Quantum spin liquids are exotic phases of quantum matter especially pertinent to many modern condensed matter systems. Dirac spin liquids (DSLs) are a class of gapless quantum spin liquids that do not have a quasi-particle description and are potentially realized in a wide variety of spin 1/2 1 / 2 magnetic systems on 2d 2 d lattices. In particular, the DSL in square lattice spin- 1/2 1 / 2 magnets is described at low energies by (2+1)d ( 2 + 1 ) d quantum electrodynamics with N_f=4 N f = 4 flavors of massless Dirac fermions minimally coupled to an emergent U(1) U ( 1 ) gauge field. The existence of a relevant, symmetry-allowed monopole perturbation renders the DSL on the square lattice intrinsically unstable. We argue that the DSL describes a stable continuous phase transition within the familiar Neel phase (or within the Valence Bond Solid (VBS) phase). In other words, the DSL is an ``unnecessary’’ quantum critical point within a single phase of matter. Our result offers a novel view of the square lattice DSL in that the critical spin liquid can exist within either the Neel or VBS state itself, and does not require leaving these conventional states.
Quantum spin liquids are exotic phases of quantum matter especially pertinent to many modern condensed matter systems. Dirac spin liquids (DSLs) are a class of gapless quantum spin liquids that do not have a quasi-particle description and are potentially realized in a wide variety of spin 1/2 1 / 2 magnetic systems on 2d 2 d lattices. In particular, the DSL in square lattice spin- 1/2 1 / 2 magnets is described at low energies by (2+1)d ( 2 + 1 ) d quantum electrodynamics with N_f=4 N f = 4 flavors of massless Dirac fermions minimally coupled to an emergent U(1) U ( 1 ) gauge field. The existence of a relevant, symmetry-allowed monopole perturbation renders the DSL on the square lattice intrinsically unstable. We argue that the DSL describes a stable continuous phase transition within the familiar Neel phase (or within the Valence Bond Solid (VBS) phase). In other words, the DSL is an ``unnecessary’’ quantum critical point within a single phase of matter. Our result offers a novel view of the square lattice DSL in that the critical spin liquid can exist within either the Neel or VBS state itself, and does not require leaving these conventional states.
Unnecessary quantum criticality in SU(3) kagome magnets
Algebraic/Dirac spin liquids (DSLs) are a class of critical quantum ground states that do not have a quasi-particle description. DSLs and related spin liquid phases often arise in strongly frustrated quantum spin systems, in which strong correlations and quantum fluctuations among constituent spins persist down to zero temperature. In this work, we analyze Mott insulating phases of SU(3) S U ( 3 ) fermions on a kagome lattice which may realize a DSL phase, described at low energies by (2 + 1)d ( 2 + 1 ) d quantum electrodynamics (QED _3 3 ) with N_f=6 N f = 6 Dirac fermions. By analyzing the action of physical symmetries on the operators of the QED _3 3 theory, we conclude that the low energy DSL is a quantum critical point that can be accessed by tuning a single microscopic parameter. Aided by the emergent symmetry and anomalies of the low energy effective theory, we conjecture and present supporting arguments that the SU(3) S U ( 3 ) Kagome magnet DSL is an unnecessary quantum critical point, lying completely within a single phase.
