Disorder operators in two-dimensional Fermi and non-Fermi liquids through multidimensional bosonization
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| Format: | Preprint |
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2024
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| author | Cai, Kang-Le Cheng, Meng |
| author_facet | Cai, Kang-Le Cheng, Meng |
| contents | Disorder operators are a type of non-local observables for quantum many-body systems, measuring the fluctuations of symmetry charges inside a region. It has been shown that disorder operators can reveal global aspects of many-body states that are otherwise difficult to access through local measurements. We study the disorder operator for U(1) (charge or spin) symmetry in two-dimensional Fermi and non-Fermi liquid states, using the multidimensional bosonization formalism. For a region $A$, the logarithm of the charge disorder parameter in a Fermi liquid with isotropic interactions scales asymptotically as $l_A\ln l_A$, with $l_A$ being the linear size of the region $A$. We calculate the proportionality coefficient in terms of Landau parameters of the Fermi liquid theory. We then study models of the Fermi surface coupled to gapless bosonic fields realizing non-Fermi liquid states. In a simple spinless model, where the fermion density is coupled to a critical scalar, we find that at the quantum critical point the scaling behavior of the charge disorder operators is drastically modified to $l_A \ln^2 l_A$. We also consider the composite Fermi liquid state and argue that the charge disorder operator scales as $l_A$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_04334 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Disorder operators in two-dimensional Fermi and non-Fermi liquids through multidimensional bosonization Cai, Kang-Le Cheng, Meng Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics Disorder operators are a type of non-local observables for quantum many-body systems, measuring the fluctuations of symmetry charges inside a region. It has been shown that disorder operators can reveal global aspects of many-body states that are otherwise difficult to access through local measurements. We study the disorder operator for U(1) (charge or spin) symmetry in two-dimensional Fermi and non-Fermi liquid states, using the multidimensional bosonization formalism. For a region $A$, the logarithm of the charge disorder parameter in a Fermi liquid with isotropic interactions scales asymptotically as $l_A\ln l_A$, with $l_A$ being the linear size of the region $A$. We calculate the proportionality coefficient in terms of Landau parameters of the Fermi liquid theory. We then study models of the Fermi surface coupled to gapless bosonic fields realizing non-Fermi liquid states. In a simple spinless model, where the fermion density is coupled to a critical scalar, we find that at the quantum critical point the scaling behavior of the charge disorder operators is drastically modified to $l_A \ln^2 l_A$. We also consider the composite Fermi liquid state and argue that the charge disorder operator scales as $l_A$. |
| title | Disorder operators in two-dimensional Fermi and non-Fermi liquids through multidimensional bosonization |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2404.04334 |