Continuous transition between Ising magnetic order and a chiral spin liquid

Shankar, G.; Lin, Chi-Lun; Maciejko, Joseph

doi:10.1103/physrevb.106.245107

Cited by 1 publication

(2 citation statements)

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“…An analogous calculation for SO(N ) gauge theory with Majorana matter was done in Ref. [41], which studied confinement transitions out of a chiral spin liquid. Readers uninterested in the technical details of the calculation can safely proceed to the next section with just the final result [Eq.…”

Section: Resummation Of the Instanton Gasmentioning

confidence: 99%

“…We find that such an "adjoint mass" results in the existence of Euclidean zero modes (of the 3D massive Dirac operator) bound to instantons, distinct from the zero-energy modes that appear in the massless limit. Resumming the instanton gas results in the generation of an instanton-induced term in the effective Lagrangian dubbed the 't Hooft vertex [24,[41][42][43][44][45], which in this case turns out to be equivalent to the zero mode-dressed monopole operator found in the CFT approach. For ordered phases with (broken) symmetries fully captured by a fermion mass, we show that requiring the associated 't Hooft vertex to satisfy the same symmetries can be sufficient to compute monopole quantum numbers under microscopic symmetries.…”

Section: Introductionmentioning

confidence: 99%

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Monopoles in Dirac spin liquids and their symmetries from instanton calculus

Ganesh,

Maciejko

2024

SciPost Phys.

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The Dirac spin liquid (DSL) is a two-dimensional (2D) fractionalized Mott insulator featuring massless Dirac spinon excitations coupled to a compact U(1) gauge field, which allows for flux-tunneling instanton events described by magnetic monopoles in (2+1)D Euclidean spacetime. The state-operator correspondence of conformal field theory has been used recently to define associated monopole operators and determine their quantum numbers, which encode the microscopic symmetries of conventional ordered phases proximate to the DSL. In this work, we utilize semiclassical instanton methods not relying on conformal invariance to construct monopole operators directly in (2+1)D spacetime as instanton-induced ’t Hooft vertices, i.e., fermion-number-violating effective interactions originating from zero modes of the Euclidean Dirac operator in an instanton background. In the presence of a flavor-adjoint fermion mass, resummation of the instanton gas is shown to select the correct monopole to be proliferated, in accordance with predictions of the state-operator correspondence. We also show that our instanton-based approach is able to determine monopole quantum numbers on bipartite lattices.

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Section: Resummation Of the Instanton Gasmentioning

confidence: 99%