标题： 构造描述具有平衡增益损耗的系统的伪厄米特矩阵 显示英文标题

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

摘要： 我们提出了一种在任意大的有限维向量空间中构造伪厄米矩阵的一般方法。 确保伪厄米算符整个谱实数的正定度规，以及用于定义关联向量空间中修正内积的度规也被给出。 对于N维向量空间的构造基于SU(N)基元表示的生成元和恒等算符。 我们将结果应用于构建一个具有平衡增益损耗的N大小的通用伪厄米晶格模型。 该系统可以适用于周期性或开放边界条件，并且通过构造，保证了整个谱完全实数以及幺正时间演化。 最近邻(NN)和次近邻(NNN)相互作用具有平衡增益损耗的紧束缚模型和Su-Schrieffer-Heeger(SSH)模型作为极限情况出现。 显示英文摘要

摘要： 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.