Gross-Neveu-Yukawa models at four loops and quantum critical behavior of Dirac systems

ORAL

Abstract

Dirac and Weyl fermions appear as quasi-particle excitations in many different condensed-matter systems. They display various quantum transitions which represent unconventional universality classes related to the variants of the Gross-Neveu model. In my talk, I present a study of the bosonized version of the standard Gross-Neveu models -- the Gross-Neveu-Yukawa theories -- at four-loop order, and compute critical exponents in 4−epsilon dimensions for general number of fermion flavors. Our results fully encompass the previously known two-loop calculations, and agree with the known four-loop results in the purely bosonic limit of the theory. We also find the exponents to satisfy the emergent super-scaling relations in the limit of a single-component fermion, order by order up to four loops. Finally, we apply the computed series for the exponents and their Pade approximants to several phase transitions of current interest: metal-insulator transitions of spin-1/2 and spinless fermions on the honeycomb lattice, emergent supersymmetric surface field theory in topological phases, as well as the disorder-induced quantum transition in Weyl semimetals. Comparison with the results of other analytical and numerical methods is discussed.

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Presenters

  • Michael Scherer

    University of Cologne

Authors

  • Michael Scherer

    University of Cologne

  • Alexey Feofanov

    University of Innsbruck, University of Waterloo, Korea University, Okinawa Institute of Science and Technology, University of California - Los Angeles, The University of Manchester, University of Puerto Rico at Humacao, Department of Physics & Electronics, University of Puerto Rico at Cayey, Department of Mathematics-Physics, Oak Ridge National Lab, Max Planck Institute for Chemical Physics of Solids, Department of Physics, University of Puerto Rico, Electrical Engineering Department, University of Arkansas, Department of Physics, University of Arkansas, School of Basic Sciences at IIT Mandi, H.P., India, Computational Biology, Flatiron Institute, Physics, Hong Kong Univ of Sci & Tech, University of California, Los Angeles, Max Planck Inst, Institute for Theoretical Physics, University of Cologne, Department of Physics, Simon Fraser University, Deutsches Elektronen Synchrotron (DESY), Institut fur Theoretische Physik, Univerisitat zu Berlin, Institut fur Physik, Univerisitat zu Berlin, Plymouth State University, The Graduate Center, CUNY, Nordita, KTH Royal Institute of Technology and Stockholm University, Univ of Connecticut - Storrs, Univ Stuttgart, University of Chicago, University of Texas at El Paso, University of Tulsa, California Institute of Technology, Georgia Institute of Technology, Universite Paris Diderot, Laboratoire MPQ, Universita di Trento, BEC Center, ICTP Trieste, Universita di Pisa, Inst of Physics Academia Sinica, Batelle, Cal State Univ- San Bernardino, Chemical Engineering, University of Michigan, QCD Labs, Department of Applied Physics, Aalto University, Yale University, MIT, Harvard Univ, Chemical & Environmental Engineering, University of California, Riverside, University of Frankfurt, Germany, University of Hamburg, Germany, Naval Research Laboratory, Cornell Univ, National Institute for Material Science, U.S. Naval Research Laboratory, Washington DC, Materials Engineering, University of Santa Barbara, Institute of Physics, Chinese Academy of Sciences, Univ of Texas, Arlington, MIT Lincoln Laboratory, University of Sydney, Iowa State University, Purdue University, Kansas State University, University of Maryland, John Hopkins University, Universite de Sherbrooke, Physics, Konkuk University, Perimeter Institute, University of Waterloo, D-Wave, San Jose State University, Université de Sherbrooke, Institute of Physics, EPFL - Lausanne​

