dorsal/arxiv
View SchemaCorrelations, spectral gap, and entanglement in harmonic quantum systems on generic lattices
| Authors | M. Cramer, J. Eisert |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0509167 |
| URL | https://arxiv.org/abs/quant-ph/0509167 |
| DOI | 10.1088/1367-2630/8/5/071 |
| Journal | New J. Phys. 8, 71 (2006) |
Abstract
We investigate the relationship between the gap between the energy of the ground state and the first excited state and the decay of correlation functions in harmonic lattice systems. We prove that in gapped systems, the exponential decay of correlations follows for both the ground state and thermal states. Considering the converse direction, we show that an energy gap can follow from algebraic decay and always does for exponential decay. The underlying lattices are described as general graphs of not necessarily integer dimension, including translationally invariant instances of cubic lattices as special cases. Any local quadratic couplings in position and momentum coordinates are allowed for, leading to quasi-free (Gaussian) ground states. We make use of methods of deriving bounds to matrix functions of banded matrices corresponding to local interactions on general graphs. Finally, we give an explicit entanglement-area relationship in terms of the energy gap for arbitrary, not necessarily contiguous regions on lattices characterized by general graphs.
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"abstract": "We investigate the relationship between the gap between the energy of the\nground state and the first excited state and the decay of correlation functions\nin harmonic lattice systems. We prove that in gapped systems, the exponential\ndecay of correlations follows for both the ground state and thermal states.\nConsidering the converse direction, we show that an energy gap can follow from\nalgebraic decay and always does for exponential decay. The underlying lattices\nare described as general graphs of not necessarily integer dimension, including\ntranslationally invariant instances of cubic lattices as special cases. Any\nlocal quadratic couplings in position and momentum coordinates are allowed for,\nleading to quasi-free (Gaussian) ground states. We make use of methods of\nderiving bounds to matrix functions of banded matrices corresponding to local\ninteractions on general graphs. Finally, we give an explicit entanglement-area\nrelationship in terms of the energy gap for arbitrary, not necessarily\ncontiguous regions on lattices characterized by general graphs.",
"arxiv_id": "quant-ph/0509167",
"authors": [
"M. Cramer",
"J. Eisert"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"math-ph",
"math.MP"
],
"doi": "10.1088/1367-2630/8/5/071",
"journal_ref": "New J. Phys. 8, 71 (2006)",
"title": "Correlations, spectral gap, and entanglement in harmonic quantum systems on generic lattices",
"url": "https://arxiv.org/abs/quant-ph/0509167"
},
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