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arXiv:1507.06624 · Physical review. D/Physical review. D.

Matrix product states and the non-Abelian rotor model

Ashley Milsted

Published Apr 8, 2016• 23 citations
arXivHTMLPDF

Abstract

We use uniform matrix product states to study the ($1+1$)D $O(2)$ and $O(4)$ rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free non-Abelian lattice gauge theory on a ``Hawaiian earring'' graph for $U(1)$ and $SU(2)$, respectively. Applying tangent space methods to obtain ground states and determine the mass gap and the $\ensuremath{\beta}$ function, we find excellent agreement with known results, locating the Berezinskii-Kosterlitz-Thouless transition for $O(2)$ and successfully entering the asymptotic weak-coupling regime for $O(4)$. To obtain a finite local Hilbert space, we truncate in the space of generalized Fourier modes of the gauge group, comparing the effects of different cutoff values. We find that higher modes become important in the crossover and weak-coupling regimes of the non-Abelian theory, where entanglement also suddenly increases. This could have important consequences for tensor network state studies of Yang-Mills on higher-dimensional graphs.

DOI
10.1103/physrevd.93.085012

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Non-stabilizerness and entanglement in (2+1)(2+1)(2+1)-dimensional SU(2) lattice gauge theory using tensor networks
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