dorsal/arxiv
View SchemaNature and Measure of Entanglement in Quantum Phase Transitions
| Authors | Rolando Somma, Gerardo Ortiz, Howard Barnum, Emanuel Knill, Lorenza Viola |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403035 |
| URL | https://arxiv.org/abs/quant-ph/0403035 |
| DOI | 10.1103/PhysRevA.70.042311 |
| Journal | Phys. Rev. A 70, 042311/1-21 (2004) |
Abstract
Characterizing and quantifying quantum correlations in states of many-particle systems is at the core of a full understanding of phase transitions in matter. In this work, we continue our investigation of the notion of generalized entanglement [Barnum et al. Phys. Rev. A 68, 032308 (2003)] by focusing on a simple Lie-algebraic measure of purity of a quantum state relative to an observable set. For the algebra of local observables on multi-qubit systems, the resulting local purity measure is equivalent to a recently introduced global entanglement measure [Meyer and Wallach, J. Math. Phys. 43, 4273 (2002)]. In the condensed-matter setting, the notion of Lie-algebraic purity is exploited to identify and characterize the quantum phase transitions present in two exactly solvable models: the Lipkin-Meshkov-Glick model, and the spin-1/2 anisotropic XY model in a transverse magnetic field. For the latter, we argue that a natural fermionic observable-set arising after the Jordan-Wigner transformation, better characterizes the transition than alternative measures based on qubits. This illustrates the usefulness of going beyond the standard subsystem-based framework while providing a global disorder parameter for this model. Our results show how generalized entanglement leads to useful tools for distinguishing between the ordered and disordered phases in the case of broken symmetry quantum phase transitions. Additional implications and possible extensions of concepts to other systems of interest in condensed matter physics are also discussed.
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"abstract": "Characterizing and quantifying quantum correlations in states of\nmany-particle systems is at the core of a full understanding of phase\ntransitions in matter. In this work, we continue our investigation of the\nnotion of generalized entanglement [Barnum et al. Phys. Rev. A 68, 032308\n(2003)] by focusing on a simple Lie-algebraic measure of purity of a quantum\nstate relative to an observable set. For the algebra of local observables on\nmulti-qubit systems, the resulting local purity measure is equivalent to a\nrecently introduced global entanglement measure [Meyer and Wallach, J. Math.\nPhys. 43, 4273 (2002)]. In the condensed-matter setting, the notion of\nLie-algebraic purity is exploited to identify and characterize the quantum\nphase transitions present in two exactly solvable models: the\nLipkin-Meshkov-Glick model, and the spin-1/2 anisotropic XY model in a\ntransverse magnetic field. For the latter, we argue that a natural fermionic\nobservable-set arising after the Jordan-Wigner transformation, better\ncharacterizes the transition than alternative measures based on qubits. This\nillustrates the usefulness of going beyond the standard subsystem-based\nframework while providing a global disorder parameter for this model. Our\nresults show how generalized entanglement leads to useful tools for\ndistinguishing between the ordered and disordered phases in the case of broken\nsymmetry quantum phase transitions. Additional implications and possible\nextensions of concepts to other systems of interest in condensed matter physics\nare also discussed.",
"arxiv_id": "quant-ph/0403035",
"authors": [
"Rolando Somma",
"Gerardo Ortiz",
"Howard Barnum",
"Emanuel Knill",
"Lorenza Viola"
],
"categories": [
"quant-ph",
"cond-mat.str-el"
],
"doi": "10.1103/PhysRevA.70.042311",
"journal_ref": "Phys. Rev. A 70, 042311/1-21 (2004)",
"title": "Nature and Measure of Entanglement in Quantum Phase Transitions",
"url": "https://arxiv.org/abs/quant-ph/0403035"
},
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