Twisted quantum doubles are sign problem-free
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914544183410688 |
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| author | Shackleton, Leyna |
| author_facet | Shackleton, Leyna |
| contents | The sign problem is one of the central obstacles to efficiently simulating quantum many-body systems. It is commonly believed that some phases of matter, such as the double semion model, have an intrinsic sign problem and can never be realized in a local sign problem-free Hamiltonian due to the non-positivity of the wavefunction. We show that this is not the case. Despite failing to be stoquastic - the standard criteria for the existence of a sign problem - the double semion model as well as all twisted quantum double phases of matter for finite groups $\mathcal{G}$ can be realized in local Hamiltonians that are sign problem-free within a stochastic series expansion. The lack of a sign problem is not fine-tuned and does not require the Hamiltonian to be exactly solvable, with sign problem-free perturbations allowing access to a variety of topological phase transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03708 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twisted quantum doubles are sign problem-free Shackleton, Leyna Strongly Correlated Electrons The sign problem is one of the central obstacles to efficiently simulating quantum many-body systems. It is commonly believed that some phases of matter, such as the double semion model, have an intrinsic sign problem and can never be realized in a local sign problem-free Hamiltonian due to the non-positivity of the wavefunction. We show that this is not the case. Despite failing to be stoquastic - the standard criteria for the existence of a sign problem - the double semion model as well as all twisted quantum double phases of matter for finite groups $\mathcal{G}$ can be realized in local Hamiltonians that are sign problem-free within a stochastic series expansion. The lack of a sign problem is not fine-tuned and does not require the Hamiltonian to be exactly solvable, with sign problem-free perturbations allowing access to a variety of topological phase transitions. |
| title | Twisted quantum doubles are sign problem-free |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2509.03708 |