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Charting the space of ground states with tensor networks
by Marvin Qi, David T. Stephen, Xueda Wen, Daniel Spiegel, Markus J. Pflaum, Agnès Beaudry, Michael Hermele
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Submission summary
| Authors (as registered SciPost users): | Marvin Qi |
| Submission information | |
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| Preprint Link: | scipost_202306_00044v3 (pdf) |
| Date accepted: | May 12, 2025 |
| Date submitted: | April 23, 2025, 10:58 p.m. |
| Submitted by: | Qi, Marvin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We employ matrix product states (MPS) and tensor networks to study topological properties of the space of ground states of gapped many-body systems. We focus on families of states in one spatial dimension, where each state can be represented as an injective MPS of finite bond dimension. Such states are short-range entangled ground states of gapped local Hamiltonians. To such parametrized families over X we associate a gerbe, which generalizes the line bundle of ground states in zero-dimensional families (i.e. in few-body quantum mechanics). The nontriviality of the gerbe is measured by a class in H3(X, Z), which is believed to classify one-dimensional parametrized systems. We show that when the gerbe is nontrivial, there is an obstruction to representing the family of ground states with an MPS tensor that is continuous everywhere on X. We illustrate our construction with two examples of nontrivial parametrized systems over X = S3 and X = RP2 ×S1. Finally, we sketch using tensor network methods how the construction extends to higher dimensional parametrized systems, with an example of a two-dimensional parametrized system that gives rise to a nontrivial 2-gerbe over X = S4.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
Updated journal references and included references to relevant articles that have appeared since the posting of this work to arXiv.
Published as SciPost Phys. 18, 168 (2025)