Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension
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| Format: | Preprint |
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2024
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| author | Sommer, Ophelia Evelyn Vishwanath, Ashvin Wen, Xueda |
| author_facet | Sommer, Ophelia Evelyn Vishwanath, Ashvin Wen, Xueda |
| contents | We propose a systematic wave function based approach to construct topological invariants for families of lattice systems that are short-range entangled using local parameter spaces. This construction is particularly suitable when given a family of tensor networks that can be viewed as the ground states of $d$ dimensional lattice systems, for which we construct the closed $(d+2)$-form higher Berry curvature, which is a generalization of the well known 2-form Berry curvature. Such $(d+2)$-form higher Berry curvature characterizes a flow of $(d+1)$-form higher Berry curvature in the system. Our construction is equally suitable for constructing other higher pumps, such as the (higher) Thouless pump in the presence of a global on-site $U(1)$ symmetry, which corresponds to a closed $d$-form. The cohomology classes of such higher differential forms are topological invariants and are expected to be quantized for short-range entangled states. We illustrate our construction with exactly solvable lattice models that are in nontrivial higher Berry classes in $d=2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_05323 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension Sommer, Ophelia Evelyn Vishwanath, Ashvin Wen, Xueda Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics We propose a systematic wave function based approach to construct topological invariants for families of lattice systems that are short-range entangled using local parameter spaces. This construction is particularly suitable when given a family of tensor networks that can be viewed as the ground states of $d$ dimensional lattice systems, for which we construct the closed $(d+2)$-form higher Berry curvature, which is a generalization of the well known 2-form Berry curvature. Such $(d+2)$-form higher Berry curvature characterizes a flow of $(d+1)$-form higher Berry curvature in the system. Our construction is equally suitable for constructing other higher pumps, such as the (higher) Thouless pump in the presence of a global on-site $U(1)$ symmetry, which corresponds to a closed $d$-form. The cohomology classes of such higher differential forms are topological invariants and are expected to be quantized for short-range entangled states. We illustrate our construction with exactly solvable lattice models that are in nontrivial higher Berry classes in $d=2$. |
| title | Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2405.05323 |