Signatures of Fractionalization in Spin Liquids from Interlayer Thermal Transport

Quantum spin liquids (QSLs) are intriguing phases of matter possessing fractionalized excitations.Several quasi-two-dimensional materials have been proposed as candidate QSLs, but direct evidence for fractionalization in these systems is still lacking.In this paper, we show that the interplane thermal conductivity in layered QSLs carries a unique signature of fractionalization.We examine several types of gapless QSL phases-a Z 2 QSL with either a Dirac spectrum or a spinon Fermi surface, and a Uð1Þ QSL with a Fermi surface-and consider both clean and disordered systems.In all cases, the in-plane and c-axis thermal conductivities have a different power-law dependence on temperature because of the different mechanisms of transport in the two directions: In the planes, the thermal current is carried by fractionalized excitations, whereas the interplane current is carried by integer (nonfractional) excitations.In layered Z 2 and Uð1Þ QSLs with a Fermi surface, and in the disordered Z 2 QSL with a Dirac dispersion, the c-axis thermal conductivity is parametrically smaller than the in-plane one but parametrically larger than the phonon contribution at low temperatures.Quantum spin liquids (QSLs) are intriguing phases of matter possessing fractionalized excitations.Several quasi-two-dimensional materials have been proposed as candidate QSLs, but direct evidence for fractionalization in these systems is still lacking.In this paper, we show that the interplane thermal conductivity in layered QSLs carries a unique signature of fractionalization.We examine several types of gapless QSL phases-a Z 2 QSL with either a Dirac spectrum or a spinon Fermi surface, and a Uð1Þ QSL with a Fermi surface-and consider both clean and disordered systems.In all cases, the in-plane and c-axis thermal conductivities have a different power-law dependence on temperature because of the different mechanisms of transport in the two directions: In the planes, the thermal current is carried by fractionalized excitations, whereas the interplane current is carried by integer (nonfractional) excitations.In layered Z 2 and Uð1Þ QSLs with a Fermi surface, and in the disordered Z 2 QSL with a Dirac dispersion, the c-axis thermal conductivity is parametrically smaller than the in-plane one but parametrically larger than the phonon contribution at low temperatures.

arXiv:1708.02584Physical Review XSep 11, 201818 citations

Coexisting localized and itinerant gapless excitations in a quantum spin liquid candidate 1T-TaS $_2$ Coexisting localized and itinerant gapless excitations in a quantum spin liquid candidate 1T-TaS$_2$

H. Murayama, Yuki Sato, Xiangzhuo Xing +6 more

To reveal the nature of elementary excitations in a quantum spin liquid (QSL), we measured low temperature thermal conductivity and specific heat of 1T-TaS $_2$ , a QSL candidate material with frustrated triangular lattice of spin-1/2. The nonzero temperature linear specific heat coefficient $γ$ and the finite residual linear term of the thermal conductivity in the zero temperature limit $κ_0/T=κ/T(T\rightarrow 0)$ are clearly resolved. This demonstrates the presence of highly mobile gapless excitations, which is consistent with fractionalized spinon excitations that form a Fermi surface. Remarkably, an external magnetic field strongly suppresses $γ$ , whereas it enhances $κ_0/T$ . This unusual contrasting behavior in the field dependence of specific heat and thermal conductivity can be accounted for by the presence of two types of gapless excitations with itinerant and localized characters, as recently predicted theoretically (I. Kimchi et al., arXiv:1803.00013 (2018)). This unique feature of 1T-TaS $_2$ provides new insights into the influence of quenched disorder on the QSL.To reveal the nature of elementary excitations in a quantum spin liquid (QSL), we measured low temperature thermal conductivity and specific heat of 1T-TaS$_2$, a QSL candidate material with frustrated triangular lattice of spin-1/2. The nonzero temperature linear specific heat coefficient $γ$ and the finite residual linear term of the thermal conductivity in the zero temperature limit $κ_0/T=κ/T(T\rightarrow 0)$ are clearly resolved. This demonstrates the presence of highly mobile gapless excitations, which is consistent with fractionalized spinon excitations that form a Fermi surface. Remarkably, an external magnetic field strongly suppresses $γ$, whereas it enhances $κ_0/T$. This unusual contrasting behavior in the field dependence of specific heat and thermal conductivity can be accounted for by the presence of two types of gapless excitations with itinerant and localized characters, as recently predicted theoretically (I. Kimchi et al., arXiv:1803.00013 (2018)). This unique feature of 1T-TaS$_2$ provides new insights into the influence of quenched disorder on the QSL.

