The Loschmidt Index
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...
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| Format: | Article |
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2021-05-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.10.5.100 |
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doaj-d1e08a6a353d4c0e8367686450b16f8b2021-05-04T07:11:03ZengSciPostSciPost Physics2542-46532021-05-0110510010.21468/SciPostPhys.10.5.100The Loschmidt IndexDiego Liska, Vladimir GritsevWe 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.https://scipost.org/SciPostPhys.10.5.100 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Diego Liska, Vladimir Gritsev |
| spellingShingle |
Diego Liska, Vladimir Gritsev The Loschmidt Index SciPost Physics |
| author_facet |
Diego Liska, Vladimir Gritsev |
| author_sort |
Diego Liska, Vladimir Gritsev |
| title |
The Loschmidt Index |
| title_short |
The Loschmidt Index |
| title_full |
The Loschmidt Index |
| title_fullStr |
The Loschmidt Index |
| title_full_unstemmed |
The Loschmidt Index |
| title_sort |
loschmidt index |
| publisher |
SciPost |
| series |
SciPost Physics |
| issn |
2542-4653 |
| publishDate |
2021-05-01 |
| description |
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. |
| url |
https://scipost.org/SciPostPhys.10.5.100 |
| work_keys_str_mv |
AT diegoliskavladimirgritsev theloschmidtindex AT diegoliskavladimirgritsev loschmidtindex |
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