تقرير
Random insights into the complexity of two-dimensional tensor network calculations
| العنوان: | Random insights into the complexity of two-dimensional tensor network calculations |
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| المؤلفون: | Gonzalez-Garcia, Sofia, Sang, Shengqi, Hsieh, Timothy H., Boixo, Sergio, Vidal, Guifre, Potter, Andrew C., Vasseur, Romain |
| المصدر: | Phys. Rev. B 109, 235102 (2024) |
| سنة النشر: | 2023 |
| المجموعة: | Condensed Matter Quantum Physics |
| مصطلحات موضوعية: | Quantum Physics, Condensed Matter - Other Condensed Matter, Condensed Matter - Statistical Mechanics |
| الوصف: | Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law, and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically a computationally hard problem. Yet approximation schemes for computing properties of 2d PEPS are regularly used, and empirically seen to succeed, for a large subclass of (not too entangled) condensed matter ground states. Adopting the philosophy of random matrix theory, in this work we analyze the complexity of approximately contracting a 2d random PEPS by exploiting an analytic mapping to an effective replicated statistical mechanics model that permits a controlled analysis at large bond dimension. Through this statistical-mechanics lens, we argue that: i) although approximately sampling wave-function amplitudes of random PEPS faces a computational-complexity phase transition above a critical bond dimension, ii) one can generically efficiently estimate the norm and correlation functions for any finite bond dimension. These results are supported numerically for various bond-dimension regimes. It is an important open question whether the above results for random PEPS apply more generally also to PEPS representing physically relevant ground states |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevB.109.235102 |
| URL الوصول: | http://arxiv.org/abs/2307.11053 |
| رقم الأكسشن: | edsarx.2307.11053 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevB.109.235102 |
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