Quantum critical scaling of the geometric tensors

Details Quantum critical scaling of the geometric tensors Quantum critical scaling of the geometric tensors

2007-05-15

arxiv.org/abs/0705.2211v2

Phys. Rev. Lett. 99, 095701 (2007)

Physics

Quantum Physics

Typos corrected

Scientific paper

10.1103/PhysRevLett.99.095701

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 paper 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.

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