Higher Berry curvature from matrix product states
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918102836445184 |
|---|---|
| author | Shiozaki, Ken Heinsdorf, Niclas Ohyama, Shuhei |
| author_facet | Shiozaki, Ken Heinsdorf, Niclas Ohyama, Shuhei |
| contents | The higher Berry curvature was introduced by Kapustin and Spodyneiko as an extension of the Berry curvature in quantum mechanical systems with finite degrees of freedom to quantum many-body systems in finite spatial dimensions. In this paper, we propose an alternative formulation of the higher Berry curvature using translationally invariant matrix product states. They are the ground states of a set of gapped Hamiltonians which are evolved adiabatically through a discretized parameter space. Because matrix product states transform under a projective representation, evaluating the Berry curvature on a closed loop through parameter space is not sufficient to fix all the gauge degrees of freedom. To obtain a gauge-invariant real quantity, the higher-dimensional Berry curvature is evaluated on small tetrahedra in parameter space. Our numerical calculations confirm that the higher Berry curvature varies continuously throughout an adiabatic evolution and becomes quantized over a closed 3-dimensional parameter space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08109 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higher Berry curvature from matrix product states Shiozaki, Ken Heinsdorf, Niclas Ohyama, Shuhei Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics The higher Berry curvature was introduced by Kapustin and Spodyneiko as an extension of the Berry curvature in quantum mechanical systems with finite degrees of freedom to quantum many-body systems in finite spatial dimensions. In this paper, we propose an alternative formulation of the higher Berry curvature using translationally invariant matrix product states. They are the ground states of a set of gapped Hamiltonians which are evolved adiabatically through a discretized parameter space. Because matrix product states transform under a projective representation, evaluating the Berry curvature on a closed loop through parameter space is not sufficient to fix all the gauge degrees of freedom. To obtain a gauge-invariant real quantity, the higher-dimensional Berry curvature is evaluated on small tetrahedra in parameter space. Our numerical calculations confirm that the higher Berry curvature varies continuously throughout an adiabatic evolution and becomes quantized over a closed 3-dimensional parameter space. |
| title | Higher Berry curvature from matrix product states |
| topic | Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2305.08109 |