Speaker
Description
The study of the simple spin models provides an insight into the nature
of phase transitions. Given the growth of the attention to the
non-Hermitian systems in the recent years, it is interesting to look
into phase transitions in non-Hermitian systems.
Here, I present a theoretical study of quantum phases and quantum phase
transitions occurring in non-Hermitian transverse-field Ising spin
model. A non-Hermitian part of the Hamiltonian is implemented via
imaginary staggered longitudinal magnetic field corresponding to a local
staggered gain and loss terms, γ, which guarantees PT-symmetry of the
system
Using a numerical diagonalization of the Hamiltonian for spin chains of
a finite size N accompanied by a scaling procedure for the coherence
length ξ, a complete quantum phase diagram γ-J (J is an adjacent spins
interaction strength) is established. We obtain two quantum phases for J
< 0, i.e., PT-symmetry broken (complex eigenvalues) antiferromagnetic
state and PT-symmetry preserved (real eigenvalue) paramagnetic state,
which are separated by the line of Exceptional points. For J > 0, the
PT-symmetry of the ground state is retained in a whole region of
parameter space of J and γ, and a system shows two intriguing quantum
phase transitions between ferromagnetic and paramagnetic states for a
fixed parameter γ > 1.
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