Confined and Deconfined Phases of Qubit Regularized Lattice Gauge Theories

Abstract

We construct simple qubit-regularized Hamiltonian lattice gauge theories formulated in the monomer--dimer--tensor-network (MDTN) basis that are free of sign problems in the pure gauge sector. These models naturally realize both confined and deconfined phases. Using classical Monte Carlo methods, we investigate the associated finite-temperature phase transitions and show that they exhibit the expected universality classes of conventional SU(N) lattice gauge theories in various spacetime dimensions. Furthermore, we argue that second-order quantum phase transitions separating the confined and deconfined phases are likely to exist. Such critical points would provide a nonperturbative route to defining continuum limits of qubit-regularized gauge theories, potentially allowing Yang--Mills theory and related continuum gauge theories to emerge from finite-dimensional lattice constructions.

Figures (6)

• Figure 1: Illustation of dimer-tensor (left) and monomer-tensors (right). Each circle stands for an index of either dimer-tensor or the monomer-tensor that transforms according the irrep of ${\mathrm{SU}}(N)$ shown in the figure.
• Figure 2: Pictorial representation of the projection of dimer and monomer tensors onto the gauge-invariant physical subspace at a lattice site $s$. In the illustration, the local site Hilbert space before imposing Gauss's law is $\mathcal{H}_s^{g} = \lambda_{\ell_1} \otimes \lambda_{\ell_2} \otimes \lambda_{\ell_3} \otimes \lambda_{\ell_4} \otimes \lambda_s \, ,$ where the four link representations correspond to the links attached to the site. Imposing Gauss's law amounts to projecting onto the singlet (gauge-invariant) subspace of $\mathcal{H}_s^{g}$. We denote a basis of this singlet subspace by the index $\alpha_s = 1,2,\dots,\mathcal{D}_s$, where $\mathcal{D}_s$ is its dimension.
• Figure 3: Action of the operator $\hat{{\cal U}}_P$ on a plaquette in the ${\mathrm{SU}}(3)$ qubit-regularized gauge theory. The blue, red, and yellow circles represent the irreps $\mathbf{1}$, $\mathbf{3}$, and $\bar{\mathbf{3}}$, respectively.
• Figure 4: A simple conjectured finite-temperature phase diagram of the qubit-regularized model described by the Hamiltonian in \ref{['eq:QRH']}. A massive continuum QFT may emerge from an appropriate relevant perturbation near the quantum critical point.
• Figure 5: Finite temperature critical behavior of \ref{['eq:QRH']} when $\delta=0$ with ${\mathrm{SU}}(2)$ and ${\mathrm{SU}}(3)$ gauge symmetries. The results shown are obtained using Monte Carlo methods in two (top row) and three (bottom row) spatial dimensions.