Strong and weak symmetries and their spontaneous symmetry breaking in mixed states emerging from the quantum Ising model under multiple decoherence
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913818377977856 |
|---|---|
| author | Orito, Takahiro Kuno, Yoshihito Ichinose, Ikuo |
| author_facet | Orito, Takahiro Kuno, Yoshihito Ichinose, Ikuo |
| contents | Discovering and categorizing quantum orders in mixed many-body systems are currently one of the most important problems. Specific types of decoherence applied to typical quantum many-body states can induce a novel kind of mixed state accompanying characteristic symmetry orders, which has no counterparts in pure many-body states. We study phenomena generated by interplay between two types of decoherence applied to the one-dimensional transverse field Ising model (TFIM). We show that in the doubled Hilbert space formalism, the decoherence can be described by filtering operation applied to matrix product states (MPS) defined in the doubled Hilbert system. The filtering operation induces specific deformation of the MPS, which approximates the ground state of a certain parent Hamiltonian in the doubled Hilbert space. In the present case, such a parent Hamiltonian is the quantum Ashkin-Teller model, having a rich phase diagram with a critical lines and quantum phase transitions. By investigating the deformed MPS, we find various types of mixed states emergent from the ground states of the TFIM, and clarify phase transitions between them. In that study, strong and weak $Z_2$ symmetries play an important role, for which we introduce efficient order parameters, such as Rényi-2 correlators, entanglement entropy, etc., in the doubled Hilbert space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong and weak symmetries and their spontaneous symmetry breaking in mixed states emerging from the quantum Ising model under multiple decoherence Orito, Takahiro Kuno, Yoshihito Ichinose, Ikuo Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons Discovering and categorizing quantum orders in mixed many-body systems are currently one of the most important problems. Specific types of decoherence applied to typical quantum many-body states can induce a novel kind of mixed state accompanying characteristic symmetry orders, which has no counterparts in pure many-body states. We study phenomena generated by interplay between two types of decoherence applied to the one-dimensional transverse field Ising model (TFIM). We show that in the doubled Hilbert space formalism, the decoherence can be described by filtering operation applied to matrix product states (MPS) defined in the doubled Hilbert system. The filtering operation induces specific deformation of the MPS, which approximates the ground state of a certain parent Hamiltonian in the doubled Hilbert space. In the present case, such a parent Hamiltonian is the quantum Ashkin-Teller model, having a rich phase diagram with a critical lines and quantum phase transitions. By investigating the deformed MPS, we find various types of mixed states emergent from the ground states of the TFIM, and clarify phase transitions between them. In that study, strong and weak $Z_2$ symmetries play an important role, for which we introduce efficient order parameters, such as Rényi-2 correlators, entanglement entropy, etc., in the doubled Hilbert space. |
| title | Strong and weak symmetries and their spontaneous symmetry breaking in mixed states emerging from the quantum Ising model under multiple decoherence |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2412.12738 |