Abstract
We employ two different Lipkin-like, exactly solvable models so as to display features of the competition between different fermion–fermion quantum interactions (at finite temperatures). One of our two interactions mimics the pairing interaction responsible for superconductivity. The other interaction is a monopole one that resembles the so-called quadrupole one, much used in nuclear physics as a residual interaction. The pairing versus monopole effects here observed afford for some interesting insights into the intricacies of the quantum many body problem, in particular with regards to so-called quantum phase transitions (strictly, level crossings).
Highlights
The Lipkin Model (LM) is a celebrated exactly solvable model for nuclear physics [1,2]
A relevant Casimir operator emerges in the model that commutes with all the quasi-spin operators (QSPO) [1,2]
In addition to serving as a test ground for assessing many body methodologies, the Lipkin model has considerable value as a conceptual tool for the exploration of questions of principle related to the many-body problem. This is the sense in which our present discussion proceeds, because our treatment of competing quantum phase transitions below could be viewed as the addressing of a possibly new quantum phenomenon
Summary
The Lipkin Model (LM) is a celebrated exactly solvable model for nuclear physics [1,2]. In addition to serving as a test ground for assessing many body methodologies, the Lipkin model has considerable value as a conceptual tool for the exploration of questions of principle related to the many-body problem. This is the sense in which our present discussion proceeds, because our treatment of competing quantum phase transitions below could be viewed as the addressing of a possibly new quantum phenomenon. A second important component of the nucleon–nucleon interaction is a quadrupole force [2] In this effort, we wish to exactly examine the competition between the pairing interaction and a monopole force. The exactly solvable juxtaposition of the CP and PM models that we advance in this paper offers rich structural quantum details that deserve our attention
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