129 research outputs found
Crossovers and critical scaling in the one-dimensional transverse-field Ising model
We consider the scaling behavior of thermodynamic quantities in the
one-dimensional transverse-field Ising model near its quantum critical point
(QCP). Our study has been motivated by the question about the thermodynamical
signatures of this paradigmatic quantum critical system and, more generally, by
the issue of how quantum criticality accumulates entropy. We find that the
crossovers in the phase diagram of temperature and (the non-thermal control
parameter) transverse field obey a general scaling ansatz, and so does the
critical scaling behavior of the specific heat and magnetic expansion
coefficient. Furthermore, the Gr\"{u}neisen ratio diverges in a power-law way
when the QCP is accessed as a function of the transverse field at zero
temperature, which follows the prediction of quantum critical scaling. However,
at the critical field, upon decreasing the temperature, the Gr\"uneisen ratio
approaches a constant instead of showing the expected divergence. We are able
to understand this unusual result in terms of a peculiar form of the quantum
critical scaling function for the free energy; the contribution to the
Gr\"uneisen ratio vanishes at the linear order in a suitable Taylor expansion
of the scaling function. In spite of this special form of the scaling function,
we show that the entropy is still maximized near the QCP, as expected from the
general scaling argument. Our results establish the telltale thermodynamic
signature of a transverse-field Ising chain, and will thus facilitate the
experimental identification of this model quantum-critical system in real
materials.Comment: 7 pages, 5 figure
Comment on "Quantitative Condition is Necessary in Guaranteeing the Validity of the Adiabatic Approximation" [arXiv:1004.3100]
Recently, the authors of Ref.1[arXiv:1004.3100] claimed that they have proven
the traditional adiabatic condition is a necessary condition. Here, it is
claimed that there are some mistakes and an artificial over-strong constraint
in [1], making its result inconvincible.Comment: 1 pag
Nonadiabatic Nonlinear Optics and Quantum Geometry -- Application to the Twisted Schwinger Effect
We study the tunneling mechanism of nonlinear optical processes in solids
induced by strong coherent laser fields. The theory is based on an extension of
the Landau-Zener model with nonadiabatic geometric effects. In addition to the
rectification effect known previously, we find two effects, namely perfect
tunneling and counterdiabaticity at fast sweep speed. We apply this theory to
the twisted Schwinger effect, i.e., nonadiabatic pair production of particles
by rotating electric fields, and find a nonperturbative generation mechanism of
the opto-valley polarization and photo-current in Dirac and Weyl fermions.Comment: 24 pages, Accepted by SciPos
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