Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets (2404.11654v4)
Abstract: 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 $1/2$ magnetic systems on $2d$ lattices. In particular, the DSL in square lattice spin-$1/2$ magnets is described at low energies by $(2+1)d$ quantum electrodynamics with $N_f=4$ flavors of massless Dirac fermions minimally coupled to an emergent $U(1)$ 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.
- L. Savary and L. Balents, Reports on Progress in Physics 80, 016502 (2017).
- J. Knolle and R. Moessner, Annual Review of Condensed Matter Physics 10, 451 (2019).
- The DSL used to be called the Algebraic Spin Liquid (ASL) in the literature. The terminology DSL emphasizes the origins of this state through a parton mean field description of the spin model where there are spinons with Dirac dispersion. The terminology ASL emphasizes the algebraic correlations of local operators which is a property of the low energy physics irrespective of the particular parton description. Indeed we should regard the low energy theory abstractly as described by an interacting conformal field theory with a particular global symmetry that has a particular ’t Hooft anomaly.
- I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988).
- L. B. Ioffe and A. I. Larkin, Phys. Rev. B 39, 8988 (1989).
- W. Rantner and X.-G. Wen, Physical Review Letters 86, 3871 (2001).
- M. B. Hastings, Physical Review B 63, 014413 (2000).
- T. Senthil and P. A. Lee, Phys. Rev. B 71, 174515 (2005).
- J. Alicea, Physical Review B 78 (2008), 10.1103/physrevb.78.035126.
- Z. Bi and T. Senthil, Physical Review X 9, 021034 (2019).
- W. Rantner and X.-G. Wen, Phys. Rev. B 66, 144501 (2002).
- C.-M. Jian and C. Xu, Phys. Rev. B 101, 035118 (2020).
- T. Senthil, “Deconfined quantum critical points: a review,” (2023), arXiv:2306.12638 [cond-mat.str-el] .
- We include a subscript g𝑔gitalic_g to emphasize that this is a gauge group.
- Rotations by the Z2subscript𝑍2Z_{2}italic_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT element of the center of SO(6)𝑆𝑂6SO(6)italic_S italic_O ( 6 ) can be compensated by a U(1)top𝑈subscript1𝑡𝑜𝑝U(1)_{top}italic_U ( 1 ) start_POSTSUBSCRIPT italic_t italic_o italic_p end_POSTSUBSCRIPT rotation which is why SO(6)×U(1)top𝑆𝑂6𝑈subscript1𝑡𝑜𝑝SO(6)\times U(1)_{top}italic_S italic_O ( 6 ) × italic_U ( 1 ) start_POSTSUBSCRIPT italic_t italic_o italic_p end_POSTSUBSCRIPT is modded by Z2subscript𝑍2Z_{2}italic_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT.
- The Lorentz symmetry is obviously not present in the lattice model but is an emergent low energy symmetry, as can be shown explicitly within a large-Nfsubscript𝑁𝑓N_{f}italic_N start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT expansionHermele et al. (2005).
- A. Polyakov, Nuclear Physics B 120, 429 (1977).
- N. Karthik and R. Narayanan, Physical Review D 94, 065026 (2016a).
- N. Karthik and R. Narayanan, Physical Review D 93, 045020 (2016b).
- N. Karthik and R. Narayanan, (2024), arXiv:2401.01856 [hep-lat] .
- M. Levin and T. Senthil, Phys. Rev. B 70, 220403 (2004).
- C. Wang and T. Senthil, Phys. Rev. B 89, 195124 (2014).
- A. Tanaka and X. Hu, Physical Review Letters 95, 036402 (2005).
- T. Senthil and M. P. A. Fisher, Physical Review B 74, 064405 (2006).
- Here we make the further assumption that other SO(5)𝑆𝑂5SO(5)italic_S italic_O ( 5 ) breaking perturbations with higher scaling dimension (at the QED33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT fixed point) generated once κ≠0𝜅0\kappa\neq 0italic_κ ≠ 0 stay sufficiently small that we can ignore them and study the theory in the (κ,λ)𝜅𝜆(\kappa,\lambda)( italic_κ , italic_λ ) plane; then the κ=0𝜅0\kappa=0italic_κ = 0 theory is SO(5)𝑆𝑂5SO(5)italic_S italic_O ( 5 ) invariant.
- R. Ma and C. Wang, Physical Review B 102, 020407 (2020).
- A. Nahum, Physical Review B 102, 201116 (2020).
Collections
Sign up for free to add this paper to one or more collections.