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Landau's spontaneous symmetry breaking theory is a fundamental theory thatdescribes the collective behaviors in many-body systems. It was well known thatfor usual spontaneous symmetry breaking in Hermitian systems, theorder-disorder phase transition with gap closing and spontaneous symmetrybreaking occur at the same critical point. In this paper, we generalized theLandau's spontaneous symmetry breaking theory to the cases in non-Hermitian(NH) many-body systems with biorthogonal Z2 symmetry and tried to discovercertain universal features. We were surprised to find that the effect of the NHterms splits the spontaneous biorthogonal Z2 symmetry breaking from a(biorthogonal) order-disorder phase transition with gap closing. The suddenchange of similarity for two degenerate ground states indicates a new type ofquantum phase transition without gap closing accompanied by spontaneousbiorthogonal Z2 symmetry breaking. We will take the NH transverse Ising modelas an example to investigate the anomalous spontaneous symmetry breaking. Thenumerical results were consistent with the theoretical predictions.

Anomalous Spontaneous Symmetry Breaking in non-Hermitian Systems with Biorthogonal Z2-symmetry