Abstract
A projected entangled pair state (PEPS) with ancillas can be evolved in imaginary time to obtain thermal states of a strongly correlated quantum system on a two-dimensional lattice. Every application of a Suzuki-Trotter gate multiplies the PEPS bond dimension by a factor . It has to be renormalized back to the original . In order to preserve the accuracy of the Suzuki-Trotter (ST) decomposition, the renormalization in principle has to take into account full environment made of the new tensors with the bond dimension . Here, we propose a self-consistent renormalization procedure operating with the original bond dimension , but without compromising the accuracy of the ST decomposition. The iterative procedure renormalizes the bond using full environment made of renormalized tensors with the bond dimension . After every renormalization, the new renormalized tensors are used to update the environment, and then the renormalization is repeated again and again until convergence. As a benchmark application, we obtain thermal states of the transverse field quantum Ising model on a square lattice, both infinite and finite, evolving the system across a second-order phase transition at finite temperature.
7 More- Received 25 November 2014
- Revised 30 January 2015
DOI:https://doi.org/10.1103/PhysRevB.92.035120
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