Abstract
Quantum phase transitions are usually studied in terms of Hermitian Hamiltonians. However, cold-atom experiments are intrinsically non-Hermitian due to spontaneous decay. Here, we show that non-Hermitian systems exhibit quantum phase transitions that are beyond the paradigm of Hermitian physics. We consider the non-Hermitian XY model, which can be implemented using three-level atoms with spontaneous decay. We exactly solve the model in one dimension and show that there is a quantum phase transition from short-range order to quasi-long-range order despite the absence of a continuous symmetry in the Hamiltonian. The ordered phase has a frustrated spin pattern. The critical exponent $\nu$ can be 1 or 1/2. Our results can be seen experimentally with trapped ions, cavity QED, and atoms in optical lattices.
Highlights
A quantum phase transition occurs when the ground state of a many-body system experiences a sudden change as a parameter is tuned through a critical point [1]
The non-Hermitian model is heralded by the absence of a spontaneous decay event, which can be measured with a high degree of accuracy [7,8,9]
We show how non-Hermitian quantum mechanics leads to new magnetic behavior that can be observed in current cold-atom setups
Summary
A quantum phase transition occurs when the ground state of a many-body system experiences a sudden change as a parameter is tuned through a critical point [1]. The non-Hermitian model is heralded by the absence of a spontaneous decay event, which can be measured with a high degree of accuracy [7,8,9]. This is similar to heralded entanglement protocols in which a measurement signals the preparation of the desired state (a). There is competition between the non-Hermitian term (measured by γ) and the anisotropic interaction (measured by J0) that coherently excites pairs of atoms This competition leads to the critical behavior discussed below
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