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arXiv:2206.14197

Translation-enriched $Z_2$ spin liquids and topological vison bands: Possible application to $α$-RuCl$_3$

Xue-Yang Song, T. Senthil

Published Jun 28, 2022• 4 citations
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Abstract

Inspired by experiments on the magnetic field induced phases of the spin-orbit coupled $2d$ Mott insulator $α$-RuCl$_3$, we study some general aspects of gapped $Z_2$ 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 $Z_2$ QSL as a candidate ground state at intermediate magnetic fields in $α$-RuCl$_3$. 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 $α$-RuCl$_3$. On general grounds continuum scattering will also be seen at multiple points in the Brillouin zone in this state.

DOI
10.48550/arxiv.2206.14197

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Kitaev quantum spin liquids (KQSLs) host fractionalized excitations described by itinerant Majorana quasiparticles and gapped Z2Z_2Z2​ fluxes (visons), providing a platform for emergent topological matter. Whether such a state survives under strong magnetic fields, however, remains an open question. The layered honeycomb magnet ααα-RuCl3_33​ is a leading candidate material: an in-plane field of ∼\sim∼ 7 T suppresses antiferromagnetic order and induces a quantum-disordered phase exhibiting signatures consistent with Majorana excitations, including an anomalous thermal Hall effect and field-angle-dependent specific heat. At higher fields, the magnetization approaches saturation, suggesting a transition to a spin-polarized state, yet the microscopic evolution between these limits remains unresolved. Here we report high-field specific heat measurements up to 24 T that reveal a distinct crossover at $μ_0H^*\approx$15 T, beyond which the perturbative Kitaev description breaks down. Above H∗H^*H∗, the characteristic six-fold angular modulation of the specific heat collapses and the excitation gap deviates from the predicted H3H^3H3 scaling. Meanwhile, the gap decreases with increasing field and the in-plane magnetization anisotropy persists up to ∼\sim∼ 24 T, both in sharp contrast to a trivial spin-polarized state, indicating that KQSL signatures are preserved even at ∼\sim∼ 90 % of magnetization saturation. These results reveal that the KQSL in ααα-RuCl3_33​ extends well beyond the perturbative window, persisting as a nonperturbative regime in which the Majorana and vison energy scales merge, before eventually giving way to spin polarization. This thermodynamic roadmap provides a basis for understanding how fractionalized phases evolve under strong magnetic fields.
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Observation of a Field-induced Quantum Spin Liquid in α\alphaα-RuCl3_33​
Topological quantum spin liquids (QSLs) are states of matter with remarkable predicted properties -- an ability to create and braid quasiparticles in certain topological QSLs equals the ability to perform topologically protected quantum computation. There are various mathematical models with topological QSL phases, but so far none has been physically realized. Here we show that α\alphaα-RuCl3_33​ exhibits a magnetic field-induced QSL ground-state. Nuclear Magnetic Resonance measurements reveal that for fields larger than ∼10\sim 10∼10 T a spin-gap opens up while resonance lines remain sharp, evidencing that spins are quantum disordered. Such a field-induced, gapped topological QSL phase has been predicted in the Kitaev model, which is closely associated to α\alphaα-RuCl3_33​. The quasiparticles in this phase of the Kitaev model have the statistical properties required for universal topological quantum computation.
Investigation of the J1J_1J1​-J2J_2J2​ Heisenberg model on the triangular lattice: A study with projected entangled-pair states
The nature of the quantum spin liquid (QSL) phase in the frustrated J1J_1J1​-J2J_2J2​ Heisenberg model on the triangular lattice remains an open and actively debated problem. In this work, we employ the infinite projected entangled-pair state (PEPS) to systematically investigate the model under different symmetry constraints. Our simulations reveal a direct transition from the 120∘120^\circ120∘ Néel state to a putative QSL at J2/J1≈0.08J_2/J_1\approx 0.08J2​/J1​≈0.08, signaled by the collapse of magnetic order. We further show that, through either an appropriate unitary rotation or spontaneous spin long-range order, the stripe antiferromagnetic phase can also be accurately captured within the infinite PEPS framework. A central focus of our study is the role played by the PEPS symmetry in approximating the QSL ground-state sandwiched between the two magnetic phases. We first found that a fully-symmetric topological Z2\mathbb{Z}_2Z2​ Resonating Valence Bond state, which can be written as a simple PEPS with bond dimension D=3D=3D=3, exhibits a reasonably good variational energy. Motivated by this finding, we have further constructed generic Z2\mathbb{Z}_2Z2​-symmetric PEPS of larger bond dimension (up to D=7D=7D=7). We found that, under wavefunction optimization, spinons condense and, simultaneously, topological vison excitations get confined, hence precluding Z2\mathbb{Z}_2Z2​ topological order. This strongly indicates the gapless (or critical) nature of the QSL phase, which is most naturally consistent with a U(1) Dirac spin liquid scenario.