Symmetry-breaking effects of instantons in parton gauge theories

Shankar, G.; Maciejko, Joseph

doi:10.1103/physrevb.104.035134

Cited by 3 publications

(23 citation statements)

References 64 publications

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“…Finally, in analogy with our previous work on bosons with U (1) symmetry [36], we show that the breaking of Z 2 symmetry in the confined, ordered phase can be understood as a nontrivial consequence of Euclidean Majorana zero modes (ZMs) bound to monopole-instantons. By contrast with monopole-instantons in U (1) theories, the latter carry here a Z 2 topological charge under the Z M 2 magnetic symmetry of SO(N ) gauge theory in (2+1)D. Under the assumption that the infrared effects of such instantons is adequately captured by a semiclassical instanton-gas treatment, the Euclidean ZMs lead to an effective interaction among Majorana fermions that is analogous to the 't Hooft vertex in quantum chromodynamics [37][38][39].…”

Section: Introductionsupporting

confidence: 72%

“…[35] in the context of dualities of (2+1)D quantum field theories with unitary gauge groups [42][43][44][45][46][47][48][49][50][51]. We also point out the key role of monopole-instantons and the Euclidean fermion ZMs bound to them in accounting for the physics of broken-symmetry phases [36].…”

Section: Warm-up: Bosons With U (1) Symmetrymentioning

confidence: 91%

“…In the presence of fermions, such instantons can additionally lead to symmetry-breaking effects [64]. In an instanton background a (g) µ of topological charge g, a (2+1)D Dirac fermion ψ of charge e and mass m possesses Euclidean ZMs given by [36]:…”

Section: Instantons Fermion Zero Modes and Superfluiditymentioning

confidence: 99%

“…where ψ 1± are the slow fields in the low-energy expansion f 1 (r) ≈ k=± e iK k •r ψ 1k (r), σ is the dual photon, ϑ is a topological angle analogous to the theta angle of 4D Yang-Mills theory, and γ is a certain 2 × 2 matrix in spinor space [36]. The operator M(x) = e 2πiσ(x) is a monopole operator that inserts 2π flux at a given point x in spacetime.…”

Section: Instantons Fermion Zero Modes and Superfluiditymentioning

confidence: 99%

“…In Sec. II, we review the parton description of bosons with U (1) symmetry [35,36], as a means to introduce the basic ideas and methods that we will generalize to Ising spins with Z 2 spin-flip symmetry. In Sec.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Continuous transition between Ising magnetic order and a chiral spin liquid

Shankar,

Lin,

Maciejko

2022

Preprint

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The competition between fractionalized spin-liquid states and magnetically ordered phases is an important paradigm in frustrated magnetism. Spin-orbit coupled Mott insulators with Ising-like magnetic anisotropies, such as Kitaev materials, are a particularly rich playground to explore this competition. In this work, we use effective field theory methods to show that a direct quantum phase transition can occur in two-dimensional (2D) Ising spin systems between a topologically ordered chiral spin liquid and a phase with magnetic long-range order. Such a transition can be protected by lattice symmetries and is described by a theory of massless Majorana fields coupled to non-Abelian SO(N ) gauge fields with a Chern-Simons term. We further show that Euclidean Majorana zero modes bound to Z2 monopole-instantons in the emergent non-Abelian gauge field are key to understanding spontaneous symmetry breaking in the ordered phase.

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Section: Introductionsupporting

confidence: 72%

Section: Warm-up: Bosons With U (1) Symmetrymentioning

confidence: 91%

Section: Instantons Fermion Zero Modes and Superfluiditymentioning

confidence: 99%

Section: Instantons Fermion Zero Modes and Superfluiditymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Continuous transition between Ising magnetic order and a chiral spin liquid

Shankar,

Lin,

Maciejko

2022

Preprint

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Continuous transition between Ising magnetic order and a chiral spin liquid

2022

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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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Symmetry-breaking effects of instantons in parton gauge theories

Cited by 3 publications

References 64 publications

Continuous transition between Ising magnetic order and a chiral spin liquid

Continuous transition between Ising magnetic order and a chiral spin liquid

Continuous transition between Ising magnetic order and a chiral spin liquid

Monopoles in Dirac spin liquids and their symmetries from instanton calculus

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