Random-mass disorder in the critical Gross-Neveu-Yukawa models
An important yet largely unsolved problem in the statistical mechanics of disordered quantum systems is to understand how quenched disorder affects quantum phase transitions in systems of itinerant fermions. In the clean limit, continuous quantum phase transitions of the symmetry-breaking type in Di...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-01-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321320303266 |
| _version_ | 1818426715769143296 |
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| author | Hennadii Yerzhakov Joseph Maciejko |
| author_facet | Hennadii Yerzhakov Joseph Maciejko |
| author_sort | Hennadii Yerzhakov |
| collection | DOAJ |
| description | An important yet largely unsolved problem in the statistical mechanics of disordered quantum systems is to understand how quenched disorder affects quantum phase transitions in systems of itinerant fermions. In the clean limit, continuous quantum phase transitions of the symmetry-breaking type in Dirac materials such as graphene and the surfaces of topological insulators are described by relativistic (2+1)-dimensional quantum field theories of the Gross-Neveu-Yukawa (GNY) type. We study the universal critical properties of the chiral Ising, XY, and Heisenberg GNY models perturbed by quenched random-mass disorder, both uncorrelated or with long-range power-law correlations. Using the replica method combined with a controlled triple epsilon expansion below four dimensions, we find a variety of new finite-randomness critical and multicritical points with nonzero Yukawa coupling between low-energy Dirac fields and bosonic order parameter fluctuations, and compute their universal critical exponents. Analyzing bifurcations of the renormalization-group flow, we find instances of the fixed-point annihilation scenario—continuously tuned by the power-law exponent of long-range disorder correlations and associated with an exponentially large crossover length—as well as the transcritical bifurcation and the supercritical Hopf bifurcation. The latter is accompanied by the birth of a stable limit cycle on the critical hypersurface, which represents the first instance of fermionic quantum criticality with emergent discrete scale invariance. |
| first_indexed | 2024-12-14T14:34:15Z |
| format | Article |
| id | doaj.art-7fd65cac2e3741d39da0fe3dcc132773 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-14T14:34:15Z |
| publishDate | 2021-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-7fd65cac2e3741d39da0fe3dcc1327732022-12-21T22:57:44ZengElsevierNuclear Physics B0550-32132021-01-01962115241Random-mass disorder in the critical Gross-Neveu-Yukawa modelsHennadii Yerzhakov0Joseph Maciejko1Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, CanadaDepartment of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada; Theoretical Physics Institute (TPI), University of Alberta, Edmonton, Alberta T6G 2E1, Canada; Corresponding author.An important yet largely unsolved problem in the statistical mechanics of disordered quantum systems is to understand how quenched disorder affects quantum phase transitions in systems of itinerant fermions. In the clean limit, continuous quantum phase transitions of the symmetry-breaking type in Dirac materials such as graphene and the surfaces of topological insulators are described by relativistic (2+1)-dimensional quantum field theories of the Gross-Neveu-Yukawa (GNY) type. We study the universal critical properties of the chiral Ising, XY, and Heisenberg GNY models perturbed by quenched random-mass disorder, both uncorrelated or with long-range power-law correlations. Using the replica method combined with a controlled triple epsilon expansion below four dimensions, we find a variety of new finite-randomness critical and multicritical points with nonzero Yukawa coupling between low-energy Dirac fields and bosonic order parameter fluctuations, and compute their universal critical exponents. Analyzing bifurcations of the renormalization-group flow, we find instances of the fixed-point annihilation scenario—continuously tuned by the power-law exponent of long-range disorder correlations and associated with an exponentially large crossover length—as well as the transcritical bifurcation and the supercritical Hopf bifurcation. The latter is accompanied by the birth of a stable limit cycle on the critical hypersurface, which represents the first instance of fermionic quantum criticality with emergent discrete scale invariance.http://www.sciencedirect.com/science/article/pii/S0550321320303266 |
| spellingShingle | Hennadii Yerzhakov Joseph Maciejko Random-mass disorder in the critical Gross-Neveu-Yukawa models Nuclear Physics B |
| title | Random-mass disorder in the critical Gross-Neveu-Yukawa models |
| title_full | Random-mass disorder in the critical Gross-Neveu-Yukawa models |
| title_fullStr | Random-mass disorder in the critical Gross-Neveu-Yukawa models |
| title_full_unstemmed | Random-mass disorder in the critical Gross-Neveu-Yukawa models |
| title_short | Random-mass disorder in the critical Gross-Neveu-Yukawa models |
| title_sort | random mass disorder in the critical gross neveu yukawa models |
| url | http://www.sciencedirect.com/science/article/pii/S0550321320303266 |
| work_keys_str_mv | AT hennadiiyerzhakov randommassdisorderinthecriticalgrossneveuyukawamodels AT josephmaciejko randommassdisorderinthecriticalgrossneveuyukawamodels |