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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2504.13258 |
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| _version_ | 1866914131769032704 |
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| author | Perugu, Rishik Haldar, Arijit Banerjee, Sumilan |
| author_facet | Perugu, Rishik Haldar, Arijit Banerjee, Sumilan |
| contents | Non-equilibrium dynamics of unentangled and entangled pure states in interacting quantum systems is crucial for harnessing quantum information and to understand quantum thermalization. We develop a general Schwinger-Keldysh (SK) field theory for non-equilibrium dynamics of pure states of fermions. We apply our formalism to study the time evolution of initial density inhomogeneity and multi-point correlations of pure states in the complex Sachdev-Ye-Kitaev (SYK) models. We demonstrate a remarkable universality in the dynamics of pure states in the SYK model. We show that dynamics of almost all pure states in a fixed particle number sector is solely determined by a set of universal large-$N$ Kadanoff-Baym equations. Moreover, irrespective of the initial state the site- and disorder-averaged Green's function thermalizes instantaneously, whereas local and non-local Green's functions have finite thermalization rate. We provide understanding of our numerical and analytical large-$N$ results through random-matrix theory (RMT) analysis. Furthermore, we show that the thermalization of an initial pure product state in the non-interacting SYK$_2$ model is independent of fermion filling and an initial density inhomogeneity decays with weak but long lived oscillations due to dephasing. In contrast, the interacting SYK$_{q\geq 4}$ model thermalizes slower than the non-interacting model and exhibits filling-dependent monotonic relaxation of initial inhomogeneity. For evolution of entangled pure states, we show that the initial entanglement is encoded in the non-local and/or multi-point quantum correlations that relax as the system thermalizes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13258 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model Perugu, Rishik Haldar, Arijit Banerjee, Sumilan Strongly Correlated Electrons High Energy Physics - Theory Non-equilibrium dynamics of unentangled and entangled pure states in interacting quantum systems is crucial for harnessing quantum information and to understand quantum thermalization. We develop a general Schwinger-Keldysh (SK) field theory for non-equilibrium dynamics of pure states of fermions. We apply our formalism to study the time evolution of initial density inhomogeneity and multi-point correlations of pure states in the complex Sachdev-Ye-Kitaev (SYK) models. We demonstrate a remarkable universality in the dynamics of pure states in the SYK model. We show that dynamics of almost all pure states in a fixed particle number sector is solely determined by a set of universal large-$N$ Kadanoff-Baym equations. Moreover, irrespective of the initial state the site- and disorder-averaged Green's function thermalizes instantaneously, whereas local and non-local Green's functions have finite thermalization rate. We provide understanding of our numerical and analytical large-$N$ results through random-matrix theory (RMT) analysis. Furthermore, we show that the thermalization of an initial pure product state in the non-interacting SYK$_2$ model is independent of fermion filling and an initial density inhomogeneity decays with weak but long lived oscillations due to dephasing. In contrast, the interacting SYK$_{q\geq 4}$ model thermalizes slower than the non-interacting model and exhibits filling-dependent monotonic relaxation of initial inhomogeneity. For evolution of entangled pure states, we show that the initial entanglement is encoded in the non-local and/or multi-point quantum correlations that relax as the system thermalizes. |
| title | Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.13258 |