86 research outputs found
Fidelity approach to the disordered quantum XY model
We study the random XY spin chain in a transverse field by analyzing the
susceptibility of the ground state fidelity, numerically evaluated through a
standard mapping of the model onto quasi-free fermions. It is found that the
fidelity susceptibility and its scaling properties provide useful information
about the phase diagram. In particular it is possible to determine the Ising
critical line and the Griffiths phase regions, in agreement with previous
analytical and numerical results.Comment: 4 pages, 3 figures; references adde
Exact infinite-time statistics of the Loschmidt echo for a quantum quench
The equilibration dynamics of a closed quantum system is encoded in the
long-time distribution function of generic observables. In this paper we
consider the Loschmidt echo generalized to finite temperature, and show that we
can obtain an exact expression for its long-time distribution for a closed
system described by a quantum XY chain following a sudden quench. In the
thermodynamic limit the logarithm of the Loschmidt echo becomes normally
distributed, whereas for small quenches in the opposite, quasi-critical regime,
the distribution function acquires a universal double-peaked form indicating
poor equilibration. These findings, obtained by a central limit theorem-type
result, extend to completely general models in the small-quench regime.Comment: 4 pages, 2 figure
Quantum Chernoff Bound metric for the XY model at finite temperature
We explore the finite temperature phase diagram of the anisotropic XY spin
chain using the Quantum Chernoff Bound metric on thermal states. The analysis
of the metric elements allows to easily identify, in terms of different scaling
with temperature, quasi-classical and quantum-critical regions. These results
extend recent ones obtained using the Bures metric and show that different
information-theoretic notions of distance can carry the same sophisticated
information about the phase diagram of an interacting many-body system
featuring quantum-critical points.Comment: 6 pages, 1 figure, 2 table
Operator Quantum Geometric Tensor and Quantum Phase Transitions
We extend the quantum geometric tensor from the state space to the operator
level,and investigate its properties like the additivity for factorizable
models and the splitting of two kinds contributions for the case of stationary
reference states. This operator-quantum-geometric tensor (OQGT) is shown to
reflect the sensitivity of unitary operations against perturbations of multi
parameters. General results for the cases of time evolutions with given
stationary reference states are obtained. By this approach, we get exact
results for the rotated XY models, and show relations between the OQGT and
quantum criticality.Comment: One more reference added. 6 pages,2 figs. Accepted by EP
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