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Physical review. B./Physical review. B

Translation-enriched Z 2 spin liquids and topological vison bands: Possible application to α − RuCl 3

Xue-Yang Song, T. Senthil

Published Jul 14, 2025• 0 citations
Publisher

Abstract

Inspired by experiments on the magnetic field induced phases of the spin-orbit coupled two dimension (2⁢D) Mott insulator 𝛼−RuCl3, we study some general aspects of gapped 𝑍2 quantum spin liquids (QSL) enriched by lattice translation symmetry. We show that there are 12 distinct such phases with different implementations of translation symmetry. In some of these phases the vison excitations of this QSL may form topological Chern bands. We explore a phenomenological description of a putative 𝑍2 QSL as a candidate ground state at intermediate magnetic fields in 𝛼−RuCl3. This state has broad continuum spectra in neutron scattering, a “bosonic” thermal Hall signal that goes to zero at zero temperature, and is naturally proximate to a zigzag magnetic ordered state, all of which are also seen in 𝛼−RuCl3. On general grounds, continuum scattering will also be seen at multiple points in the Brillouin zone in this state.

DOI
10.1103/zbbd-dqzb

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Inspired by experiments on the magnetic field induced phases of the spin-orbit coupled two dimension (2⁢D) Mott insulator 𝛼−RuCl3, we study some general aspects of gapped 𝑍2 quantum spin liquids (QSL) enriched by lattice translation symmetry. We show that there are 12 distinct such phases with different implementations of translation symmetry. In some of these phases the vison excitations of this QSL may form topological Chern bands. We explore a phenomenological description of a putative 𝑍2 QSL as a candidate ground state at intermediate magnetic fields in 𝛼−RuCl3. This state has broad continuum spectra in neutron scattering, a “bosonic” thermal Hall signal that goes to zero at zero temperature, and is naturally proximate to a zigzag magnetic ordered state, all of which are also seen in 𝛼−RuCl3. On general grounds, continuum scattering will also be seen at multiple points in the Brillouin zone in this state.
Translation-enriched Z2Z_2Z2​ spin liquids and topological vison bands: Possible application to ααα-RuCl3_33​
Inspired by experiments on the magnetic field induced phases of the spin-orbit coupled 2d2d2d Mott insulator ααα-RuCl3_33​, we study some general aspects of gapped Z2Z_2Z2​ Quantum Spin Liquids (QSL) enriched by lattice translation symmetry. We show that there are 121212 distinct such phases with different implementations of translation symmetry. In some of these phases the vison excitations of this QSL may form topological Chern bands. We explore a phenomenological description of a putative Z2Z_2Z2​ QSL as a candidate ground state at intermediate magnetic fields in ααα-RuCl3_33​. This state has broad continuum spectra in neutron scattering, a "bosonic" thermal Hall signal that goes to zero at zero temperature, and a natural connection with a zigzag magnetic ordered state, all of which are also seen in ααα-RuCl3_33​. On general grounds continuum scattering will also be seen at multiple points in the Brillouin zone in this state.
Abstract We present comprehensive inelastic neutron spectroscopic maps of the magnetic field-induced disordered phase of the Kitaev quantum spin liquid candidate material α-RuCl 3 . For fields along both in-plane high symmetry directions we observe that the spin excitation spectrum at and above a magnetic field of 8 T is gapped. Excitation modes then sharpen for increasing field but are consistently broader than experimental resolution even at 13.5 T. The out-of-plane dispersion diminishes in the 7-10 T regime, signifying enhanced two-dimensional behavior as the in-plane liquid correlations are established. In this regime, excitations are very broad and largely flat for all accessible energy-momenta, which is kinematically at odds with a magnon-decay picture. By contrast, a continuum of fractionalized excitations naturally yields a broad continuum response, which crucially may be accompanied by sharper modes of bound states of fractionalized excitations. Their damping by the continuum accounts for the observed spectral broadening and field dependence. Our results provide strong evidence for the existence of fractionalized excitations in α-RuCl 3 in a magnetic field.
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Abstract Pursuing the exotic quantum spin liquid (QSL) state in the Kitaev material α-RuCl3 has intrigued great research interest recently. A fascinating question is on the possible existence of a field-induced QSL phase in this compound. Here we perform high-field magnetization measurements of α-RuCl3 up to 102 T employing the non-destructive and destructive pulsed magnets. Under the out-of-plane field along the c* axis (i.e., perpendicular to the honeycomb plane), two quantum phase transitions are uncovered at respectively 35 T and about 83 T, between which lies an intermediate phase as the predicted QSL. This is in sharp contrast to the case with in-plane fields, where a single transition is found at around 7 T and the intermediate QSL phase is absent instead. By measuring the magnetization data with fields tilted from the c* axis up to 90° (i.e., in-plane direction), we obtain the field-angle phase diagram that contains the zigzag, paramagnetic, and QSL phases. Based on the K-J-Γ- Γ′{{{\Gamma }}}^{{\prime} }Γ′ Γ ′ model for α-RuCl3 with a large Kitaev term we perform density matrix renormalization group simulations and reproduce the quantum phase diagram in excellent agreement with experiments.
Abstract Among the quantum many-body models that host anyon excitation and topological orders, quantum dimer models (QDM) provide a suitable playground for studying the relation between single-anyon and multi-anyon continuum spectra. However, as the prototypical correlated system with local constraints, the generic solution of QDM at different lattice geometry and parameter regimes is still missing due to the lack of controlled methodologies. Here we obtain, via sweeping cluster quantum Monte Carlo algorithm, the excitation spectra in different phases of the triangular lattice QDM. Our results reveal the single vison excitations inside the Z2 quantum spin liquid (QSL) and its condensation towards the 12×12\sqrt{12}\times \sqrt{12}12​×12​ 12 × 12 valence bond solid (VBS), and demonstrate the translational symmetry fractionalization and emergent O(4) symmetry at the QSL-VBS transition. We find the single vison excitations, whose convolution qualitatively reproduces the dimer spectra, are not free but subject to interaction effects throughout the transition. The nature of the VBS with its O(4) order parameters are unearthed in full scope. Our approach opens the avenue for generic solution of the static and dynamic properties of QDMs and has relevance towards the realization and detection of fractional excitations in programmable quantum simulators.
We report on terahertz spectroscopy of quantum spin dynamics in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, a system proximate to the Kitaev honeycomb model, as a function of temperature and magnetic field. We follow the evolution of an extended magnetic continuum below the structural phase transition at Ts2=62  K{T}_{s2}=62\text{ }\text{ }\mathrm{K}Ts2​=62  K. With the onset of a long-range magnetic order at TN=6.5  K{T}_{N}=6.5\text{ }\text{ }\mathrm{K}TN​=6.5  K, spectral weight is transferred to a well-defined magnetic excitation at $\ensuremath{\hbar}{\ensuremath{\omega}}_{1}=2.48\text{ }\text{ }\mathrm{meV}$, which is accompanied by a higher-energy band at $\ensuremath{\hbar}{\ensuremath{\omega}}_{2}=6.48\text{ }\text{ }\mathrm{meV}$. Both excitations soften in a magnetic field, signaling a quantum phase transition close to Bc=7  T{B}_{c}=7\text{ }\text{ }\mathrm{T}Bc​=7  T, where a broad continuum dominates the dynamical response. Above Bc{B}_{c}Bc​, the long-range order is suppressed, and on top of the continuum, emergent magnetic excitations evolve. These excitations follow clear selection rules and exhibit distinct field dependencies, characterizing the dynamical properties of a possibly field-induced quantum spin liquid.