Quantum critical scaling of the geometric tensors

Abstract

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.

Typos corrected

References in corpus (3)

• Quantum Phase Transitions and Bipartite Entanglement
• Geometric phases and criticality in spin chain systems
• Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions

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• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Fidelity analysis of topological quantum phase transitions
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Operator fidelity susceptibility, decoherence and quantum criticality
• Fidelity approach to Gaussian transitions
• Ground-state fidelity of Luttinger liquids: A wave functional approach