arXiv:1803.06100Mar 16, 201812 citations

Gapless spin liquids: Stability and possible experimental relevance

Maissam Barkeshli, Hong Yao, Steven Allan Kivelson

For certain crystalline systems, most notably the organic compound EtMe ${}_{3}$ Sb[Pd(dmit) ${}_{2}$ ] ${}_{2}$ , experimental evidence has accumulated of an insulating state with a high density of gapless neutral excitations that produce Fermi-liquid-like power laws in thermodynamic quantities and thermal transport. This has been taken as evidence of a fractionalized spin-liquid state. In this Rapid Communication, we argue that if the experiments are taken at face value, the most promising spin-liquid candidates are a ${Z}_{4}$ spin liquid with a spinon-Fermi surface and no broken symmetries, or a ${Z}_{2}$ spin liquid with a spinon-Fermi surface and at least one of the following spontaneously broken: (a) time-reversal and inversion, (b) translation, or (c) certain point-group symmetries. We present a solvable model on the triangular lattice with an (a) type ${Z}_{2}$ spin-liquid ground state.For certain crystalline systems, most notably the organic compound EtMe${}_{3}$Sb[Pd(dmit)${}_{2}$]${}_{2}$, experimental evidence has accumulated of an insulating state with a high density of gapless neutral excitations that produce Fermi-liquid-like power laws in thermodynamic quantities and thermal transport. This has been taken as evidence of a fractionalized spin-liquid state. In this Rapid Communication, we argue that if the experiments are taken at face value, the most promising spin-liquid candidates are a ${Z}_{4}$ spin liquid with a spinon-Fermi surface and no broken symmetries, or a ${Z}_{2}$ spin liquid with a spinon-Fermi surface and at least one of the following spontaneously broken: (a) time-reversal and inversion, (b) translation, or (c) certain point-group symmetries. We present a solvable model on the triangular lattice with an (a) type ${Z}_{2}$ spin-liquid ground state.

arXiv:1208.3869Physical Review BApr 2, 201333 citations

Spin-lattice coupling in U(1) quantum spin liquids

Sangjin Lee, Eun-Gook Moon

Quantum spin liquids (QSLs) are exotic phases with intrinsic massive entanglements. Instead of microscopic spins, fractionalized particles and gauge fluctuations are emergent, revealing QSLs' exotic natures. Quantum spins with strong spin-orbit coupling on a pyrochlore lattice, for example ${\mathrm{Pr}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ , are suggested to host a U(1) QSL with emergent photons, gapless excitations, as well as emergent monopoles. One of the key issues in QSLs is an interplay between emergent degrees of freedom of QSLs and conventional degrees of freedom, and we investigate the interplay by constructing a general theory of spin-lattice coupling in U(1) QSLs. We find that the coupling induces characteristic interplay between phonons and photons. For example, photons become qualitatively more stable than phonons at low temperature. We also propose mechanisms to detect emergent photons in experiments such as sound attenuation and thermal transport relying on spin-lattice coupling in U(1) QSLs.Quantum spin liquids (QSLs) are exotic phases with intrinsic massive entanglements. Instead of microscopic spins, fractionalized particles and gauge fluctuations are emergent, revealing QSLs' exotic natures. Quantum spins with strong spin-orbit coupling on a pyrochlore lattice, for example ${\mathrm{Pr}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$, are suggested to host a U(1) QSL with emergent photons, gapless excitations, as well as emergent monopoles. One of the key issues in QSLs is an interplay between emergent degrees of freedom of QSLs and conventional degrees of freedom, and we investigate the interplay by constructing a general theory of spin-lattice coupling in U(1) QSLs. We find that the coupling induces characteristic interplay between phonons and photons. For example, photons become qualitatively more stable than phonons at low temperature. We also propose mechanisms to detect emergent photons in experiments such as sound attenuation and thermal transport relying on spin-lattice coupling in U(1) QSLs.

