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arXiv:2304.08635 · npj Quantum Materials

Electromagnetic signatures of a chiral quantum spin liquid

Saikat Banerjee, Wei Kang Zhu, Shi‐Zeng Lin

Published Oct 25, 2023• 16 citations
arXivHTMLPDF

Abstract

Abstract Quantum spin liquid (QSL) has become an exciting topic in interacting spin systems that do not order magnetically down to the lowest experimentally accessible temperature; however, conclusive experimental evidence remains lacking. Motivated by the recent surge of theoretical and experimental interest in a half-filled Hubbard model on the triangular lattice, where chiral QSL can be stabilized, we investigate the electromagnetic signature of the chiral QSL to aid experimental detection. We systematically studied the electrical charge and orbital electrical current associated with a spinon excitation in the chiral QSL based on parton mean-field theory and unbiased density-matrix renormalization group calculations. We then calculated both longitudinal and transverse optical conductivities below the Mott gap. We also conduct quantum field theory analysis to unravel the connection between spinon excitation and emergent and physical gauge fields. Our results show that the chiral QSL phase has a clear electromagnetic response even in a Mott insulator regime, which can facilitate the experimental detection of this long-sought-after phase.

DOI
10.1038/s41535-023-00595-2

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Abstract Quantum spin liquid (QSL) has become an exciting topic in interacting spin systems that do not order magnetically down to the lowest experimentally accessible temperature; however, conclusive experimental evidence remains lacking. Motivated by the recent surge of theoretical and experimental interest in a half-filled Hubbard model on the triangular lattice, where chiral QSL can be stabilized, we investigate the electromagnetic signature of the chiral QSL to aid experimental detection. We systematically studied the electrical charge and orbital electrical current associated with a spinon excitation in the chiral QSL based on parton mean-field theory and unbiased density-matrix renormalization group calculations. We then calculated both longitudinal and transverse optical conductivities below the Mott gap. We also conduct quantum field theory analysis to unravel the connection between spinon excitation and emergent and physical gauge fields. Our results show that the chiral QSL phase has a clear electromagnetic response even in a Mott insulator regime, which can facilitate the experimental detection of this long-sought-after phase.
Motivated by experimental studies that have found signatures of a quantum spin liquid phase in organic crystals whose structure is well described by the two-dimensional triangular lattice, we study the Hubbard model on this lattice at half filling using the infinite-system density matrix renormalization group (iDMRG) method. On infinite cylinders with finite circumference, we identify an intermediate phase between observed metallic behavior at low interaction strength and Mott insulating spin-ordered behavior at strong interactions. Chiral ordering from spontaneous breaking of time-reversal symmetry, a fractionally quantized spin Hall response, and characteristic level statistics in the entanglement spectrum in the intermediate phase provide strong evidence for the existence of a chiral spin liquid in the full two-dimensional limit of the model.
Quantum spin liquids (QSLs) host emergent, fractionalized fermionic excitations that are charge-neutral. Identifying clear experimental signatures of these excitations remains a central challenge in the field of strongly correlated systems, as they do not couple to conventional electromagnetic probes. Here, we propose lattice strain as a powerful and tunable probe: Mechanical deformation of the lattice generates large pseudomagnetic fields, inducing pseudo-Landau levels that serve as distinctive spectroscopic signatures of these excitations. Using the Kitaev model on the honeycomb lattice, we show that distinct QSL phases exhibit strikingly different strain responses. The semimetallic Kitaev spin liquid and the gapped chiral spin liquid display pronounced Landau quantization and a diamagnetic-like response to strain, whereas the Majorana metal phase shows a paramagnetic-like response without forming Landau levels. These contrasting behaviors provide a direct route to experimentally identifying and distinguishing QSL phases hosting fractionalized excitations. We further outline how local resonant ultrasound spectroscopy can detect the strain-induced resonances associated with these responses, offering a practical pathway towards identifying fractionalized excitations in candidate materials.
Unambiguous identification of the Kitaev quantum spin liquid (QSL) in materials remains a huge challenge despite many encouraging signs from various measurements. To facilitate the experimental detection of the Kiteav QSL, here we propose to use remnant charge response in Mott insulators hosting QSL to identify the key signatures of QSL. We predict an emergent orbital magnetization in a Kitaev system in an external magnetic field. The direction of the orbital magnetization can be flipped by rotating the external magnetic field in the honeycomb plane. The orbital magnetization is demonstrated explicitly through a detailed microscopic analysis of the multiorbital Hubbard-Kanamori Hamiltonian and also supported by a phenomenological picture. We first derive the localized electrical loop current operator in terms of the spin degrees of freedom. Thereafter, utilizing the Majorana representation, we estimate the loop currents in the ground state of the chiral Kitaev QSL state, and obtain the consequent current textures, which are responsible for the emergent orbital magnetization. Finally, we discuss the possible experimental techniques to visualize the orbital magnetization which can be considered as the signatures of the underlying excitations.
Whereas a quantum spin liquid (QSL) phase has been identified in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on a triangular lattice via numerical calculations, debate persists about whether or not such a QSL is gapped or gapless with contradictory conclusions from different techniques. Moreover, information about excitations and dynamics is crucial for the experimental detection of such a phase. In this paper, we use exact diagonalization to characterize signatures of a QSL phase on the triangular lattice through the dynamical spin structure factor $\mathcal{S}(q,\ensuremath{\omega})$ and Raman susceptibility $\ensuremath{\chi}(\ensuremath{\omega})$. We find that spectra for the QSL phase show distinct features compared to those of neighboring phases; and both the Raman spectra and spin structure factor show gapped behavior in the QSL phase. Interestingly, there is a prominent excitation mode in the Raman A2{A}_{2}A2​ channel, indicating a strong subleading tendency toward a chiral spin liquid phase.
Spinon-Induced Phonon Dynamics in Chiral and πππ-Flux Quantum Spin Liquids
Quantum spin liquids (QSLs) are magnetic phases that evade long-range order down to the lowest temperatures due to strong quantum fluctuations. Their lack of conventional order parameters, however, makes experimental identification challenging. In this work, we investigate how distinct QSL phases affect phonon dynamics through spinon-phonon coupling. By computing the phonon self-energy, we show that the phonon spectrum remains unrenormalized by spinon interactions, while sound attenuation and phonon thermal conductivity exhibit distinct signatures of the underlying QSL phase. These response functions therefore provide experimentally accessible fingerprints for distinguishing different QSL backgrounds. Remarkably, we find that a chiral QSL coupled to phonons does not generate a phonon thermal Hall effect despite explicitly breaking time-reversal symmetry. Our results establish phonon transport as a potential probe for identifying and characterizing quantum spin liquids.
Quantum spin liquids emerging near the metal-insulator transition have been a longstanding issue in physics. Here, the author identifies a chiral spin liquid in the half-filled triangular-lattice Hubbard model using state-of-the-art non-Abelian density matrix renormalization. By computing the spin chirality order parameter with unprecedented system sizes and high accuracy, the findings extrapolate toward the two-dimensional limit, impacting theoretical research and experimental realizations in ultracold-atom optical lattices and transition-metal dichalcogenide moir\'e materials.