SKM 2023 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 49: Critical Phenomena and Phase Transitions

DY 49.3: Talk

Thursday, March 30, 2023, 15:30–15:45, ZEU 160

Non-Hermitian PT-symmetric Ising spin chains: novel quantum phases and quantum phase transitions — •Grigory Starkov, Mikhail Fistul, and Ilya Eremin — Ruhr-Universität Bochum, Bochum, Germany

A theoretical study of quantum phases and quantum phase transitions occurring in non-Hermitian PT-symmetric 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.

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 antiferromagnetic state and PT-symmetry preserved paramagnetic state, and the quantum phase transition line is the line of exception 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.

The qualitative quantum phase diagram is derived in the frame- work of the Bethe-Peierls approximation that is in a good accord with numerically obtained results. The quantum phase diagram can be verified in the microwave transmission experiments allowing to identify the transitions between the first excited and the ground states.