dorsal/arxiv
View SchemaGeometric Phases and Critical Phenomena in a Chain of Interacting Spins
| Authors | M. E. Reuter, M. J. Hartmann, M. B. Plenio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612194 |
| URL | https://arxiv.org/abs/quant-ph/0612194 |
| DOI | 10.1098/rspa.2007.1822 |
| Journal | Proc. Roy. Soc. Lond. A 463, 1271 (2007) |
Abstract
The geometric phase can act as a signature for critical regions of interacting spin chains in the limit where the corresponding circuit in parameter space is shrunk to a point and the number of spins is extended to infinity; for finite circuit radii or finite spin chain lengths, the geometric phase is always trivial (a multiple of 2pi). In this work, by contrast, two related signatures of criticality are proposed which obey finite-size scaling and which circumvent the need for assuming any unphysical limits. They are based on the notion of the Bargmann invariant whose phase may be regarded as a discretized version of Berry's phase. As circuits are considered which are composed of a discrete, finite set of vertices in parameter space, they are able to pass directly through a critical point, rather than having to circumnavigate it. The proposed mechanism is shown to provide a diagnostic tool for criticality in the case of a given non-solvable one-dimensional spin chain with nearest-neighbour interactions in the presence of an external magnetic field.
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"abstract": "The geometric phase can act as a signature for critical regions of\ninteracting spin chains in the limit where the corresponding circuit in\nparameter space is shrunk to a point and the number of spins is extended to\ninfinity; for finite circuit radii or finite spin chain lengths, the geometric\nphase is always trivial (a multiple of 2pi). In this work, by contrast, two\nrelated signatures of criticality are proposed which obey finite-size scaling\nand which circumvent the need for assuming any unphysical limits. They are\nbased on the notion of the Bargmann invariant whose phase may be regarded as a\ndiscretized version of Berry\u0027s phase. As circuits are considered which are\ncomposed of a discrete, finite set of vertices in parameter space, they are\nable to pass directly through a critical point, rather than having to\ncircumnavigate it. The proposed mechanism is shown to provide a diagnostic tool\nfor criticality in the case of a given non-solvable one-dimensional spin chain\nwith nearest-neighbour interactions in the presence of an external magnetic\nfield.",
"arxiv_id": "quant-ph/0612194",
"authors": [
"M. E. Reuter",
"M. J. Hartmann",
"M. B. Plenio"
],
"categories": [
"quant-ph"
],
"doi": "10.1098/rspa.2007.1822",
"journal_ref": "Proc. Roy. Soc. Lond. A 463, 1271 (2007)",
"title": "Geometric Phases and Critical Phenomena in a Chain of Interacting Spins",
"url": "https://arxiv.org/abs/quant-ph/0612194"
},
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