/2 chain (in the two-particle reduced state). We analyze its behavior across quantum phase transitions for finite system sizes, as well as in the thermodynamic limit by using Bethe Ansatz technique.
