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arXiv:2604.19161 · Physical review. B./Physical review. B

Spin-orbit-induced quantum chiral phases

Anonymous, Hyojae Jeon, Seongjun Park, Seungho Lee, Jung Hoon Han, Hyun‐Yong Lee

Published Jul 31, 2026• 0 citations
arXivHTMLPDF

Abstract

The scalar spin chirality (SSC), whose nonzero value $\langle {\bf S}_i \cdot ({\bf S}_j \times {\bf S}_k) \rangle \neq 0$ implies the breaking of time-reversal and certain point-group symmetries in the ground state, is a key quantity characterizing chiral magnetism in both classical and quantum settings. The classical SSC is manifested, for instance, in skyrmion crystal phase, while the quantum SSC is still highly sought after in various frustrated spin-1/2 models. An interesting possibility that has not been explored so far is the case in which SSC is symmetry-wise allowed, yet remains zero classically due to the collinear or coplanar arrangement of spins, but is generated by virtue of quantum fluctuation. We demonstrate the existence of precisely such a phase in a spin-1/2 triangular-lattice model with XXZ interaction, spin-orbit-induced exchange interactions, and an external magnetic field. Using iDMRG, we thoroughly map out the phase diagram of the model and identify several phases with coexisting magnetic order and SSC. The nonzero SSC arises despite the classical magnetic order being collinear or coplanar. We provide detailed magnon analysis to ascribe its origin to quantum fluctuations around classical magnetic order. The estimate of SSC from magnon analysis agrees with iDMRG results quantitatively. We map out the magnon spectrum and its Berry curvature, culminating in the prediction of finite thermal Hall conductivity in these phases with SSC.

DOI
10.1103/y9dt-b4zn

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The scalar spin chirality (SSC), whose nonzero value ⟨Si⋅(Sj×Sk)⟩≠0\langle {\bf S}_i \cdot ({\bf S}_j \times {\bf S}_k) \rangle \neq 0⟨Si​⋅(Sj​×Sk​)⟩=0 implies the breaking of time-reversal and certain point-group symmetries in the ground state, is a key quantity characterizing chiral magnetism in both classical and quantum settings. The classical SSC is manifested, for instance, in skyrmion crystal phase, while the quantum SSC is still highly sought after in various frustrated spin-1/2 models. An interesting possibility that has not been explored so far is the case in which SSC is symmetry-wise allowed, yet remains zero classically due to the collinear or coplanar arrangement of spins, but is generated by virtue of quantum fluctuation. We demonstrate the existence of precisely such a phase in a spin-1/2 triangular-lattice model with XXZ interaction, spin-orbit-induced exchange interactions, and an external magnetic field. Using iDMRG, we thoroughly map out the phase diagram of the model and identify several phases with coexisting magnetic order and SSC. The nonzero SSC arises despite the classical magnetic order being collinear or coplanar. We provide detailed magnon analysis to ascribe its origin to quantum fluctuations around classical magnetic order. The estimate of SSC from magnon analysis agrees with iDMRG results quantitatively. We map out the magnon spectrum and its Berry curvature, culminating in the prediction of finite thermal Hall conductivity in these phases with SSC.
The scalar spin chirality is a three-body physical observable that plays an outstanding role both in classical magnetism, characterizing non-coplanar spin textures, and in quantum magnetism, as an order parameter for chiral spin liquids. In quantum information, the scalar spin chirality is a witness of genuine tripartite entanglement. Here we propose an indirect measurement scheme, based on the Hadamard test, to estimate the scalar spin chirality for general quantum states. We apply our method to study chirality in two types of quantum states: generic one-magnon states of a ferromagnet, and the ground state of a model with competing symmetric and antisymmetric exchange. We show a single-shot determination of the scalar chirality is possible for chirality eigenstates, via quantum phase estimation with a single auxiliary qutrit. Our approach provides a unified theory of chirality in classical and quantum magnetism.
We study the spin-1/21/21/2 Heisenberg model on the triangular lattice with the nearest-neighbor J1>0{J}_{1}>0J1​>0, the next-nearest-neighobr J2>0{J}_{2}>0J2​>0 Heisenberg interactions, and the additional scalar chiral interaction ${J}_{\ensuremath{\chi}}({\stackrel{P\vec}{S}}_{i}\ifmmode\times\else\texttimes\fi{}{\stackrel{P\vec}{S}}_{j})\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{P\vec}{S}}_{k}$ for the three spins in all the triangles using large-scale density matrix renormalization group calculation on cylinder geometry. With increasing J2{J}_{2}J2​ (${J}_{2}/{J}_{1}\ensuremath{\le}0.3$) and ${J}_{\ensuremath{\chi}}$ (${J}_{\ensuremath{\chi}}/{J}_{1}\ensuremath{\le}1.0$) interactions, we establish a quantum phase diagram with the magnetically ordered ${120}^{\ensuremath{\circ}}$, stripe, and noncoplanar tetrahedral phase. In between these magnetic order phases, we find a chiral spin liquid (CSL) phase, which is identified as a $\ensuremath{\nu}=1/2$ bosonic fractional quantum Hall state with possible spontaneous rotational symmetry breaking. By switching on the chiral interaction, we find that the previously identified spin liquid in the ${J}_{1}\ensuremath{-}{J}_{2}$ triangular model ($0.08\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.15$) shows a phase transition to the CSL phase at very small ${J}_{\ensuremath{\chi}}$. We also compute the spin triplet gap in both spin liquid phases, and our finite-size results suggest a large gap in the odd topological sector but a small or vanishing gap in the even sector. We discuss the implications of our results on the nature of the spin liquid phases.
Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-12\frac{1}{2}21​ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in a spin-32\frac{3}{2}23​ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density-matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of the Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian chiral spin liquid emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Our numerical discovery of an exotic quantum spin liquid in a spin-32\frac{3}{2}23​ system suggests a route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.
The scalar spin chirality is a three-body physical observable that plays an outstanding role both in classical magnetism, characterizing non-co-planar spin textures, and in quantum magnetism, as an order parameter for chiral spin liquids. In quantum information, the scalar spin chirality is a witness of genuine tripartite entanglement. Here we propose an indirect measurement scheme, based on the Hadamard test, to estimate the scalar spin chirality for general quantum states. We apply our method to study chirality in two types of quantum states: generic one-magnon states of a ferromagnet, and the ground state of a model with competing symmetric and antisymmetric exchange. We show a single-shot determination of the scalar chirality is possible for chirality eigenstates, via quantum phase estimation with a single auxiliary qutrit. Our approach provides a unified theory of chirality in classical and quantum magnetism.
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Motivated by recent transport measurements in high-Tc{T}_{c}Tc​ cuprate superconductors in a magnetic field, we study the thermal Hall conductivity in materials with topological order, focusing on the contribution from neutral spinons. Specifically, different Schwinger boson mean-field Ans\"atze for the Heisenberg antiferromagnet on the square lattice are analyzed. We allow for both Dzyaloshinskii-Moriya interactions, and additional terms associated with scalar spin chiralities that break time-reversal and reflection symmetries, but preserve their product. It is shown that these scalar spin chiralities, which can either arise spontaneously or are induced by the orbital coupling of the magnetic field, can lead to spinon bands with nontrivial Chern numbers and significantly enhanced thermal Hall conductivity. Associated states with zero-temperature magnetic order, which is thermally fluctuating at any T>0T>0T>0, also show a similarly enhanced thermal Hall conductivity.