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

• URL: http://arxiv.org/abs/2502.14175v1
• Date: Thu, 20 Feb 2025 01:06:39 GMT
• Title: Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories
• Authors: Shailesh Chandrasekharan, Rui Xian Siew, Tanmoy Bhattacharya,
• Abstract summary: Traditional $mathrmSU(N)$ lattice gauge theories (LGTs) can be formulated using an orthonormal basis constructed from the irreducible representations (irreps) $V_lambda$ of the $mathrmSU(N)$ gauge symmetry. Here, we investigate finite-temperature confinement-deconfinement transitions in a simple qubit-regularized $mathrmSU(2)$ and $mathrmSU(3)$ gauge theory.
• Score: 2.646330573001491
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• Abstract: Traditional $\mathrm{SU}(N)$ lattice gauge theories (LGTs) can be formulated using an orthonormal basis constructed from the irreducible representations (irreps) $V_{\lambda}$ of the $\mathrm{SU}(N)$ 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 $\{\lambda_\ell\}$ and monomer tensors on sites labeled by $\{\lambda_s\}$. These tensors naturally define a local site Hilbert space, $\mathcal{H}^g_s$, on which gauge transformations act. Gauss's law introduces an additional index $\alpha_s = 1, 2, \dots, \mathcal{D}(\mathcal{H}_s^g)$ that labels an orthonormal basis of the gauge-invariant subspace of $\mathcal{H}^g_s$. This monomer-dimer tensor-network (MDTN) basis, $\left| \{\lambda_s\},\{\lambda_\ell\},\{\alpha_s\}\right\rangle$, of the physical Hilbert space enables the construction of new qubit-regularized $\mathrm{SU}(N)$ 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 $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ gauge theory in $d=2$ and $d=3$ spatial dimensions, formulated using the MDTN basis, and show that they reproduce the universal results of traditional LGTs at these transitions. Additionally, in $d=1$, 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.

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