scholarly journals Separability and ground-state factorization in quantum spin systems

2009 ◽  
Vol 79 (22) ◽  
Author(s):  
Salvatore M. Giampaolo ◽  
Gerardo Adesso ◽  
Fabrizio Illuminati
Keyword(s):  
Ground State ◽  
Quantum Spin ◽  
Spin Systems ◽  
Quantum Spin Systems

scholarly journals QUANTUM DISCORD IN THE GROUND STATE OF SPIN CHAINS

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345030 ◽  
Author(s):  
MARCELO S. SARANDY ◽  
THIAGO R. DE OLIVEIRA ◽  
LUIGI AMICO
Keyword(s):  
Ground State ◽  
Quantum Discord ◽  
Quantum Phase Transitions ◽  
Spatial Dimension ◽  
Quantum Systems ◽  
Quantum Spin ◽  
Spin Systems ◽  
Quantum Spin Systems ◽  
Quantum Spin Chain ◽  
Quantum Critical Points

The ground state of a quantum spin chain is a natural playground for investigating correlations. Nevertheless, not all correlations are genuinely of quantum nature. Here we review the recent progress to quantify the "quantumness" of the correlations throughout the phase diagram of quantum spin systems. Focusing to one spatial dimension, we discuss the behavior of quantum discord (QD) close to quantum phase transitions (QPT). In contrast to the two-spin entanglement, pairwise discord is effectively long-ranged in critical regimes. Besides the features of QPT, QD is especially feasible to explore the factorization phenomenon, giving rise to nontrivial ground classical states in quantum systems. The effects of spontaneous symmetry breaking are also discussed as well as the identification of quantum critical points through correlation witnesses.

scholarly journals LOCALIZED ENDOMORPHISMS IN KITAEV'S TORIC CODE ON THE PLANE

2011 ◽  
Vol 23 (04) ◽  
pp. 347-373 ◽  
Author(s):  
PIETER NAAIJKENS
Keyword(s):  
Representation Theory ◽  
Group Algebra ◽  
Ground State ◽  
Algebraic Approach ◽  
Quantum Spin ◽  
Spin Systems ◽  
Quantum Spin Systems ◽  
Quantum Double ◽  
Code Model ◽  
Toric Code

We consider various aspects of Kitaev's toric code model on a plane in the C*-algebraic approach to quantum spin systems on a lattice. In particular, we show that elementary excitations of the ground state can be described by localized endomorphisms of the observable algebra. The structure of these endomorphisms is analyzed in the spirit of the Doplicher–Haag–Roberts program (specifically, through its generalization to infinite regions as considered by Buchholz and Fredenhagen). Most notably, the statistics of excitations can be calculated in this way. The excitations can equivalently be described by the representation theory of [Formula: see text], i.e. Drinfel'd's quantum double of the group algebra of ℤ2.

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