Explorations in Dirac Fermions and Spin Liquids

Quantum impurities serve as in-situ probes of the frustrated quantum magnets, and Dirac spin liquids are an important class of quantum spin liquids. Here, we present a general method, a combination of the Chern-Simons fermionization and the Wess-Zumino-Witten theory, to study the quantum impurity in Dirac spin liquids. Under the Chern-Simons fermionization, the gauge fluctuations are apparently suppressed and the low-energy physics is described by a number of Dirac valleys with valley-dependent pseudospin-momentum locking. The (2+1)D effective theory can be further reduced into the (1+1)D Wess-Zumino-Witten theory by rotational symmetry, where the pseudospin-exchange between Dirac fermions and the impurity can then be solved by the non-Abelian bosonization. Consequently, fixed points of Fermi liquid and non-Fermi liquid are identified, respectively, depending on the relevance of the impurity scattering among the Dirac valleys. This leads to experimental fingerprints for Dirac spin liquids, including a Kondo-induced magneto-thermal effect, a non-monotonous thermal conductivity during the crossover, and an anisotropic spin correlation function.Quantum impurities serve as in-situ probes of the frustrated quantum magnets, and Dirac spin liquids are an important class of quantum spin liquids. Here, we present a general method, a combination of the Chern-Simons fermionization and the Wess-Zumino-Witten theory, to study the quantum impurity in Dirac spin liquids. Under the Chern-Simons fermionization, the gauge fluctuations are apparently suppressed and the low-energy physics is described by a number of Dirac valleys with valley-dependent pseudospin-momentum locking. The (2+1)D effective theory can be further reduced into the (1+1)D Wess-Zumino-Witten theory by rotational symmetry, where the pseudospin-exchange between Dirac fermions and the impurity can then be solved by the non-Abelian bosonization. Consequently, fixed points of Fermi liquid and non-Fermi liquid are identified, respectively, depending on the relevance of the impurity scattering among the Dirac valleys. This leads to experimental fingerprints for Dirac spin liquids, including a Kondo-induced magneto-thermal effect, a non-monotonous thermal conductivity during the crossover, and an anisotropic spin correlation function.

arXiv:2010.05022Oct 10, 20200 citations

An introduction to Quantum Spin Liquids

Subhro Bhattacharjee

Texts and readings in physical sciencesJan 1, 20172 citations

Introduction to Quantum Spin Liquids

C. Lhuillier, Grégoire Misguich

Springer series in solid-state sciencesSep 29, 201011 citations

Theory of Dirac spin liquids on spin- $S$ triangular lattice: possible application to $α$ -CrOOH(D)Theory of Dirac spin liquids on spin-$S$ triangular lattice: possible application to $α$-CrOOH(D)

