Abstract
We investigate the ground state phase diagram of square ice — a U(1) lattice gauge theory in two spatial dimensions — using gauge invariant tensor network techniques. By correlation function, Wilson loop, and entanglement diagnostics, we characterize its phases and the transitions between them, finding good agreement with previous studies. We study the entanglement properties of string excitations on top of the ground state, and provide direct evidence of the fact that the latter are described by a conformal field theory. Our results pave the way to the application of tensor network methods to confining, two-dimensional lattice gauge theories, to investigate their phase diagrams and low-lying excitations.
Highlights
While our algorithm is amenable to both periodic- and open boundary conditions along they-direction at a comparable computational cost, we opted for the cylindrical conditions in all simulations as to minimize finite-size and boundary effects
We have reported a gauge invariant tensor network investigation of square ice — a U(1) quantum link model in two spatial dimensions
Our results on the phase diagram are quantitatively consistent with previous results in the literature, and represent an important systematic benchmark for the accuracy and reliability of tensor network methods applied to confining lattice gauge theories in more than one dimension
Summary
Since the formulation of the density-matrix renormalization group algorithm by White in 1992 [1], numerical techniques based on tensor network (TN) ansätze have found widespread application in condensed matter theory [2,3]. The vision behind this programme is to extend these methods to higher-dimensional LGTs displaying confinement, and render numerical regimes accessible, which are typically not tractable with Monte Carlo (MC) techniques These include finite chemical potentials and real-time dynamics — describing, for instance, the time-evolution of many-body systems governed by quantum-chromodynamics [25, 26]. We provide entanglement-based evidence for the fact that such string excitations are described by a conformal field theory with central charge c = 1 — effectively behaving as a compactified boson This approach has never been applied to LGTs, and, compared to other methods based on energy spectroscopy of the Lüscher term [33], it allows us to estimate the central charge from moderate system size simulations.
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