Non-Hermitian coupled cluster method for non-stationary systems and its interaction-picture reinterpretation

Abstract

The interaction picture in a non-Hermitian realization is discussed in detail and considered for its practical use in many-body quantum physics. The resulting non-Hermitian interaction-picture (NHIP) description of dynamics, in which both the wave functions and operators belonging to physical observables cease to remain constant in time, is a non-Hermitian generalization of the traditional Dirac picture of standard quantum mechanics, which itself is widely used in quantum field theory calculations. Particular attention is also paid here to the variational (or, better, bivariational) and dynamical (i.e., non-stationary) aspects that are characteristic of the coupled cluster method (CCM) techniques that nowadays form one of the most versatile and most accurate of all available formulations of quantum many-body theory. In so doing we expose and exploit multiple parallels between the NHIP and the CCM in its time-dependent versions. * raymond.bishop@manchester.ac.uk † znojil@ujf.cas.cz

Hybrid form of quantum theory with non-Hermitian Hamiltonians

“…The main idea of our present methodical innovation can be traced back to the Dyson's physicsrooted papers [1] in which the essence of the success (i.e., the sufficiently persuasive reason for the preference of the use of the non-Hermitian Hamiltonian model H (Dyson) ) lied in the access to some additional information about the properties (i.e., typically, correlations [7] or clusterings [20]) of the system in question. Naturally, such a supplementary knowledge facilitated the specification of the "good" forms of the mapping Ω.…”

Quantum phase transitions in nonhermitian harmonic oscillator

“…( 8 ). Redundant as this step may seem to be, the work in the latter space is often recommended in conventional textbooks, mainly for establishing easier contacts with experimentalists (cf., e.g., 21 , 33 ).…”

Paths of unitary access to exceptional points

“…What was particularly successful are the variational (or, more precisely, bi-variational) realizations of the CCM philosophy, with emphasis put upon the construction of ground states, and with a well-founded preference of mappings (9) in the exponential form Ω = exp S where S is represented in a suitable operator basis. The latter, apparently purely technical restriction seems to be responsible for the success of the method which is currently "one of the most versatile and most accurate of all available formulations of quantum many-body theory" [42]. In paper [42], extensive 3HS-CCM parallels have been found.…”

“…The latter, apparently purely technical restriction seems to be responsible for the success of the method which is currently "one of the most versatile and most accurate of all available formulations of quantum many-body theory" [42]. In paper [42], extensive 3HS-CCM parallels have been found. The respective strengths and weaknesses of the two approaches look mutually complementary.…”