Quantum orders and symmetric spin liquids

Abstract

A quantum spin liquid is an exotic quantum state of matter in which spins are highly entangled and remain disordered down to zero temperature. Such a state of matter is potentially relevant to high-temperature superconductivity and quantum-information applications, and experimental identification of a quantum spin liquid state is of fundamental importance for our understanding of quantum matter. Theoretical studies have proposed various quantum-spin-liquid ground states 1-4 , most of which are characterized by exotic spin excitations with fractional quantum numbers (termed 'spinon'). Here, we report neutron scattering measurements that reveal broad spin excitations covering a wide region of the Brillouin zone in a triangular antiferromagnet YbMgGaO 4. The observed diffusive spin excitation persists at the lowest measured energy and shows a clear upper excitation edge, which is consistent with the particle-hole excitation of a spinon Fermi surface. Our results therefore point to a QSL state with a spinon Fermi surface in YbMgGaO 4 that has a perfect spin-1/2 triangular lattice as in the original proposal 4 of quantum spin liquids. In 1973, Anderson proposed the pioneering idea of the quantum spin liquid (QSL) in the study of the triangular lattice Heisenberg antiferromagnet 4. This idea was revived after the discovery in 1986 of high-temperature superconductivity 5. A QSL, as currently understood, does not fit into Landau's conventional paradigm of symmetry breaking phases 1,2,6,7 , and is 2 instead an exotic state of matter characterized by spinon excitations and emergent gauge structures 1-3,6. The search for QSLs in models and materials 8-12 has been partly facilitated by the Oshikawa-Hastings-Lieb-Schultz-Mattis (OHLSM) theorem that may hint at the possibility of QSLs in Mott insulators with odd electron fillings and a global U(1) spin rotational symmetry 13-15. Indeed, a continuum of spin excitations has been observed in a kagome-lattice material ZnCu 3 (OD) 6 Cl 2 (refs 12,16). However, the requirement of the U(1) spin rotational symmetry, prevents the application of OHLSM theorem in strong spin-orbit-coupled (SOC) Mott insulators in which the spin rotational symmetry is completely absent. A recent theory addressed this limitation of the OHLSM theorem, arguing that, as long as time-reversal symmetry is preserved, the ground state of an SOC Mott insulator with odd electron fillings must be exotic 17. The newly discovered triangular antiferromagnet YbMgGaO 4 (refs 18,19) displays no indication of magnetic ordering or symmetry breaking at temperatures as low as 30 mK despite approximately 4 K for the spin interaction energy scale. Because of the strong SOC of the Yb electrons, YbMgGaO 4 was the first QSL to be proposed beyond the OHLSM theorem 19. The thirteen 4 f electrons of the Yb 3+ ion form the spin-orbit-entangled Kramers doublets that are split by the D 3d crystal electric fields 20-22. At temperatures considerably lower than the crystal field gap (∼ 420 K), the magnetic properties are captured by the g...

Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate

“…This idea was revived after the discovery in 1986 of high-temperature superconductivity 5 . A QSL, as currently understood, does not fit into Landau's conventional paradigm of symmetry breaking phases 1,2,6,7 , and is arXiv:1607.02615v2 [cond-mat.str-el] 31 Jul 2017 2 instead an exotic state of matter characterized by spinon excitations and emergent gauge structures [1][2][3]6 . The search for QSLs in models and materials [8][9][10][11][12] has been partly facilitated by the Oshikawa-Hastings-Lieb-Schultz-Mattis (OHLSM) theorem that may hint at the possibility of QSLs in Mott insulators with odd electron fillings and a global U(1) spin rotational symmetry [13][14][15] .…”

“…Such a state of matter is potentially relevant to high-temperature superconductivity and quantum-information applications, and experimental identification of a quantum spin liquid state is of fundamental importance for our understanding of quantum matter. Theoretical studies have proposed various quantum-spin-liquid ground states [1][2][3][4] , most of which are characterized by exotic spin excitations with fractional quantum numbers (termed 'spinon'). Here, we report neutron scattering measurements that reveal broad spin excitations covering a wide region of the Brillouin zone in a triangular antiferromagnet YbMgGaO 4 .…”

Quantum Field Theory of Many-Body Systems

“…In fact, the string picture works in any dimension.) As in the case of particle condensation, the PSG that characterizes different string condensed states can also protect the gaplessness of the emergent gauge bosons and fermions [Wen (2002b); Wen and Zee (2002)]. …”

“…Much of this progress has occurred in three areas of research: (1) the study of topological phases in condensed matter systems such as FQH systems [Wen and Niu (1990); Blok and Wen (1990); Read (1990); Fröhlich and Kerler (1991)], quantum dimer models [Rokhsar and Kivelson (1988); Read and Chakraborty (1989); Moessner and Sondhi (2001); Ardonne et al (2004)], quantum spin models [Kalmeyer and Laughlin (1987) ;Wen et al (1989); Wen (1990); Read and Sachdev (1991); Wen (1991a); Senthil and Fisher (2000); Wen (2002b); Sachdev and Park (2002) ;Balents et al (2002)], or even superconducting states [Wen (1991b); Hansson et al (2004)], (2) the study of lattice gauge theory [Wegner (1971); Banks et al (1977); Kogut and Susskind (1975); Kogut (1979)], and (3) the study of quantum computing by anyons [Kitaev (2003); Ioffe et al (2002); Freedman et al (2002)]. The phenomenon of string condensation is important in all of these fields, though the string picture is often de-emphasized.…”

“…Later, Ref. [Wen (2002b[Wen ( , 2003b] attempted to characterize and classify quantum order -a generalization of topological order to gapless phases -using the projective symmetry group (PSG) formalism. String condensed states are typically topologically ordered.…”