Duality and universal transport in mixed-dimension electrodynamics

Hsiao, Wei-Han; Son, D.

doi:10.1103/physrevb.96.075127

Cited by 36 publications

(68 citation statements)

References 31 publications

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“…The duality implies a inverse relation between the conductivities of the two theories, as discussed in Section 2.4.1 [9]. The same results is obtained in the case of electrodynamics of scalar particles [21]; there is a difference of a factor of two in the relation (2.50), i.e.…”

Section: )supporting

confidence: 61%

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Quantization of a self-dual conformal theory in (2 + 1) dimensions

Andreucci

Cappelli

Maffi

2020

J. High Energ. Phys.

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Compact nonlocal Abelian gauge theory in (2 + 1) dimensions, also known as loop model, is a massless theory with a critical line that is explicitly covariant under duality transformations. It corresponds to the large N F limit of self-dual electrodynamics in mixed three-four dimensions. It also provides a bosonic description for surface excitations of three-dimensional topological insulators. Upon mapping the model to a local gauge theory in (3 + 1) dimensions, we compute the spectrum of electric and magnetic solitonic excitations and the partition function on the three torus T 3 . Analogous results for the S 2 × S 1 geometry show that the theory is conformal invariant and determine the manifestly self-dual spectrum of conformal fields, corresponding to order-disorder excitations with fractional statistics.

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Section: )supporting

confidence: 61%

“…to the background defines the induced current, while the second derivative introduces the conductivity. As a consequence, the duality implies a reciprocal relation between conductivity tensors, σ ij (τ ) and σ kn ( τ ), i, j, k, n = 1, 2, of the two theories, as follows [9]:…”

Section: Bosonic Particle-vortex Dualitymentioning

confidence: 99%

Quantization of a self-dual conformal theory in (2 + 1) dimensions

Andreucci

Cappelli

Maffi

2020

J. High Energ. Phys.

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“…These basic dualities supported by our work represent a significant step in our understanding of ð2 þ 1ÞD conformal field theories. They also form the foundation of a large number of other recently proposed dualities [20,48,50,52,[75][76][77][78][79]. Moreover, they lend support to many other dualities that follow from the same logic and reasoning, such as the duality of Majorana fermions discussed in Refs.…”

Section: Discussionmentioning

confidence: 53%

Duality between the Deconfined Quantum-Critical Point and the Bosonic Topological Transition

et al. 2017

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Recently, significant progress has been made in (2 þ 1)-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden dualities; i.e., seemingly different field theories may actually be identical in the infrared limit. Among all the proposed dualities, one has attracted particular interest in the field of strongly correlated quantum-matter systems: the one relating the easy-plane noncompact CP 1 model (NCCP 1 ) and noncompact quantum electrodynamics (QED) with two flavors (N ¼ 2) of massless two-component Dirac fermions. The easyplane NCCP 1 model is the field theory of the putative deconfined quantum-critical point separating a planar (XY) antiferromagnet and a dimerized (valence-bond solid) ground state, while N ¼ 2 noncompact QED is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator. In this work, we present strong numerical support for the proposed duality. We realize the N ¼ 2 noncompact QED at a critical point of an interacting fermion model on the bilayer honeycomb lattice and study it using determinant quantum Monte Carlo (QMC) simulations. Using stochastic series expansion QMC simulations, we study a planar version of the S ¼ 1=2 J-Q spin Hamiltonian (a quantum XY model with additional multispin couplings) and show that it hosts a continuous transition between the XY magnet and the valence-bond solid. The duality between the two systems, following from a mapping of their phase diagrams extending from their respective critical points, is supported by the good agreement between the critical exponents according to the proposed duality relationships. In the J-Q model, we find both continuous and first-order transitions, depending on the degree of planar anisotropy, with deconfined quantum criticality surviving only up to moderate strengths of the anisotropy. This explains previous claims of no deconfined quantum criticality in planar two-component spin models, which were in the stronganisotropy regime, and opens doors to further investigations of the global phase diagram of systems hosting deconfined quantum-critical points.

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“…Note added.-Recently, Hsiao and Son [72] also studied (2 þ 1)-dimensional Dirac fermions with marginally longrange interactions at self-duality (similar to our Sec. VI), focusing, in particular, on transport properties.…”

supporting

confidence: 53%

Symmetry and Duality in Bosonization of Two-Dimensional Dirac Fermions

2017

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Recent work on a family of boson-fermion mappings has emphasized the interplay of symmetry and duality: Phases related by a particle-vortex duality of bosons (fermions) are related by time-reversal symmetry in their fermionic (bosonic) formulation. We present exact mappings for a number of concrete models that make this property explicit on the operator level. We illustrate the approach with one-and two-dimensional quantum Ising models and then similarly explore the duality web of complex bosons and Dirac fermions in (2 þ 1) dimensions. We generalize the latter to systems with long-range interactions and discover a continuous family of dualities embedding the previously studied cases.

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Duality and universal transport in mixed-dimension electrodynamics

Cited by 36 publications

References 31 publications

Quantization of a self-dual conformal theory in (2 + 1) dimensions

Quantization of a self-dual conformal theory in (2 + 1) dimensions

Duality between the Deconfined Quantum-Critical Point and the Bosonic Topological Transition

Symmetry and Duality in Bosonization of Two-Dimensional Dirac Fermions

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