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The Loschmidt Index

by Diego Liska, Vladimir Gritsev

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Submission summary

Authors (as registered SciPost users): Diego Liska
Submission information
Preprint Link:  (pdf)
Date accepted: 2021-04-26
Date submitted: 2021-04-22 12:45
Submitted by: Liska, Diego
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


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.

Published as SciPost Phys. 10, 100 (2021)

List of changes

Added comment after Eq. (10)
Added reference [6]

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