arXiv:1802.05280Physical review. B./Physical review. BJan 10, 20194 citations

Detecting fractionalization in critical spin liquids using color centers

So Takei, Yaroslav Tserkovnyak

Quantum spin liquids are highly entangled ground states of insulating spin systems, in which magnetic ordering is prevented down to the lowest temperatures due to quantum fluctuations. One of the most extraordinary characteristics of quantum spin liquid phases is their ability to support fractionalized, low-energy quasiparticles known as spinons, which carry spin-1/2 but bear no charge. Relaxometry based on color centers in crystalline materials—of which nitrogen-vacancy (NV) centers in diamond are a well-explored example—provides an exciting new platform to probe the spin spectral functions of magnetic materials with both energy and momentum resolution and to search for signatures of these elusive, fractionalized excitations. In this work, we theoretically investigate the color-center relaxometry of two archetypal quantum spin liquids: the two-dimensional U(1) quantum spin liquid with a spinon Fermi surface and the spin-1/2 antiferromagnetic spin chain. The former is characterized by a metallic, spin-split ground state of mobile, interacting spinons, which closely resembles a spin-polarized Fermi liquid ground state but with neutral quasiparticles. We show that the observation of the Stoner continuum and the collective spin wave mode in the spin spectral function would provide a strong evidence for the existence of spinons and fractionalization. In one dimension, mobile spinons form a Luttinger liquid ground state. We show that the spin spectral function exhibits strong features representing the collective density and spin-wave modes, which are broadened in an algebraic fashion with an exponent characterized by the Luttinger parameter. The possibilities of measuring these collective modes and detecting the power-law decay of the spectral weight using NV relaxometry are discussed. We also examine how the transition rates are modified by marginally irrelevant operators in the Heisenberg limit. Published by the American Physical Society 2024Quantum spin liquids are highly entangled ground states of insulating spin systems, in which magnetic ordering is prevented down to the lowest temperatures due to quantum fluctuations. One of the most extraordinary characteristics of quantum spin liquid phases is their ability to support fractionalized, low-energy quasiparticles known as spinons, which carry spin-1/2 but bear no charge. Relaxometry based on color centers in crystalline materials—of which nitrogen-vacancy (NV) centers in diamond are a well-explored example—provides an exciting new platform to probe the spin spectral functions of magnetic materials with both energy and momentum resolution and to search for signatures of these elusive, fractionalized excitations. In this work, we theoretically investigate the color-center relaxometry of two archetypal quantum spin liquids: the two-dimensional U(1) quantum spin liquid with a spinon Fermi surface and the spin-1/2 antiferromagnetic spin chain. The former is characterized by a metallic, spin-split ground state of mobile, interacting spinons, which closely resembles a spin-polarized Fermi liquid ground state but with neutral quasiparticles. We show that the observation of the Stoner continuum and the collective spin wave mode in the spin spectral function would provide a strong evidence for the existence of spinons and fractionalization. In one dimension, mobile spinons form a Luttinger liquid ground state. We show that the spin spectral function exhibits strong features representing the collective density and spin-wave modes, which are broadened in an algebraic fashion with an exponent characterized by the Luttinger parameter. The possibilities of measuring these collective modes and detecting the power-law decay of the spectral weight using NV relaxometry are discussed. We also examine how the transition rates are modified by marginally irrelevant operators in the Heisenberg limit. Published by the American Physical Society 2024

arXiv:2305.07112Physical Review ResearchJan 11, 20247 citations

Spinon-Induced Phonon Dynamics in Chiral and $π$ -Flux Quantum Spin LiquidsSpinon-Induced Phonon Dynamics in Chiral and $π$-Flux Quantum Spin Liquids

Zachary Hizon, Kristian Hauser A. Villegas

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 (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.

arXiv:2609.19050Jul 21, 20260 citations

Coexisting localized and itinerant gapless excitations in a quantum spin liquid candidate 1T-TaS

_2

To reveal the nature of elementary excitations in a quantum spin liquid (QSL), we measured low temperature thermal conductivity and specific heat of 1T-TaS

_2

, a QSL candidate material with frustrated triangular lattice of spin-1/2. The nonzero temperature linear specific heat coefficient

γ

and the finite residual linear term of the thermal conductivity in the zero temperature limit

κ_0/T=κ/T(T\rightarrow 0)

are clearly resolved. This demonstrates the presence of highly mobile gapless excitations, which is consistent with fractionalized spinon excitations that form a Fermi surface. Remarkably, an external magnetic field strongly suppresses

γ

, whereas it enhances

κ_0/T

. This unusual contrasting behavior in the field dependence of specific heat and thermal conductivity can be accounted for by the presence of two types of gapless excitations with itinerant and localized characters, as recently predicted theoretically (I. Kimchi et al., arXiv:1803.00013 (2018)). This unique feature of 1T-TaS

_2

provides new insights into the influence of quenched disorder on the QSL.

For certain crystalline systems, most notably the organic compound EtMe

{}_{3}

Sb[Pd(dmit)

{}_{2}

]

{}_{2}

, experimental evidence has accumulated of an insulating state with a high density of gapless neutral excitations that produce Fermi-liquid-like power laws in thermodynamic quantities and thermal transport. This has been taken as evidence of a fractionalized spin-liquid state. In this Rapid Communication, we argue that if the experiments are taken at face value, the most promising spin-liquid candidates are a

{Z}_{4}

spin liquid with a spinon-Fermi surface and no broken symmetries, or a

{Z}_{2}

spin liquid with a spinon-Fermi surface and at least one of the following spontaneously broken: (a) time-reversal and inversion, (b) translation, or (c) certain point-group symmetries. We present a solvable model on the triangular lattice with an (a) type

{Z}_{2}

spin-liquid ground state.

{\mathrm{Pr}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}

, are suggested to host a U(1) QSL with emergent photons, gapless excitations, as well as emergent monopoles. One of the key issues in QSLs is an interplay between emergent degrees of freedom of QSLs and conventional degrees of freedom, and we investigate the interplay by constructing a general theory of spin-lattice coupling in U(1) QSLs. We find that the coupling induces characteristic interplay between phonons and photons. For example, photons become qualitatively more stable than phonons at low temperature. We also propose mechanisms to detect emergent photons in experiments such as sound attenuation and thermal transport relying on spin-lattice coupling in U(1) QSLs.

Spinon-Induced Phonon Dynamics in Chiral and

π

-Flux Quantum Spin Liquids