Vladimir Calvera, Wang, Chong

Triangular lattice quantum antiferromagnet has recently emerged to be a promising playground for realizing Dirac spin liquids (DSLs) -- a class of highly entangled quantum phases hosting emergent gauge fields and gapless Dirac fermions. While previous theories and experiments focused mainly on $S=1/2$ spin systems, more recently signals of a DSL were detected in an $S=3/2$ system $α$ -CrOOH(D). In this work we develop a theory of DSLs on triangular lattice with spin- $S$ moments. We argue that in the most natural scenario, a spin- $S$ system realizes a $U(2S)$ DSL, described at low energy by gapless Dirac fermions coupled with an emergent $U(2S)$ gauge field (also known as $U(2S)$ QCD $_3$ ). An appealing feature of this scenario is that at sufficiently large $S$ , the $U(2S)$ QCD becomes intrinsically unstable toward spontaneous symmetry breaking and confinement. The confined phase is simply the $120^{\circ}$ coplanar magnetic order, which agrees with semiclassical (large- $S$ ) results on simple Heisenberg-like models. Other scenarios are nevertheless possible, especially at small $S$ when quantum fluctuations are strong. For $S=3/2$ , we argue that a $U(1)$ DSL is also theoretically possible and phenomenologically compatible with existing measurements. One way to distinguish the $U(3)$ DSL from the $U(1)$ DSL is to break time-reversal symmetry, for example by adding a spin chirality term $\vec{S}_i\cdot(\vec{S}_j\times\vec{S}_k)$ in numerical simulations: the $U(1)$ DSL becomes the standard Kalmeyer-Laughlin chiral spin liquid with semion/anti-semion excitation; the $U(3)$ DSL, in contrast, becomes a non-abelian chiral spin liquid described by the $SU(2)_3$ topological order, with Fibonacci-like anyons.Triangular lattice quantum antiferromagnet has recently emerged to be a promising playground for realizing Dirac spin liquids (DSLs) -- a class of highly entangled quantum phases hosting emergent gauge fields and gapless Dirac fermions. While previous theories and experiments focused mainly on $S=1/2$ spin systems, more recently signals of a DSL were detected in an $S=3/2$ system $α$-CrOOH(D). In this work we develop a theory of DSLs on triangular lattice with spin-$S$ moments. We argue that in the most natural scenario, a spin-$S$ system realizes a $U(2S)$ DSL, described at low energy by gapless Dirac fermions coupled with an emergent $U(2S)$ gauge field (also known as $U(2S)$ QCD$_3$). An appealing feature of this scenario is that at sufficiently large $S$, the $U(2S)$ QCD becomes intrinsically unstable toward spontaneous symmetry breaking and confinement. The confined phase is simply the $120^{\circ}$ coplanar magnetic order, which agrees with semiclassical (large-$S$) results on simple Heisenberg-like models. Other scenarios are nevertheless possible, especially at small $S$ when quantum fluctuations are strong. For $S=3/2$, we argue that a $U(1)$ DSL is also theoretically possible and phenomenologically compatible with existing measurements. One way to distinguish the $U(3)$ DSL from the $U(1)$ DSL is to break time-reversal symmetry, for example by adding a spin chirality term $\vec{S}_i\cdot(\vec{S}_j\times\vec{S}_k)$ in numerical simulations: the $U(1)$ DSL becomes the standard Kalmeyer-Laughlin chiral spin liquid with semion/anti-semion excitation; the $U(3)$ DSL, in contrast, becomes a non-abelian chiral spin liquid described by the $SU(2)_3$ topological order, with Fibonacci-like anyons.

arXiv:2012.09809Dec 17, 20205 citations

Beyond Landau's theory of Fermi liquids

Hagen M. Kleinert

Physics Letters AJul 1, 19814 citations

Theory of Dirac spin liquids on spin-

S

triangular lattice: possible application to

α

-CrOOH(D)

S=1/2

spin systems, more recently signals of a DSL were detected in an

S=3/2

system

α

-CrOOH(D). In this work we develop a theory of DSLs on triangular lattice with spin-

S

moments. We argue that in the most natural scenario, a spin-

S

system realizes a

U(2S)

DSL, described at low energy by gapless Dirac fermions coupled with an emergent

U(2S)

gauge field (also known as

U(2S)

QCD

_3

). An appealing feature of this scenario is that at sufficiently large

S

, the

U(2S)

QCD becomes intrinsically unstable toward spontaneous symmetry breaking and confinement. The confined phase is simply the

120^{\circ}

coplanar magnetic order, which agrees with semiclassical (large-

S

) results on simple Heisenberg-like models. Other scenarios are nevertheless possible, especially at small

S

when quantum fluctuations are strong. For

S=3/2

, we argue that a

U(1)

DSL is also theoretically possible and phenomenologically compatible with existing measurements. One way to distinguish the

U(3)

DSL from the

U(1)

DSL is to break time-reversal symmetry, for example by adding a spin chirality term

\vec{S}_i\cdot(\vec{S}_j\times\vec{S}_k)

in numerical simulations: the

U(1)

DSL becomes the standard Kalmeyer-Laughlin chiral spin liquid with semion/anti-semion excitation; the

U(3)

DSL, in contrast, becomes a non-abelian chiral spin liquid described by the

SU(2)_3

topological order, with Fibonacci-like anyons.