Quantum fidelity in the thermodynamic limit

Abstract

We study quantum fidelity, the overlap between two ground states of a many-body system, focusing on the thermodynamic regime. We show how drop of fidelity near a critical point encodes universal information about a quantum phase transition. Our general scaling results are illustrated in the quantum Ising chain for which a remarkably simple expression for fidelity is found.

4 pages, 4 figures, rearranged a bit to improve presentation

References in corpus (9)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Ground state fidelity from tensor network representations
• Detection of quantum critical points by a probe qubit
• Direct observation of quantum criticality in Ising spin chains
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field

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• Fidelity susceptibility and Loschmidt echo for generic paths in a three spin interacting transverse Ising model
• Ground-State Fidelity and Kosterlitz-Thouless Phase Transition for Spin 1/2 Heisenberg Chain with Next-to-the-Nearest-Neighbor Interaction
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