Construction of Pseudo-hermitian matrices describing systems with balanced loss-gain

• URL: http://arxiv.org/abs/2401.01126v1
• Date: Tue, 2 Jan 2024 09:45:12 GMT
• Title: Construction of Pseudo-hermitian matrices describing systems with balanced loss-gain
• Abstract summary: 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 is presented. We apply the results to construct a generic pseudo-hermitian lattice model of size N with balanced loss-gain.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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