The Loschmidt Index

Abstract

We study the nodes of the wavefunction overlap between ground states of a parameter-dependent Hamiltonian. These nodes are topological, and we can use them to analyze in a unifying way both equilibrium and dynamical quantum phase transitions in multi-band systems. We define the Loschmidt index as the number of nodes in this overlap and discuss the relationship between this index and the wrapping number of a closed auxiliary hypersurface. This relationship allows us to compute this index systematically, using an integral representation of the wrapping number. We comment on the relationship between the Loschmidt index and other well-established topological numbers. As an example, we classify the equilibrium and dynamical quantum phase transitions of the XY model by counting the nodes in the wavefunction overlaps.

11 pages, 4 figures

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Cited by in corpus (4)

• Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems
• Dynamical singularity of the rate function for quench dynamics in finite-size quantum systems
• Relation between equilibrium quantum phase transitions and dynamical quantum phase transitions in two-band systems
• Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions