Matrix product states and the nonabelian rotor model

TL;DR

This paper employs uniform matrix product states to analyze (1+1)D nonabelian rotor models, accurately locating phase transitions and exploring the role of Fourier mode truncation in gauge theories.

Contribution

It introduces a MPS-based approach to study nonabelian rotor models, assessing Fourier mode truncation effects and entanglement in weak-coupling regimes.

Findings

Accurately locates BKT transition in O(2) model.

Successfully probes asymptotic weak-coupling regime in O(4) model.

Higher Fourier modes become significant in crossover and weak-coupling regimes.

Abstract

We use uniform matrix product states (MPS) to study the (1+1)D $O(2)$ and $O(4)$ rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free nonabelian 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 $\beta$ function, we find excellent agreement with known results, locating the BKT 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 nonabelian theory, where entanglement also suddenly increases. This could have important consequences for TNS studies of Yang-Mills on higher dimensional graphs.