Abstract
We study the $SU(2)$ gauge-Higgs model in two Euclidean dimensions using the tensor renormalization group (TRG) approach. We derive a tensor formulation for this model in the unitary gauge and compare the expectation values of different observables between TRG and Monte Carlo simulations finding excellent agreement between the two methods. In practice we find the TRG method to be far superior to Monte Carlo simulation for calculations of the Polyakov loop correlation function which is used to extract the static quark potential.
Highlights
It is usually very difficult to extract the emergent, long distance properties of quantum field theories or many-body systems from the underlying partition function
In recent years it has been appreciated that it is sometimes more efficient to carry out this operation on alternative representations of the partition function called tensor networks
We will derive an explicit tensor network representation of a two-dimensional non-Abelian gauge theory coupled to matter and show how a particular TRG method—the higher-order tensor renormalization group (HOTRG) algorithm [3]—can be used to efficiently calculate the free energy and other observables in the theory. We will compare these results with conventional Monte Carlo (MC) calculations to test the validity of our tensor renormalization group procedure
Summary
It is usually very difficult to extract the emergent, long distance properties of quantum field theories or many-body systems from the underlying partition function. We will derive an explicit tensor network representation of a two-dimensional non-Abelian gauge theory coupled to matter and show how a particular TRG method—the higher-order tensor renormalization group (HOTRG) algorithm [3]—can be used to efficiently calculate the free energy and other observables in the theory. We will compare these results with conventional Monte Carlo (MC) calculations to test the validity of our tensor renormalization group procedure. VI we give concluding remarks and discuss future directions for this work
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