  • Alexey Feofanov

    University of Innsbruck, University of Waterloo, Korea University, Okinawa Institute of Science and Technology, University of California - Los Angeles, The University of Manchester, University of Puerto Rico at Humacao, Department of Physics & Electronics, University of Puerto Rico at Cayey, Department of Mathematics-Physics, Oak Ridge National Lab, Max Planck Institute for Chemical Physics of Solids, Department of Physics, University of Puerto Rico, Electrical Engineering Department, University of Arkansas, Department of Physics, University of Arkansas, School of Basic Sciences at IIT Mandi, H.P., India, Computational Biology, Flatiron Institute, Physics, Hong Kong Univ of Sci & Tech, University of California, Los Angeles, Max Planck Inst, Institute for Theoretical Physics, University of Cologne, Department of Physics, Simon Fraser University, Deutsches Elektronen Synchrotron (DESY), Institut fur Theoretische Physik, Univerisitat zu Berlin, Institut fur Physik, Univerisitat zu Berlin, Plymouth State University, The Graduate Center, CUNY, Nordita, KTH Royal Institute of Technology and Stockholm University, Univ of Connecticut - Storrs, Univ Stuttgart, University of Chicago, University of Texas at El Paso, University of Tulsa, California Institute of Technology, Georgia Institute of Technology, Universite Paris Diderot, Laboratoire MPQ, Universita di Trento, BEC Center, ICTP Trieste, Universita di Pisa, Inst of Physics Academia Sinica, Batelle, Cal State Univ- San Bernardino, Chemical Engineering, University of Michigan, QCD Labs, Department of Applied Physics, Aalto University, Yale University, MIT, Harvard Univ, Chemical & Environmental Engineering, University of California, Riverside, University of Frankfurt, Germany, University of Hamburg, Germany, Naval Research Laboratory, Cornell Univ, National Institute for Material Science, U.S. Naval Research Laboratory, Washington DC, Materials Engineering, University of Santa Barbara, Institute of Physics, Chinese Academy of Sciences, Univ of Texas, Arlington, MIT Lincoln Laboratory, University of Sydney, Iowa State University, Purdue University, Kansas State University, University of Maryland, John Hopkins University, Universite de Sherbrooke, Physics, Konkuk University, Perimeter Institute, University of Waterloo, D-Wave, San Jose State University, Université de Sherbrooke, Institute of Physics, EPFL - Lausanne​

  • Alexey Feofanov

    University of Innsbruck, University of Waterloo, Korea University, Okinawa Institute of Science and Technology, University of California - Los Angeles, The University of Manchester, University of Puerto Rico at Humacao, Department of Physics & Electronics, University of Puerto Rico at Cayey, Department of Mathematics-Physics, Oak Ridge National Lab, Max Planck Institute for Chemical Physics of Solids, Department of Physics, University of Puerto Rico, Electrical Engineering Department, University of Arkansas, Department of Physics, University of Arkansas, School of Basic Sciences at IIT Mandi, H.P., India, Computational Biology, Flatiron Institute, Physics, Hong Kong Univ of Sci & Tech, University of California, Los Angeles, Max Planck Inst, Institute for Theoretical Physics, University of Cologne, Department of Physics, Simon Fraser University, Deutsches Elektronen Synchrotron (DESY), Institut fur Theoretische Physik, Univerisitat zu Berlin, Institut fur Physik, Univerisitat zu Berlin, Plymouth State University, The Graduate Center, CUNY, Nordita, KTH Royal Institute of Technology and Stockholm University, Univ of Connecticut - Storrs, Univ Stuttgart, University of Chicago, University of Texas at El Paso, University of Tulsa, California Institute of Technology, Georgia Institute of Technology, Universite Paris Diderot, Laboratoire MPQ, Universita di Trento, BEC Center, ICTP Trieste, Universita di Pisa, Inst of Physics Academia Sinica, Batelle, Cal State Univ- San Bernardino, Chemical Engineering, University of Michigan, QCD Labs, Department of Applied Physics, Aalto University, Yale University, MIT, Harvard Univ, Chemical & Environmental Engineering, University of California, Riverside, University of Frankfurt, Germany, University of Hamburg, Germany, Naval Research Laboratory, Cornell Univ, National Institute for Material Science, U.S. Naval Research Laboratory, Washington DC, Materials Engineering, University of Santa Barbara, Institute of Physics, Chinese Academy of Sciences, Univ of Texas, Arlington, MIT Lincoln Laboratory, University of Sydney, Iowa State University, Purdue University, Kansas State University, University of Maryland, John Hopkins University, Universite de Sherbrooke, Physics, Konkuk University, Perimeter Institute, University of Waterloo, D-Wave, San Jose State University, Université de Sherbrooke, Institute of Physics, EPFL - Lausanne​

