Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories

Traditional lattice gauge theories (LGTs) can be formulated using an orthonormal basis constructed from the irreducible representations (irreps) of the gauge symmetry. On a lattice, the elements of this basis are tensor networks comprising dimer tensors on the links labeled by a set of irreps and monomer tensors on sites labeled by . These tensors naturally define a local site Hilbert space, , on which gauge transformations act. Gauss’s law introduces an additional index that labels an orthonormal basis of the gauge-invariant subspace of . This monomer-dimer tensor-network (MDTN) basis, , of the physical Hilbert space enables the construction of new qubit-regularized gauge theories that are free of sign problems while preserving key features of traditional LGTs. Here, we investigate finite-temperature confinement-deconfinement transitions in a simple qubit-regularized SU(2) and SU(3) gauge theory in and spatial dimensions, formulated using the MDTN basis, and show that they reproduce the universal results of traditional LGTs at these transitions. Additionally, in , we demonstrate using a plaquette chain that the string tension at zero temperature can be continuously tuned to zero by adjusting a model parameter that plays the role of the gauge coupling in traditional LGTs.

Duke Scholars

Author Rui Xian Siew  

Author Shailesh Chandrasekharan Physics