Finite time path field theory perturbative methods for local quantum spin chain quenches
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917849424986112 |
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| author | Kuić, Domagoj Knapp, Alemka Šaponja-Milutinović, Diana |
| author_facet | Kuić, Domagoj Knapp, Alemka Šaponja-Milutinović, Diana |
| contents | We discuss local magnetic field quenches using perturbative methods of finite time path field theory (FTPFT) in the following spin chains: Ising and XY in a transverse magnetic field. Their common characteristics are: (i) they are integrable via mapping to a second quantized noninteracting fermion problem; and (ii) when the ground state is nondegenerate (true for finite chains except in special cases), it can be represented as a vacuum of Bogoliubov fermions. By switching on a local magnetic field perturbation at finite time, the problem becomes nonintegrable and must be approached via numeric or perturbative methods. Using the formalism of FTPFT based on Wigner transforms (WTs) of projected functions, we show how to: (i) calculate the basic ``bubble'' diagram in the Loschmidt echo (LE) of a quenched chain to any order in the perturbation; and (ii) resum the generalized Schwinger--Dyson equation for the fermion two-point retarded functions in the ``bubble'' diagram, hence achieving the resummation of perturbative expansion of LE for a wide range of perturbation strengths under certain analyticity assumptions. Limitations of the assumptions and possible generalizations beyond it and also for other spin chains are further discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_03832 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite time path field theory perturbative methods for local quantum spin chain quenches Kuić, Domagoj Knapp, Alemka Šaponja-Milutinović, Diana Quantum Physics Statistical Mechanics High Energy Physics - Theory Mathematical Physics We discuss local magnetic field quenches using perturbative methods of finite time path field theory (FTPFT) in the following spin chains: Ising and XY in a transverse magnetic field. Their common characteristics are: (i) they are integrable via mapping to a second quantized noninteracting fermion problem; and (ii) when the ground state is nondegenerate (true for finite chains except in special cases), it can be represented as a vacuum of Bogoliubov fermions. By switching on a local magnetic field perturbation at finite time, the problem becomes nonintegrable and must be approached via numeric or perturbative methods. Using the formalism of FTPFT based on Wigner transforms (WTs) of projected functions, we show how to: (i) calculate the basic ``bubble'' diagram in the Loschmidt echo (LE) of a quenched chain to any order in the perturbation; and (ii) resum the generalized Schwinger--Dyson equation for the fermion two-point retarded functions in the ``bubble'' diagram, hence achieving the resummation of perturbative expansion of LE for a wide range of perturbation strengths under certain analyticity assumptions. Limitations of the assumptions and possible generalizations beyond it and also for other spin chains are further discussed. |
| title | Finite time path field theory perturbative methods for local quantum spin chain quenches |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2409.03832 |