BERRY PHASE AND CRITICAL BEHAVIOR OF THE XY SPIN CHAIN WITH THREE-SITE INTERACTION

2012 ◽  
Vol 26 (22) ◽  
pp. 1250141 ◽  
Author(s):  
HANLI LIAN
Keyword(s):  
Spin Chain ◽  
Berry Phase ◽  
Finite Size ◽  
Transverse Magnetic ◽  
Anomalous Behavior ◽  
Quantum Criticality ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Surrounding Environment ◽  
Xy Spin Chain

By calculating the Berry Phase (BP) of a central spin, the quantum criticality of the surrounding environment described by an XY spin chain with the three-site interaction in a transverse magnetic field is explored. The BP presents anomalous behavior along the critical region. The finite-size scaling behaviors suggest that the BP of the central spin can well capture the critical properties of the XY spin chain with the three-site interaction.

scholarly journals Motions of the String Solutions in the XXZ Spin Chain Under a Varying Twist

1997 ◽  
Vol 12 (04) ◽  
pp. 801-838 ◽  
Author(s):  
N. Fumita ◽  
H. Itoyama ◽  
T. Oota
Keyword(s):  
Ground State ◽  
Spin Chain ◽  
Imaginary Axis ◽  
Berry Phase ◽  
Numerical Study ◽  
Twist Angle ◽  
Finite Size ◽  
Bound State ◽  
Branch Points ◽  
Finite Size Corrections

We determine the motions of the roots of the Bethe ansatz equation for the ground state in the XXZ spin chain under a varying twist angle. This is done by analytic as well as numerical study in a finite size system. In the attractive critical regime 0 < Δ < 1, we reveal intriguing motions of strings due to the finite size corrections to the length of the strings: in the case of two-strings, the roots collide into the branch points perpendicularly to the imaginary axis, while in the case of three-strings, they fluctuate around the center of the string. These are successfully generalized to the case of n-string. These results are used to determine the final configuration of the momenta as well as that of the phase shift functions. We obtain these as well as the period and the Berry phase in the regime Δ ≤ -1 also, establishing the continuity of the previous results at -1 < Δ < 0 to this regime. We argue that the Berry phase can be used as a measure of the statistics of the quasiparticle (or the bound state) involved in the process.

QUANTUM CORRELATIONS OF TWO QUBITS COUPLED IN A THERMAL EQUILIBRIUM ENVIRONMENT

2012 ◽  
Vol 26 (25) ◽  
pp. 1250165
Author(s):  
AIPING ZHANG ◽  
FULI LI
Keyword(s):  
Magnetic Field ◽  
Spin Chain ◽  
Thermal Effects ◽  
Thermal Equilibrium ◽  
Composite System ◽  
Quantum Correlations ◽  
Transverse Magnetic ◽  
Initial State ◽  
Thermal Equilibrium State ◽  
Xy Spin Chain

Quantum correlations (including entanglement and quantum discord) of two qubits symmetrically coupled to the surrounding XY spin chain in the presence of a transverse magnetic field are studied. We investigate the dynamic evolution of the quantum correlations of the two qubits when the surrounding spin chain is in the thermal equilibrium state. Numerical results show that the thermal effects can accelerate the decay process of the quantum correlations if the initial state of the composite system is not in the decoherence free space. When the temperature is high enough, the quantum phase transition driven by the external magnetic field completely disappear.

scholarly journals SYNCHRONIZATION OF NETWORKS WITH VARIABLE LOCAL PROPERTIES

2007 ◽  
Vol 17 (07) ◽  
pp. 2501-2507 ◽  
Author(s):  
JESÚS GÓMEZ-GARDEÑES ◽  
YAMIR MORENO
Keyword(s):  
Finite Size ◽  
Clustering Coefficient ◽  
Scaling Analysis ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Complete Synchronization ◽  
Scale Free ◽  
Kuramoto Oscillators ◽  
Local Properties ◽  
The Stability

We study the synchronization transition of Kuramoto oscillators in scale-free networks that are characterized by tunable local properties. Specifically, we perform a detailed finite size scaling analysis and inspect how the critical properties of the dynamics change when the clustering coefficient and the average shortest path length are varied. The results show that the onset of synchronization does depend on these properties, though the dependence is smooth. On the contrary, the appearance of complete synchronization is radically affected by the structure of the networks. Our study highlights the need of exploring the whole phase diagram and not only the stability of the fully synchronized state, where most studies have been done up to now.

