Non-trivial extensions of Landau-Fermi liquid theory
Many-body perturbation theory & quantum statistical field theory
Quantum criticality in electron liquids
I am also very interested (and currently beginning projects) in many-body chaos, many-body entanglement, and applications of holography to many-body fermionic systems.
2017 - present
Publications/Preprints:
J.T. Heath & K.S. Bedell. J. Phys. A: Math. Theor. 52 315001 (2019); arXiv:1709.04483
J.T. Heath & K.S. Bedell. J. Phys.: Condens. Matter 32 485602 (2020); arXiv:1903.00619
Developed a theory of quantum statistics describing Majorana-like fermions that conserve total particle number. Also predicted exotic thermodynamic observables in said system.
Extended the Majorana-like gas to an interacting "Landau-Majorana" liquid, and subsequently described collective modes and Fermi surface instabilities.
Currently extending the interacting Landau-Majorana liquid to explain thermodynamic signatures of an exotic metallic phase in certain Kitaev magnets.
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2017 - present
Publications/Preprints:
J.T. Heath & K.S. Bedell. New J. Phys. 22 063011 (2020); arXiv:1906.00929
Luttinger's theorem states that the volume of the Fermi surface remains invariant as we turn on some arbitrary interaction. However, when and where Luttinger's theorem applies is an open question.
Developed the necessary and sufficient conditions on the fermionic self energy under which Luttinger's theorem may be applied.
Currently researching possible extensions of Landau-Fermi liquid theory by exploiting Luttinger's theorem in a system where the quasiparticle paradigm breaks down.
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2019 - present
Publications/Preprints:
J.T. Heath. J. Low Temp. Phys. 201, 200-212 (2020); arXiv:2001.08230
Investigated Fermi liquid properties of systems with power-law Green's functions, finding that Luttinger's theorem and the Landau quasiparticle paradigm are incompatible in the presence of non-trivial power-law behavior
Such a work has potential to describe the exotic fermionic phases seen in underdoped pseudogap phase and the optimally-doped "strange metal" phase of the cuprate superconductors
Currently attempting to rigorously investigate the behavior of Fermi liquids in the presence of non-trivial scaling of charge carriers
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2020 - present
Publications/Preprints:
J.T. Heath & K.S. Bedell. Submitted to SciPost Physics; arXiv:2008.07535
Currently looking into the interplay of phase separation and ferromagnetism in a generic fermionic liquid via a gauge-dependent extension of conventional Landau-Fermi liquid theory
Such a work has important implications for spintronics, where manipulation of an electron's spin could be utilized for efficient data storage, transfer, and computing
I am also investigating the possibility of an analog Higgs mechanism in an itinerant ferromagnet via the same gauge-dependent Landau-Fermi liquid approach
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2019 - 2020
Publications/Preprints:
J.T. Heath, M.P. Gochan, & K.S. Bedell. J. Phys. A: Math. Theor. 53 225203 (2020); arXiv:1912.03427
M.P. Gochan, J.T. Heath, & K.S. Bedell. J. Phys.: Condens. Matter 32 345602 (2020); arXiv:1912.02699
Investigated the implications of dimensional reduction on Landau-Fermi liquid transport via a Chebyshev polynomial expansion of the two-dimensional Landau parameter
Found exotic behavior of zero sound in 2D Fermi liquids, along with increased stability against Fermi surface deformations unseen in the 3D system
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Email: heathjo@bc.edu
Twitter: @JoshuahHeath
Office: Higgins 328, 140 Commonwealth Ave.
Chestnut Hill, MA