scholarly journals Emptiness formation probability for the anisotropic XY spin chain in a magnetic field

2003 ◽  
Vol 316 (5) ◽  
pp. 342-349 ◽  
Author(s):  
Alexander G. Abanov ◽  
Fabio Franchini
Keyword(s):  
Magnetic Field ◽  
Spin Chain ◽  
Formation Probability ◽  
Xy Spin Chain

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.

LOSCHMIDT ECHO OF A CENTRAL SPIN COUPLED TO AN XY SPIN CHAIN WITH DZYALOSHINSKY–MORIYA INTERACTION

2011 ◽  
Vol 25 (08) ◽  
pp. 589-597 ◽  
Author(s):  
HAN LI LIAN ◽  
DONG PING TIAN
Keyword(s):  
Magnetic Field ◽  
Spin Chain ◽  
Anisotropy Parameter ◽  
Dm Interaction ◽  
Local Oscillation ◽  
Knee Point ◽  
Xy Spin Chain ◽  
Loschmidt Echo ◽  
Evolution Behavior ◽  
Moriya Interaction

By introducing the Dzyaloshinsky–Moriya (DM) interaction, the Loschmidt Echo (LE) of a quantum system consisting of a central spin and its surrounding environment characterized by an XY spin chain was investigated. The analytical expression of the LE was obtained. The effects of magnetic field, DM interaction, spin chain size, and anisotropy parameter on the evolution behavior of the LE were discussed numerically. At the critical points of magnetic field, the LE presents an obvious decay following with local oscillation. The decaying and oscillation behavior of the LE can be tuned by the intensity of the DM interaction. With increasing the spin chain size, the decaying amplitude is increased and the following oscillation behavior vanishes for the spin chain with larger size. The effect of the anisotropy parameter on the LE presents different properties at both sides of the knee point. The effect of the DM interaction on the decay of the LE is also related to the value of anisotropy parameter.

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.

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