Using a loop-cluster algorithm we investigate the spin-1 2 Heisenberg antiferromagnet on a square lattice with exchange coupling J and an additional four-spin interaction of strength Q. We confirm the existence of a phase transition separating antiferromagnetism at J/Q > J c /Q from a valence bond solid (VBS) state at J/Q < J c /Q. Although our Monte Carlo data are consistent with those of previous studies, we do not confirm the existence of a deconfined quantum critical point. Instead, using a flowgram method on lattices as large as 80 2 , we find evidence for a weak first-order phase transition. We also present a detailed study of the antiferromagnetic phase. For J/Q > J c /Q the staggered magnetization, the spin stiffness and the spinwave velocity of the antiferromagnet are determined by fitting Monte Carlo data to analytic results from the systematic low-energy effective field theory for magnons. Finally, we also investigate the physics of the VBS state at J/Q < J c /Q and we show that long but finite antiferromagnetic correlations are still present.

We investigate the utility of partially twisted boundary conditions in lattice calculations of meson observables. For dynamical simulations, we show that the pion dispersion relation is modified by volume effects. In the isospin limit, we demonstrate that the pion electromagnetic form factor can be computed on the lattice at continuous values of the momentum transfer. Furthermore, the finite volume effects are under theoretical control for extraction of the pion charge radius.

The (2 + 1)-d U (1) quantum link model is a gauge theory, amenable to quantum simulation, with a spontaneously broken SO(2) symmetry emerging at a quantum phase transition. Its low-energy physics is described by a (2 + 1)-d RP (1) effective field theory, perturbed by a dangerously irrelevant SO(2) breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon. At the quantum phase transition, the model mimics some features of deconfined quantum criticality, but remains linearly confining. Deconfinement only sets in at high temperature.Quantum link models (QLMs) are lattice gauge theories formulated in terms of discrete quantum degrees of freedom. U (1) and SU (2) QLMs were first constructed by Horn in 1981 [1], and further investigated in [2]. In [3] QLMs were introduced as an alternative nonperturbative regularization of Abelian and non-Abelian gauge theories, in which ordinary gauge fields emerge dynamically from the dimensional reduction of discrete quantum link variables. Dimensional reduction of discrete variables is a generic phenomenon in asymptotically free theories, which gives rise to the D-theory formulation of quantum field theory [4]. In the D-theory formulation of 4-d Quantum Chromodynamics (QCD), the confining gluon field emerges by dimensional reduction from a deconfined Coulomb phase of a (4 + 1)-d SU (3) QLM [5]. Chiral quarks arise naturally as domain wall fermions located at the two 4-d sides of a (4 + 1)-d slab. The (2 + 1)-d U (1) QLM has also been investigated in the context of quantum spin liquids [6]. With staggered background charges ±1, it is equivalent to a quantum dimer model [7][8][9]. Furthermore, Kitaev's toric code [10] is a Z(2) QLM. In contrast to Wilson's lattice gauge theory [11], QLMs have a finite-dimensional Hilbert space per link, which makes them ideally suited for the construction of atomic quantum simulators for dynamical Abelian [12][13][14][15][16] and non-Abelian gauge theories [17][18][19][20]. A long-term goal of this research is to quantum simulate QCD in the D-theory formulation with ultracold matter, in order to address the real-time evolution of strongly interacting systems in nuclear and particle physics, as well as their dynamics at non-zero baryon density.In this paper, we investigate the (2+1)-d U (1) QLM, in order to demonstrate that, despite its structural simplicity, it displays highly non-trivial dynamics, and thus is ideally suited to demonstrate the power of gauge theory quantum simulators. We consider the model with a plaquette coupling J and a Rokhsar-Kivelson (RK) coupling λ. The phase diagram is sketched in Fig.1. At zero temperature, the model is confining for λ < 1. At finite temperature T , it has a deconfinement phase transition above which there is a massless mode transforming non-trivially under the U (1) center symmetry. Due to the Mermin- FIG. 1. [Color online]Schematic sketch of the λ-T phase diagram. The insets indicate the location of the peaks in the probability distribution of the order p...

The quantum dimer model on the square lattice is equivalent to a U (1) gauge theory. Quantum Monte Carlo calculations reveal that, for values of the Rokhsar-Kivelson (RK) coupling λ < 1, the theory exists in a confining columnar phase. The interfaces separating distinct columnar phases display plaquette order, which, however, is not realized as a bulk phase. Static "electric" charges are confined by flux tubes that consist of multiple strands, each carrying a fractionalized flux 1 4 . A soft pseudo-Goldstone mode emerges around λ ≈ 0, long before one reaches the RK point at λ = 1.