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1. Yukawa-Lorentz symmetry in non-Hermitian Dirac materials

   https://doi.org/10.1038/s42005-024-01629-2  

   Juričić, Vladimir; Roy, Bitan (December 2024, Communications Physics)

   Abstract Lorentz space–time symmetry represents a unifying feature of the fundamental forces, typically manifest at sufficiently high energies, while in quantum materials it emerges in the deep low-energy regime. However, its fate in quantum materials coupled to an environment thus far remained unexplored. We here introduce a general framework of constructing symmetry-protected Lorentz-invariant non-Hermitian (NH) Dirac semimetals (DSMs), realized by invoking masslike anti-Hermitian Dirac operators to its Hermitian counterpart. Such NH DSMs feature purely real or imaginary isotropic linear band dispersion, yielding a vanishing density of states. Dynamic mass orderings in NH DSMs thus take place for strong Hubbard-like local interactions through a quantum phase transition, hosting a non-Fermi liquid, beyond which the system becomes an insulator. We show that depending on the internal Clifford algebra between the NH Dirac operator and candidate mass order-parameter, the resulting quantum-critical fluid either remains coupled with the environment or recovers full Hermiticity by decoupling from the bath, while always enjoying an emergent Yukawa-Lorentz symmetry in terms of a unique terminal velocity. We showcase the competition between such mass orderings, their hallmarks on quasi-particle spectra in the ordered phases, and the relevance of our findings for correlated designer NH Dirac materials. 

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2. Quantum electrodynamics of non-Hermitian Dirac fermions

   https://doi.org/10.1007/JHEP01(2024)143  

   Murshed, Sk Asrap; Roy, Bitan (January 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We develop an effective quantum electrodynamics for non-Hermitian (NH) Dirac materials interacting with photons. These systems are described by nonspatial symmetry protected Lorentz invariant NH Dirac operators, featuring two velocity parametersυ_Handυ_NHassociated with the standard Hermitian and a masslike anti-Hermitian Dirac operators, respectively. They display linear energy-momentum relation, however, in terms of an effective Fermi velocity$$ {\upsilon}_{\textrm{F}}=\sqrt{\upsilon_{\textrm{H}}^2-{\upsilon}_{\textrm{NH}}^2} $$ ${\upsilon }_F=\sqrt{{\upsilon }_H^2-{\upsilon }_{\mathrm{NH}}^2}$of NH Dirac fermions. Interaction with the fluctuating electromagnetic radiation then gives birth to an emergent Lorentz symmetry in this family of NH Dirac materials in the deep infrared regime, where the system possesses a unique terminal velocityυ_F=c, withcbeing the speed of light. While in two dimensions such a terminal velocity is set by the speed of light in the free space, dynamic screening in three spatial dimensions permits its nonuniversal values. Manifestations of such an emergent spacetime symmetry on the scale dependence of various physical observables in correlated NH Dirac materials are discussed. 

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3. Field Theory of Interacting Boundary Gravitons

   https://doi.org/10.21468/SciPostPhys.13.2.038  

   Ebert, Stephen; Hijano, Eliot; Kraus, Per; Monten, Ruben; Myers, Richard M. (January 2022, SciPost Physics)

   Pure three-dimensional gravity is a renormalizable theory with twofree parameters labelled byG $G$and\Lambda $\Lambda$.As a consequence, correlation functions of the boundary stress tensor inAdS_3 ${}_3$are uniquely fixed in terms of one dimensionless parameter, which is thecentral charge of the Virasoro algebra. The same argument implies thatAdS_3 ${}_3$gravity at a finite radial cutoff is a renormalizable theory, but nowwith one additional parameter corresponding to the cutoff location. Thistheory is conjecturally dual to aT\overline{T} $T\overline{T}$-deformedCFT, assuming that such theories actually exist. To elucidate this, westudy the quantum theory of boundary gravitons living on a cutoff planarboundary and the associated correlation functions of the boundary stresstensor. We compute stress tensor correlation functions to two-loop order(G $G$being the loop counting parameter), extending existing tree levelresults. This is made feasible by the fact that the boundary gravitonaction simplifies greatly upon making a judicious field redefinition,turning into the Nambu-Goto action. After imposing Lorentz invariance,the correlators at this order are found to be unambiguous up to a singleundetermined renormalization parameter. 

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4. Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons

   https://doi.org/10.21468/SciPostPhys.15.2.043  

   Tanhayi Ahari, Mostafa; Bandyopadhyay, Sumanta; Nussinov, Zohar; Seidel, Alexander; Ortiz, Gerardo (January 2023, SciPost Physics)

   We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor\nu=2/3 $\nu =2/3$. The emergent Entangled Pauli Principle (EPP), introduced in [Phys. Rev. B 98, 161118(R) (2018)] and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-bodyM $M$-clustering property within any given number of Landau levels, that is, wave functions withM $M$th-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for theM=3 $M=3$case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of [Phys. Rev. X 1, 021015 (2011)] to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement. 

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5. Non-invertible Peccei-Quinn symmetry, natural 2HDM alignment, and the visible axion

   https://doi.org/10.1007/JHEP02(2025)178  

   Delgado, Antonio; Koren, Seth (February 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> We identify$$ {m}_{12}^2 $$ $m_{12}^2$as a spurion of non-invertible Peccei-Quinn symmetry in the type II 2HDM with gauged quark flavor. Thus a UV theory which introduces quark color-flavor monopoles can naturally realize alignment without decoupling and can furthermore revive the Weinberg-Wilczek axion. As an example we consider the SU(9) theory of color-flavor unification, which needs no new fermions. This is the first model-building use of non-invertible symmetry to find a Dirac natural explanation for a smallrelevantparameter. 

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