Projected entangled pair states with flexible geometry
Projected entangled pair states (PEPS) are a class of quantum many-body states that generalize matrix product states for one-dimensional systems to higher dimensions. In recent years, PEPS have advanced understanding of strongly correlated systems, especially in two dimensions, e.g., quantum spin li...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.L012002 |
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| author | Siddhartha Patra Sukhbinder Singh Román Orús |
| author_facet | Siddhartha Patra Sukhbinder Singh Román Orús |
| author_sort | Siddhartha Patra |
| collection | DOAJ |
| description | Projected entangled pair states (PEPS) are a class of quantum many-body states that generalize matrix product states for one-dimensional systems to higher dimensions. In recent years, PEPS have advanced understanding of strongly correlated systems, especially in two dimensions, e.g., quantum spin liquids. Typically described by tensor networks on regular lattices (e.g., square, cubic), PEPS have also been adapted for irregular graphs; however, the computational cost becomes prohibitive for dense graphs with large vertex degrees. In this paper, we present a PEPS algorithm to simulate low-energy states and dynamics defined on arbitrary, fluctuating, and densely connected graphs. We introduce a cut-off, κ∈N, to constrain the vertex degree of the PEPS to a set but tunable value, which is enforced in the optimization by applying a simple edge-deletion rule, allowing the geometry of the PEPS to change and adapt dynamically to the system's correlation structure. We benchmark our flexible PEPS algorithm with simulations of classical spin glasses and quantum annealing on densely connected graphs with hundreds of spins, and also study the impact of tuning κ when simulating a uniform quantum spin model on a regular (square) lattice. Our paper opens the way to apply tensor network algorithms to arbitrary, even fluctuating, background geometries. |
| format | Article |
| id | doaj-art-ddf8b280f8684d5ba66bc41eedcb5847 |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-ddf8b280f8684d5ba66bc41eedcb58472025-01-06T15:45:16ZengAmerican Physical SocietyPhysical Review Research2643-15642025-01-0171L01200210.1103/PhysRevResearch.7.L012002Projected entangled pair states with flexible geometrySiddhartha PatraSukhbinder SinghRomán OrúsProjected entangled pair states (PEPS) are a class of quantum many-body states that generalize matrix product states for one-dimensional systems to higher dimensions. In recent years, PEPS have advanced understanding of strongly correlated systems, especially in two dimensions, e.g., quantum spin liquids. Typically described by tensor networks on regular lattices (e.g., square, cubic), PEPS have also been adapted for irregular graphs; however, the computational cost becomes prohibitive for dense graphs with large vertex degrees. In this paper, we present a PEPS algorithm to simulate low-energy states and dynamics defined on arbitrary, fluctuating, and densely connected graphs. We introduce a cut-off, κ∈N, to constrain the vertex degree of the PEPS to a set but tunable value, which is enforced in the optimization by applying a simple edge-deletion rule, allowing the geometry of the PEPS to change and adapt dynamically to the system's correlation structure. We benchmark our flexible PEPS algorithm with simulations of classical spin glasses and quantum annealing on densely connected graphs with hundreds of spins, and also study the impact of tuning κ when simulating a uniform quantum spin model on a regular (square) lattice. Our paper opens the way to apply tensor network algorithms to arbitrary, even fluctuating, background geometries.http://doi.org/10.1103/PhysRevResearch.7.L012002 |
| spellingShingle | Siddhartha Patra Sukhbinder Singh Román Orús Projected entangled pair states with flexible geometry Physical Review Research |
| title | Projected entangled pair states with flexible geometry |
| title_full | Projected entangled pair states with flexible geometry |
| title_fullStr | Projected entangled pair states with flexible geometry |
| title_full_unstemmed | Projected entangled pair states with flexible geometry |
| title_short | Projected entangled pair states with flexible geometry |
| title_sort | projected entangled pair states with flexible geometry |
| url | http://doi.org/10.1103/PhysRevResearch.7.L012002 |
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