scholarly journals Thermodynamic Density Matrix Renormalization Group Study of the Magnetic Susceptibility of Half-Integer Quantum Spin Chains

1996 ◽  
Vol 77 (22) ◽  
pp. 4640-4643 ◽  
Author(s):  
S. Moukouri ◽  
L. G. Caron
Keyword(s):  
Magnetic Susceptibility ◽  
Renormalization Group ◽  
Density Matrix ◽  
Quantum Spin ◽  
Spin Chains ◽  
Density Matrix Renormalization Group ◽  
Quantum Spin Chains ◽  
Half Integer ◽  
Density Matrix Renormalization ◽  
Integer Quantum

RENORMALIZATION-GROUP INVESTIGATION OF THE S = 1 RANDOM ANTIFERROMAGNETIC HEISENBERG CHAIN

2006 ◽  
Vol 17 (12) ◽  
pp. 1739-1753 ◽  
Author(s):  
PÉTER LAJKÓ
Keyword(s):  
Phase Diagram ◽  
Renormalization Group ◽  
Density Matrix ◽  
Energy Scale ◽  
Quantum Spin ◽  
Spin Chains ◽  
Density Matrix Renormalization Group ◽  
Heisenberg Chain ◽  
Quantum Spin Chains ◽  
Density Matrix Renormalization

We introduce variants of the Ma-Dasgupta renormalization-group (RG) approach for random quantum spin chains, in which the energy-scale is reduced by decimation built on either perturbative or non-perturbative principles. In one non-perturbative version of the method, we require the exact invariance of the lowest gaps, while in a second class of perturbative Ma-Dasgupta techniques, different decimation rules are utilized. For the S = 1 random antiferromagnetic Heisenberg chain, both type of methods provide the same type of disorder dependent phase diagram, which is in agreement with density-matrix renormalization-group calculations and previous studies.

scholarly journals Ground state entanglement in quantum spin chains

2004 ◽  
Vol 4 (1) ◽  
pp. 48-92 ◽  
Author(s):  
J.I. Latorre ◽  
E. Rico ◽  
G. Vidal
Keyword(s):  
Renormalization Group ◽  
Ground State ◽  
Quantum Phase Transitions ◽  
Conformal Symmetry ◽  
Mass Scale ◽  
Quantum Spin ◽  
Density Matrix Renormalization Group ◽  
Quantum Spin Chains ◽  
Conformal Field ◽  
Density Matrix Renormalization

A microscopic calculation of ground state entanglement for the XY and Heisenberg models shows the emergence of universal scaling behavior at quantum phase transitions. Entanglement is thus controlled by conformal symmetry. Away from the critical point, entanglement gets saturated by a mass scale. Results borrowed from conformal field theory imply irreversibility of entanglement loss along renormalization group trajectories. Entanglement does not saturate in higher dimensions which appears to limit the success of the density matrix renormalization group technique. A possible connection between majorization and renormalization group irreversibility emerges from our numerical analysis.

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