scholarly journals A Modified Quantum Renormalization Group for XXZ Spin Chain

1998 ◽  
Vol 12 (23) ◽  
pp. 2359-2370
Author(s):  
A. Langari ◽  
V. Karimipour
Keyword(s):  
Renormalization Group ◽  
Ground State ◽  
State Energy ◽  
Spin Correlation ◽  
Quantum Spin ◽  
Spin Systems ◽  
Heisenberg Chain ◽  
Quantum Spin Systems ◽  
Xxz Model ◽  
Simple Modification

A simple modification of the standard Renormalization Group (RG) technique for the study of quantum spin systems is introduced. Our method which takes into account the effect of boundary conditions by employing the concept of superblock, may be regarded as a simple way for obtaining first estimates of many properties of spin systems. By applying this method to the XXZ spin-[Formula: see text] Heisenberg chain, we obtain the ground state energy with much higher accuracy than the standard RG. We have also obtained the staggered magnetization and the z-component of spin–spin correlation function which confirms the absence of long-range order in the massless region of the 1D XXZ model.

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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