Abstract We analyze a Higgs transition from a U(1) Dirac spin liquid to a gapless ℤ2 spin liquid. This ℤ2 spin liquid is of relevance to the spin S = 1/2 square lattice antiferromagnet, where recent numerical studies have given evidence for such a phase existing in the regime of high frustration between nearest neighbor and next-nearest neighbor antiferromagnetic interactions (the J1-J2 model), appearing in a parameter regime between the vanishing of Néel order and the onset of valence bond solid ordering. The proximate Dirac spin liquid is unstable to monopole proliferation on the square lattice, ultimately leading to Néel or valence bond solid ordering. As such, we conjecture that this Higgs transition describes the critical theory separating the gapless ℤ2 spin liquid of the J1-J2 model from one of the two proximate ordered phases. The transition into the other ordered phase can be described in a unified manner via a transition into an unstable SU(2) spin liquid, which we have analyzed in prior work. By studying the deconfined critical theory separating the U(1) Dirac spin liquid from the gapless ℤ2 spin liquid in a 1/Nf expansion, with Nf proportional to the number of fermions, we find a stable fixed point with an anisotropic spinon dispersion and a dynamical critical exponent z ≠ 1. We analyze the consequences of this anisotropic dispersion by calculating the angular profiles of the equal-time Néel and valence bond solid correlation functions, and we find them to be distinct. We also note the influence of the anisotropy on the scaling dimension of monopoles.
Theory of Dirac spin liquids on spin-S triangular lattice: possible application to α-CrOOH(D)
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) QCD3). 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∘ 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 Si⋅(Sj×Sk) 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.
Algebraic spin liquids are quantum disordered phases of insulating magnets that exhibit fractionalized gapless excitations and power-law correlations. Quantum spin liquids in this category include the experimentally established one-dimensional (1D) Luttinger liquid, as well as the U(1) Dirac spin liquid (DSL) that has been a focus of recent candidate materials searches. Most notably, several exchange-frustrated Heisenberg materials on the triangular lattice have shown evidence of the U(1) DSL. In this work, we measure the algebraic correlations of spin-singlet excitations in the J 1 − J 2 antiferromagnetic Heisenberg model on the triangular lattice, prompting a detailed investigation of this model’s stability under spin-lattice coupling with dynamical phonons using variational Monte Carlo. As seen before in 1D spin chains, we observe a low-temperature transition from a U(1) DSL to valence bond order and predict the parameter regime where the model realizes a stable DSL ground state. To achieve this, we employ a series of finite-size scaling Ansätze inspired by the low-energy DSL’s conformal description in terms of quantum electrodynamics and show that emergent monopole operators drive the instability. We compare the physics of this transition to the 1D Luttinger liquid throughout our analysis. We derive the regime of stability against spin-Peierls ordering and argue that the DSL ground state might still be achievable in candidate materials, despite its tendency to valence bond solid ordering.
Theory of Dirac Spin-Orbital Liquids: monopoles, anomalies, and applications to SU(4) honeycomb models
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 (QED3) with Nf=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 Z4. The resulting Z4 Dirac spin-orbital liquid is stable. We also discuss the continuous quantum phase transitions from the Z4 Dirac liquids to conventional symmetry-breaking orders, described by the QED3 theory with Nf=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 QED3 and match with generalized lattice Lieb-Schultz-Mattis constraints.
The interplay of symmetry and topology has been at the forefront of recent progress in quantum matter.Here, we uncover an unexpected connection between band topology and the description of competing orders in a quantum magnet.Specifically, we show that aspects of band topology protected by crystalline symmetries determine key properties of the Dirac spin liquid (DSL), which can be defined on the honeycomb, square, triangular, and kagome lattices.At low energies, the DSL on all of these lattices is described by an emergent quantum electrodynamics (QED 3 ) with N f ¼ 4 flavors of Dirac fermions coupled to a Uð1Þ gauge field.However, the symmetry properties of the magnetic monopoles, an important class of critical degrees of freedom, behave very differently on different lattices.In particular, we show that the lattice momentum and angular momentum of monopoles can be determined from the charge (or Wannier) centers of the corresponding spinon insulator.We also show that for DSLs on bipartite lattices, there always exists a monopole that transforms trivially under all microscopic symmetries owing to the existence of a parent SUð2Þ gauge theory.We connect our results to generalized Lieb-Schultz-Mattis theorems and also derive the time-reversal and reflection properties of monopoles.Our results indicate that recent insights into free-fermion band topology can also guide the description of strongly correlated quantum matter.