scholarly journals Chiral order of spin-1/2 frustrated quantum spin chains

2001 ◽  
Vol 79 (11-12) ◽  
pp. 1587-1591 ◽  
Author(s):  
T Hikihara ◽  
M Kaburagi ◽  
H Kawamura
Keyword(s):  
Nearest Neighbor ◽  
Spin Correlation ◽  
Quantum Spin ◽  
Spontaneous Breaking ◽  
Group Method ◽  
Density Matrix Renormalization Group ◽  
Quantum Spin Chains ◽  
Chiral Phase ◽  
Density Matrix Renormalization ◽  
Xy Spin Chain

The ordering of the frustrated S = 1/2 XY spin chain with the competing nearest- and next-nearest-neighbor anti-ferromagnetic couplings, J1 and J2, is studied by using the density-matrix renormalization-group method. It is found that besides the well-known spin-fluid and dimer phases the chain exhibits a gapless "chiral" phase characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κl =SxlSyl+1 – Syl Sxl+1, whereas the spin correlation decays algebraically. The dimer phase is realized for 0.33 [Formula: see text] j = J2/J1 [Formula: see text] 1.26 while the chiral phase is realized for j [Formula: see text] 1.26. PACS No.: 75.25

scholarly journals Chiral-ordered phases in a frustrated S = 1 chain with uniaxial single-ion-type anisotropy

2001 ◽  
Vol 79 (11-12) ◽  
pp. 1593-1597 ◽  
Author(s):  
T Hikihara
Keyword(s):  
Infinite System ◽  
Nearest Neighbor ◽  
Spin Correlation ◽  
Group Method ◽  
Density Matrix Renormalization Group ◽  
Renormalization Group Method ◽  
Heisenberg Chain ◽  
Density Matrix Renormalization ◽  
Chiral Phases ◽  
Ordered Phases

The ground-state phase transitions of a frustrated S = 1 Heisenberg chain with the uniaxial single-ion-type anisotropy and the frustrating next-nearest-neighbor coupling are studied. For the system, it has been shown that there are gapless and gapped chiral phases in which the chirality κl = Slx Syl+1 – Sly Sxl+1 exhibits a finite long-range order (LRO) and the spin correlation decays either algebraically or exponentially. In this study, the transitions between the Haldane and chiral phases and between the large-D (LD) and chiral phases are investigated using the infinite-system density-matrix renormalization group method. It is found that there exist two types of gapped chiral phases, "chiral Haldane" and "chiral LD" phases, in which the string LRO coexists with the chiral LRO and the string correlation decays exponentially, respectively. PACS No.: 75.30

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.

Ground state of an Ising-type spin-1/2 chain with competing interactions

2001 ◽  
Vol 79 (11-12) ◽  
pp. 1581-1585 ◽  
Author(s):  
T Tonegawa ◽  
H Matsumoto ◽  
T Hikihara ◽  
M Kaburagi
Keyword(s):  
Phase Diagram ◽  
Ground State ◽  
Nearest Neighbor ◽  
Intermediate Phase ◽  
Group Method ◽  
Density Matrix Renormalization Group ◽  
Competing Interactions ◽  
Density Matrix Renormalization ◽  
Diagonalization Method ◽  
Exact Diagonalization Method

The ground state of an Ising-type spin-1/2 chain with ferromagnetic bond-alternating nearest-neighbor and anti-ferromagnetic uniform next-nearest-neighbor interactions is studied by using the exact-diagonalization method and the density-matrix renormalization-group method. The Hamiltonian describing the system is expressed as H = – Σi h2i–1,2i – J1 Σi h2i,2i+1 + J2 Σi hi,i+2 with hi,i' = γ(Six Si'x + Siy Si'y) + Siz Si'z, where J1 [Formula: see text] 0, J2 [Formula: see text] 0, and 1 > γ [Formula: see text] 0. Special attention is paid to the ground-state phase diagram on the J1 versus J2 plane for a given value of γ. The phase diagram is composed of the ferromagnetic, intermediate, and up-up-down-down phases, the intermediate phase being characterized by its magnetization, which takes finite but unsaturated values. The phase diagram obtained for γ = 0.5 shows that the region of the intermediate phase for a given value of J1 is widest when J1 = 1.0 and becomes narrower rather rapidly as J1 decreases or increases from 1.0. The J2-dependence of the ground-state magnetization for γ = 0.5 and J1 = 0.85 is also discussed. PACS Nos.: 75.10Jm, 75.40Mg

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