Abstract
We present a theory of a hybrid quantum liquid state, $\textit{quantum spin-dipole liquid}$ (QSDL), in a hydrogen-bonded electron system, by combining a quantum proton ice and Anderson's resonating valence bond spin liquid theory, motivated by the recent experimental discovery of a quantum spin liquid with proton fluctuations in $\kappa$-H$_3$(Cat-EDT-TTF)$_2$ (a.k.a. H-Cat). In our theory, an electron spin liquid and a proton dipole liquid are realized simultaneously in the ground state called $\textit{quantum valence bond ice}$. In this state, neither of them can be established independently of the other. Analytical and numerical calculations reveal that this state has a large entanglement entropy between spins and dipoles, which is far beyond the (crude) Born-Oppenheimer approximation. We also examine the stability of QSDL with respect to perturbations and discuss implications for experiments in H-Cat and its deuterated analog D-Cat.
Highlights
Hydrogen bonds occupy a unique position in condensed matter physics, where we can expect a huge quantum paraelectricity due to its lightness
In this paper, motivated by the experimental discovery of H-Cat, we present a theory of a hybrid quantum liquid state, the quantum spin-dipole liquid (QSDL), in hydrogen-bonded electron systems by combining the concepts of Anderson’s resonating valence bond (RVB) state of electron spins and a quantum ice of protons
We have developed a theory of a hybrid quantum liquid, QSDL, by combining the quantum proton ice and Anderson’s RVB state, motivated by the recent experimental discovery of the quantum spin liquid with proton fluctuations in H-Cat
Summary
Hydrogen bonds occupy a unique position in condensed matter physics, where we can expect a huge quantum paraelectricity due to its lightness. The basic mechanism of realizing a quantum liquid was later employed in the theories of qunatum spin ice and water ice, where the RVB state is exactly realized by tuning a system into the exactly solvable Rokhsar-Kivelson (RK) point [21,22,23,24,25,26] This observation would imply that both the electron spin liquid and the proton dipole liquid can be treated in a unified manner to describe a spin-dipole coupled quantum liquid. The resulting QSDL is named quantum valence bond ice, and the property of this state will be discussed in detail from analytical and numerical perspectives Though this unified theory does not explain everything observed in H-Cat, especially the absence of a spin gap [16], we can understand some basic differences between H-Cat and D-Cat based on a universal nature of a quantum liquid. A gauge mean-field theory is known to describe a fermionic excitation from an ice state [41], which would potentially describe the observed exotic excitations [16]
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