2007/05/16 by Lorenzo Campos Venuti, Paolo Zanardi · 7 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Quantum many-body systems #Tensor decomposition and applications #quant-ph
paper · pdf · doi:10.1103/physrevlett.99.095701
published as Phys. Rev. Lett. 99, 095701 (2007) · Typos corrected
arxiv created 2007/05/16 · openalex publication_date 2007/08/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this Letter we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.