2024/01/02 by Ghosh, Pijush K.
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Other Condensed Matter (cond-mat.other) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2401.01126
We present a general construction of pseudo-hermitian matrices in an arbitrary large, but finite dimensional vector space. The positive-definite metric which ensures reality of the entire spectra of a pseudo-hermitian operator, and is used for defining a modified inner-product in the associated vector space is also presented. The construction for an N dimensional vector space is based on the generators of SU (N ) in the fundamental representation and the identity operator. We apply the results to construct a generic pseudo-hermitian lattice model of size N with balanced loss-gain. The system is amenable to periodic as well as open boundary conditions and by construction, admits entirely real spectra along with unitary time-evolution. The tight binding and Su-Schrieffer-Heeger(SSH) models with nearest neighbour(NN) and next-nearest neighbour(NNN) interaction with balanced loss-gain appear as limiting cases.