Generalized Jordan-Wigner Transformations

Batista, Cristian D.; Ortíz, Gerardo

doi:10.1103/physrevlett.86.1082

Cited by 149 publications

(192 citation statements)

References 19 publications

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“…The introduction of "quasiparticles", or transformations such as the Jordan-Wigner transformation [72,73], may further alter the algebraic language we use to analyze the system; our motivation for such transformations may be mathematical (easier solvability in one algebraic language than in another) or physical (one algebra better exhibits the physical structure of the system's dynamics, or of our interactions with it). In either case, the coherent states formalism is often known to be useful, and tools and concepts from quantum information theory, such as generalized entanglement measures, generalized LOCC and asymptotics may help as well.…”

Section: B Relevance To Condensed Matter Physicsmentioning

confidence: 99%

Generalizations of entanglement based on coherent states and convex sets

et al. 2003

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Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can be learned about entanglement from the well-studied theory of coherent states? With these questions in mind, we characterize unentangled pure states as extremal states when considered as linear functionals on the local Lie algebra. As a result, a relativized notion of purity emerges, showing that there is a close relationship between purity, coherence and (non-)entanglement. To a large extent, these concepts can be defined and studied in the even more general setting of convex cones of states. Based on the idea that entanglement is relative, we suggest considering these notions in the context of partially ordered families of Lie algebras or convex cones, such as those that arise naturally for multipartite systems. The study of entanglement includes notions of local operations and, for information-theoretic purposes, entanglement measures and ways of scaling systems to enable asymptotic developments. We propose ways in which these may be generalized to the Lie-algebraic setting, and to a lesser extent to the convex-cones setting. One of our motivations for this program is to understand the role of entanglement-like concepts in condensed matter. We discuss how our work provides tools for analyzing the correlations involved in quantum phase transitions and other aspects of condensed-matter systems. * barnum@lanl.gov † knill@lanl.gov ‡ g ortiz@lanl.gov § lviola@lanl.gov 2 Contents

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Section: B Relevance To Condensed Matter Physicsmentioning

confidence: 99%

Generalizations of entanglement based on coherent states and convex sets

et al. 2003

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“…The spin S = 1 system can be mapped into a gas of semi-hard-core bosons 13,14,15 with no more than two bosons per site. The |S z = 1 >, |S z = 0 > and |S z = −1 > states are mapped into the states with two, one and zero bosons respectively.…”

Section: Introductionmentioning

confidence: 99%

Magnetostriction in the Bose-Einstein condensate quantum magnet NiCl2–4SC(NH2)2 (Invited)

Zapf

Correa²,

Batista

et al. 2007

Journal of Applied Physics

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The quantum magnet NiCl2-4SC(NH2)2 is a candidate for observing Bose-Einstein Condensation of spin degrees of freedom in applied magnetic fields. An XY antiferromagnetic ordered state occurs in a dome-shaped region of the temperature-field phase diagram between Hc1 = 2.1 T and Hc2 = 12.6 T and below 1.2 K. BEC corresponds to the field-induced quantum phase transition into the ordered state. We investigate magnetostriction in single crystals of this compound at dilution refrigerator temperatures in magnetic fields up to 18 T, and as a function of magnetic field angle. We show that significant changes in the lattice parameters are induced by magnetic fields, and argue that these result from antiferromagnetic couplings between the Ni spins along the tetragonal c-axis. The magnetic phase diagram as a function of temperature, field, and field angle can be extracted from these data. We discuss the implications of these results to Bose-Einstein Condensation in this system.

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“…Even if a distinguishable-subsystem structure may be associated to degrees of freedom different from the original particles (such as a set of modes [3]), inequivalent factorizations may occur on the same footing. Finally, the introduction of quasiparticles, or the purposeful transformation of the algebraic language used to analyze the system [4], may further complicate the choice of preferred subsystems.…”

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confidence: 99%

A Subsystem-Independent Generalization of Entanglement

et al. 2004

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We introduce a generalization of entanglement based on the idea that entanglement is relative to a distinguished subspace of observables rather than a distinguished subsystem decomposition. A pure quantum state is entangled relative to such a subspace if its expectations are a proper mixture of those of other states. Many information-theoretic aspects of entanglement can be extended to the general setting, suggesting new ways of measuring and classifying entanglement in multipartite systems. By going beyond the distinguishable-subsystem framework, generalized entanglement also provides novel tools for probing quantum correlations in interacting many-body systems.PACS numbers: 03.67.Mn, 03.65.Ud, Entanglement is a uniquely quantum phenomenon whereby a pure state of a composite quantum system may cease to be determined by the states of its constituent subsystems [1]. Entangled pure states are those that have mixed subsystem states. To determine an entangled state requires knowledge of the correlations between the subsystems. As no pure state of a classical system can be correlated, such correlations are intrinsically non-classical, as strikingly manifested by the violation of local realism and Bell's inequalities [2]. In the science of quantum information processing (QIP), entanglement is regarded as the defining resource for quantum communication and an essential feature needed for unlocking the power of quantum computation. However, in spite of intensive investigation, a complete understanding of entanglement is far from being reached.To unambiguously define entanglement requires a preferred partition of the overall system into subsystems. In conventional QIP scenarios, subsystems are associated with spatially separated "local" parties, which legitimates the distinguishability assumption implicit in standard entanglement theory. However, because quantum correlations are at the heart of many physical phenomena, it would be desirable for a notion of entanglement to be useful in contexts other than QIP. Strongly interacting quantum systems offer compelling examples of situations where the usual subsystem-based view is inadequate. Whenever indistinguishable particles are sufficiently close to each other, quantum statistics forces the accessible state space to be a proper subspace of the full tensor product space, and exchange correlations arise that are not a usable resource in the usual QIP sense. Thus, the natural identification of particles with preferred subsystems becomes problematic. Even if a distinguishable-subsystem structure may be associated to degrees of freedom different from the original particles (such as a set of modes [3]), inequivalent factorizations may occur on the same footing. Finally, the introduction of quasiparticles, or the purposeful transformation of the algebraic language used to analyze the system [4], may further complicate the choice of preferred subsystems.While efforts are under way to obtain entanglement-like notions for bosons and fermions [3,5] and to study entanglement in quant...

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Generalized Jordan-Wigner Transformations

Cited by 149 publications

References 19 publications

Generalizations of entanglement based on coherent states and convex sets

Generalizations of entanglement based on coherent states and convex sets

Magnetostriction in the Bose-Einstein condensate quantum magnet NiCl2–4SC(NH2)2 (Invited)

A Subsystem-Independent Generalization of Entanglement

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