scholarly journals Компьютерное моделирование фазовых переходов и критических свойств фрустрированной модели Гейзенберга на кубической решетке

2020 ◽  
Vol 62 (6) ◽  
pp. 868
Author(s):  
М.К. Рамазанов ◽  
А.К. Муртазаев
Keyword(s):  
Phase Transition ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Universality Class ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Cubic Lattice ◽  
Range Of Values ◽  
Antiferromagnetic Model ◽  
Second Order Phase Transition

The phase transitions and critical properties of the Heisenberg antiferromagnetic model on a cubic lattice with nearest and next-nearest-neighbor interactions are investigated by the replica Monte Carlo method. The range of values of the interaction of the next-nearest-neighbor is considered 0.0 ≤ r ≤ 1.0. The phase diagram relating the transition temperature and the magnitude of next-nearest neighbor interactions is constructed. It is shown that a second order phase transition occurs in the r range under study. The values of all the main static critical exponents are calculated by means of the finite-size scaling theory. It is shown that the universality class of the critical behavior of this model is preserved in the range of 0.0 ≤ r ≤ 0.4.

Nonequilibrium model on Archimedean lattices

Open Physics ◽  
2014 ◽  
Vol 12 (3) ◽  
Author(s):  
F. Lima
Keyword(s):  
Majority Vote ◽  
Finite Size ◽  
Stat Phys ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Critical Temperatures ◽  
Vote Model ◽  
Monte Carlo Studies ◽  
Regular Lattices ◽  
Binder Cumulant

AbstractOn (4, 6, 12) and (4, 82) Archimedean lattices, the critical properties of the majority-vote model are considered and studied using the Glauber transition rate proposed by Kwak et al. [Kwak et al., Phys. Rev. E, 75, 061110 (2007)] rather than the traditional majority-vote with noise [Oliveira, J. Stat. Phys. 66, 273 (1992)]. We obtain T c and the critical exponents for this Glauber rate from extensive Monte Carlo studies and finite size scaling. The calculated values of the critical temperatures and Binder cumulant are T c = 0.651(3) and U 4* = 0.612(5), and T c = 0.667(2) and U 4* = 0.613(5), for (4, 6, 12) and (4, 82) lattices respectively, while the exponent (ratios) β/ν, γ/ν and 1/ν are respectively: 0.105(8), 1.48(11) and 1.16(5) for (4, 6, 12); and 0.113(2), 1.60(4) and 0.84(6) for (4, 82) lattices. The usual Ising model and the majority-vote model on previously studied regular lattices or complex networks differ from our new results.

Ising Antiferromagnet with Nearest-Neighbor and Next-Nearest-Neighbor Interactions on a Square Lattice

2014 ◽  
Vol 215 ◽  
pp. 17-21
Author(s):  
Akai K. Murtazaev ◽  
Magomedsheikh K. Ramazanov ◽  
Magomedzagir K. Badiev
Keyword(s):  
Nearest Neighbor ◽  
Finite Size ◽  
Nearest Neighbors ◽  
Correlation Radius ◽  
Square Lattice ◽  
Two Dimensional ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Ising Antiferromagnet ◽  
Antiferromagnetic Ising Model

The critical properties of two-dimensional antiferromagnetic Ising model in square lattice are investigated using the replica Monte-Carlo method with account of interactions of second nearest neighbors. The diagram of critical temperature dependence on an interaction value of second nearest neighbors is plotted. Static critical exponents of the heat capacity α, susceptibility γ, magnetization β, and correlation radius ν are calculated for this model using the finite-size scaling theory.

Geometric phase signature of quantum criticality in the XY spin chain with multiple interaction

2010 ◽  
Vol 405 (23) ◽  
pp. 4821-4824 ◽  
Author(s):  
W.W. Cheng ◽  
C.J. Shan ◽  
Y.X. Huang ◽  
T.K. Liu ◽  
H. Li
Keyword(s):  
Spin Chain ◽  
Geometric Phase ◽  
Quantum Criticality ◽  
Xy Spin Chain ◽  
Multiple Interaction
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