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arXiv:1810.12696 · Physics Letters A

Variational calculations for relativistic two dimensional strongly interacting fermions: Application to 2D liquid 3He

Hamdollah Salehi, M. T. Mohammadi Sabet, Sakineh Mizani

Published Dec 16, 2019• 0 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2019.126193

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Exotic strongly correlated quantum spin liquid (SCQSL) is formed in an insulator Herbertsmithite ZnCu3(OH)6Cl2 with such hypothetic particles as fermionic spinons carrying spin 1=2 and no charge. Here we calculate its thermodynamic and relaxation properties. Our calculations unveil the fundamental properties of SCQSL, forming strongly correlated Fermi system located at a fermion condensation quantum phase transition. These are in good agreement with experimental data and allow us to detect the behavior of SCQSL as that observed in heavy fermion metals and 2D 3He. We predict that the thermal resistivity of SCQSL under the application of magnetic fields at fixed temperature demonstrates a very specific behavior. The key features of our findings are the presence of spin-charge separation and QSL formed with itinerant heavy spinons in herbertsmithite.
Non-Fermi liquid behavior is found for the first time in a two-dimensional (2D) system with non-singular interactions using Haldane’s bosonization scheme. The bosonized system is solved exactly by a generalized Bogoliubov transformation. The fermion momentum distribution, calculated using a generalized Mattis-Lieb technique, exhibits a non-universal power law in the vicinity of the Fermi surface for intermediate interaction strengths. In recent years, there has been great interest in possible non-Fermi-liquid-like behavior in the ground state of two-dimensional (2D) strongly correlated fermionic systems [1]. It is well-known that in one dimension the ground state of a fermionic system with arbitrarily weak interactions is not a Fermi liquid but a state usually known as a Luttinger liquid [2]. For the 2D case, many studies have suggested that, in the limit of weak interactions, this behavior does not appear [3]. Studies of systems with a small number of particles also suggest Fermi liquid behavior in 2D [4]. Although Khveshchenko et al have found non-Fermi-liquid behavior in 2D, they worked only with a singular long-range current-current interaction [5]. The one-dimensional Luttinger liquid solution can be obtained by a bosonization
We show by a meta-analysis of the available Quantum Monte-Carlo (QMC) results that two-dimensional fermions with repulsive interactions exhibit universal behavior in the strongly-correlated regime, and that their freezing transition can be described using a quantum generalization of the classical Hansen-Verlet freezing criterion. We calculate the liquid-state energy and the freezing point of the 2D dipolar Fermi gas (2DDFG) using a variational method by taking ground state wave functions of 2D electron gas (2DEG) as trial states. A comparison with the recent fixed-node diffusion Monte-Carlo analysis of the 2DDFG shows that our simple variational technique captures more than 95% of the correlation energy, and predicts the freezing transition within the uncertainty bounds of QMC. Finally, we utilize the ground state wave functions of 2DDFG as trial states and provide a variational account of the effects of finite 2D confinement width. Our results indicate significant beyond mean-field effects. We calculate the frequency of collective monopole oscillations of the quasi-2D dipolar gas as an experimental demonstration of correlation effects.