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arXiv:2202.03458 · Physical review. B./Physical review. B

Hole spectral function of a chiral spin liquid in the triangular lattice Hubbard model

Wilhelm Kadow, Laurens Vanderstraeten, Michael Knap

Published Sep 14, 2022• 31 citations
arXivHTMLPDF

Abstract

Quantum spin liquids are fascinating phases of matter, hosting fractionalized spin excitations and unconventional long-range quantum entanglement. These exotic properties, however, also render their experimental characterization challenging, and finding ways to diagnose quantum spin liquids is therefore a pertinent challenge. Here, we numerically compute the spectral function of a single hole doped into the half-filled Hubbard model on the triangular lattice using techniques based on matrix product states. At half-filling the system has been proposed to realize a chiral spin liquid at intermediate interaction strength, surrounded by a magnetically ordered phase at strong interactions and a superconducting/metallic phase at weak interactions. We find that the spectra of these phases exhibit distinct signatures. By developing appropriate parton mean-field descriptions, we gain insight into the relevant low-energy features. While the magnetic phase is characterized by a dressed hole moving through the ordered spin background, we find indications of spinon dynamics in the chiral spin liquid. Our results suggest that the hole spectral function, as measured by angle-resolved photoemission spectroscopy, provides a useful tool to characterize quantum spin liquids.

DOI
10.1103/physrevb.106.094417

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Abstract The dynamical response of a quantum spin liquid upon injecting a hole is a pertinent open question. In experiments, the hole spectral function, measured momentum-resolved in angle-resolved photoemission spectroscopy (ARPES) or locally in scanning tunneling microscopy (STM), can be used to identify spin liquid materials. In this study, we employ tensor network methods to simulate the time evolution of a single hole doped into the Kitaev spin-liquid ground state. Focusing on the gapped spin liquid phase, we reveal two fundamentally different scenarios. For ferromagnetic spin couplings, the spin liquid is highly susceptible to hole doping: a Nagaoka ferromagnet forms dynamically around the doped hole, even at weak coupling. By contrast, in the case of antiferromagnetic spin couplings, the hole spectrum demonstrates an intricate interplay between charge, spin, and flux degrees of freedom, best described by a parton mean-field ansatz of fractionalized holons and spinons. Moreover, we find a good agreement of our numerical results to the analytically solvable case of slow holes. Our results demonstrate that dynamical hole spectral functions provide rich information on the structure of fractionalized quantum spin liquids.
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.
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.
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.
Recent experiments in moiré materials have enabled the realization of a variety of exotic quantum phases. In this context, the Hofstadter-Hubbard model has been proposed as a possible setting for hosting chiral spin liquid. Concurrently, significant progress has been recently made in the computational methods for two-dimensional many-body fermion systems, which makes numerically studying this challenging model a real possibility in genuine 2D geometry. Motivated by these advances, we investigate the putative chiral spin liquid phase in the triangular-lattice Hofstadter-Hubbard model using variational Monte Carlo with neural quantum states (NQS) and projected entangled pair states (PEPS). We observe spin-charge separation directly in real space through numerical spin-pumping simulation and real-time spin and charge motion. In addition, in the context of anyonic superconductivity conjectured in this model, we find a positive two-electron binding energy on small systems, but it decreases below our numerical resolution as the system size increases. Our work demonstrates NQS and PEPS as powerful tools, capable of cross-checking each other, for diagnosing topological order and fractionalized excitations in strongly correlated electronic systems.