  • Alexey Feofanov

    University of Innsbruck, University of Waterloo, Korea University, Okinawa Institute of Science and Technology, University of California - Los Angeles, The University of Manchester, University of Puerto Rico at Humacao, Department of Physics & Electronics, University of Puerto Rico at Cayey, Department of Mathematics-Physics, Oak Ridge National Lab, Max Planck Institute for Chemical Physics of Solids, Department of Physics, University of Puerto Rico, Electrical Engineering Department, University of Arkansas, Department of Physics, University of Arkansas, School of Basic Sciences at IIT Mandi, H.P., India, Computational Biology, Flatiron Institute, Physics, Hong Kong Univ of Sci & Tech, University of California, Los Angeles, Max Planck Inst, Institute for Theoretical Physics, University of Cologne, Department of Physics, Simon Fraser University, Deutsches Elektronen Synchrotron (DESY), Institut fur Theoretische Physik, Univerisitat zu Berlin, Institut fur Physik, Univerisitat zu Berlin, Plymouth State University, The Graduate Center, CUNY, Nordita, KTH Royal Institute of Technology and Stockholm University, Univ of Connecticut - Storrs, Univ Stuttgart, University of Chicago, University of Texas at El Paso, University of Tulsa, California Institute of Technology, Georgia Institute of Technology, Universite Paris Diderot, Laboratoire MPQ, Universita di Trento, BEC Center, ICTP Trieste, Universita di Pisa, Inst of Physics Academia Sinica, Batelle, Cal State Univ- San Bernardino, Chemical Engineering, University of Michigan, QCD Labs, Department of Applied Physics, Aalto University, Yale University, MIT, Harvard Univ, Chemical & Environmental Engineering, University of California, Riverside, University of Frankfurt, Germany, University of Hamburg, Germany, Naval Research Laboratory, Cornell Univ, National Institute for Material Science, U.S. Naval Research Laboratory, Washington DC, Materials Engineering, University of Santa Barbara, Institute of Physics, Chinese Academy of Sciences, Univ of Texas, Arlington, MIT Lincoln Laboratory, University of Sydney, Iowa State University, Purdue University, Kansas State University, University of Maryland, John Hopkins University, Universite de Sherbrooke, Physics, Konkuk University, Perimeter Institute, University of Waterloo, D-Wave, San Jose State University, Université de Sherbrooke, Institute of Physics, EPFL - Lausanne​

  • Alexey Feofanov

    University of Innsbruck, University of Waterloo, Korea University, Okinawa Institute of Science and Technology, University of California - Los Angeles, The University of Manchester, University of Puerto Rico at Humacao, Department of Physics & Electronics, University of Puerto Rico at Cayey, Department of Mathematics-Physics, Oak Ridge National Lab, Max Planck Institute for Chemical Physics of Solids, Department of Physics, University of Puerto Rico, Electrical Engineering Department, University of Arkansas, Department of Physics, University of Arkansas, School of Basic Sciences at IIT Mandi, H.P., India, Computational Biology, Flatiron Institute, Physics, Hong Kong Univ of Sci & Tech, University of California, Los Angeles, Max Planck Inst, Institute for Theoretical Physics, University of Cologne, Department of Physics, Simon Fraser University, Deutsches Elektronen Synchrotron (DESY), Institut fur Theoretische Physik, Univerisitat zu Berlin, Institut fur Physik, Univerisitat zu Berlin, Plymouth State University, The Graduate Center, CUNY, Nordita, KTH Royal Institute of Technology and Stockholm University, Univ of Connecticut - Storrs, Univ Stuttgart, University of Chicago, University of Texas at El Paso, University of Tulsa, California Institute of Technology, Georgia Institute of Technology, Universite Paris Diderot, Laboratoire MPQ, Universita di Trento, BEC Center, ICTP Trieste, Universita di Pisa, Inst of Physics Academia Sinica, Batelle, Cal State Univ- San Bernardino, Chemical Engineering, University of Michigan, QCD Labs, Department of Applied Physics, Aalto University, Yale University, MIT, Harvard Univ, Chemical & Environmental Engineering, University of California, Riverside, University of Frankfurt, Germany, University of Hamburg, Germany, Naval Research Laboratory, Cornell Univ, National Institute for Material Science, U.S. Naval Research Laboratory, Washington DC, Materials Engineering, University of Santa Barbara, Institute of Physics, Chinese Academy of Sciences, Univ of Texas, Arlington, MIT Lincoln Laboratory, University of Sydney, Iowa State University, Purdue University, Kansas State University, University of Maryland, John Hopkins University, Universite de Sherbrooke, Physics, Konkuk University, Perimeter Institute, University of Waterloo, D-Wave, San Jose State University, Université de Sherbrooke, Institute of Physics, EPFL - Lausanne​