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arXiv:2103.13405

Theory of Dirac Spin-Orbital Liquids: monopoles, anomalies, and applications to $SU(4)$ honeycomb models

Vladimir Calvera, Wang, Chong

Published Mar 24, 2021• 8 citations
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Abstract

Dirac spin liquids represent a class of highly-entangled quantum phases in two dimensional Mott insulators, featuring exotic properties such as critical correlation functions and absence of well-defined low energy quasi-particles. Existing numerical works suggest that the spin-orbital $SU(4)$ symmetric Kugel-Khomskii model of Mott insulators on the honeycomb lattice realizes a Dirac spin-orbital liquid, described at low energy by $(2+1)d$ quantum electrodynamics (QED$_3$) with $N_f=8$ Dirac fermions. We generalize methods previously developed for $SU(2)$ spin systems to analyze the symmetry properties and stability of the Dirac spin-orbital liquid. We conclude that the standard Dirac state in the $SU(4)$ honeycomb system, based on a simple parton mean-field ansatz, is intrinsically unstable at low energy due to the existence of a monopole perturbation that is allowed by physical symmetries and relevant under renormalization group flow. We propose two plausible alternative scenarios compatible with existing numerics. In the first scenario, we propose an alternative $U(1)$ Dirac spin-orbital liquid, which is similar to the standard one except for its monopole symmetry quantum numbers. This alternative $U(1)$ state represents a stable gapless phase. In the second scenario, we start from the standard $U(1)$ Dirac liquid and Higgs the $U(1)$ gauge symmetry down to $\mathbb{Z}_4$. The resulting $\mathbb{Z}_4$ Dirac spin-orbital liquid is stable. We also discuss the continuous quantum phase transitions from the $\mathbb{Z}_4$ Dirac liquids to conventional symmetry-breaking orders, described by the QED$_3$ theory with $N_f=8$ supplemented with a critical charge-$4$ Higgs field. We discuss possible ways to distinguish these scenarios in numerics. We also extend previous calculations of the quantum anomalies of QED$_3$ and match with generalized lattice Lieb-Schultz-Mattis constraints.

DOI
10.48550/arxiv.2103.13405

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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=1/2S=1/2S=1/2 spin systems, more recently signals of a DSL were detected in an S=3/2S=3/2S=3/2 system ααα-CrOOH(D). In this work we develop a theory of DSLs on triangular lattice with spin-SSS moments. We argue that in the most natural scenario, a spin-SSS system realizes a U(2S)U(2S)U(2S) DSL, described at low energy by gapless Dirac fermions coupled with an emergent U(2S)U(2S)U(2S) gauge field (also known as U(2S)U(2S)U(2S) QCD3_33​). An appealing feature of this scenario is that at sufficiently large SSS, the U(2S)U(2S)U(2S) QCD becomes intrinsically unstable toward spontaneous symmetry breaking and confinement. The confined phase is simply the 120∘120^{\circ}120∘ coplanar magnetic order, which agrees with semiclassical (large-SSS) results on simple Heisenberg-like models. Other scenarios are nevertheless possible, especially at small SSS when quantum fluctuations are strong. For S=3/2S=3/2S=3/2, we argue that a U(1)U(1)U(1) DSL is also theoretically possible and phenomenologically compatible with existing measurements. One way to distinguish the U(3)U(3)U(3) DSL from the U(1)U(1)U(1) DSL is to break time-reversal symmetry, for example by adding a spin chirality term S⃗i⋅(S⃗j×S⃗k)\vec{S}_i\cdot(\vec{S}_j\times\vec{S}_k)Si​⋅(Sj​×Sk​) in numerical simulations: the U(1)U(1)U(1) DSL becomes the standard Kalmeyer-Laughlin chiral spin liquid with semion/anti-semion excitation; the U(3)U(3)U(3) DSL, in contrast, becomes a non-abelian chiral spin liquid described by the SU(2)3SU(2)_3SU(2)3​ topological order, with Fibonacci-like anyons.